Category Archives: Audio

Headphones: HD580 vs. LCD-2F

I’ve been listening to headphones for decades. Over the years I’ve tried many different ones. The Sennheiser HD580 and Audeze LCD-2F are my favorites. I own a pair of each and use them daily. This is a direct comparison.

Sennheiser HD580

I bought my pair in 1999. Over the years I’ve replaced the pads and cable several times, and kept the drivers clean. They still work like new.

 

 

They aren’t made anymore, but three models currently made are almost the same:

  • Sennheiser HD600
  • Massdrop 58x
  • Massdrop 6xx

Audeze LCD-2F (Fazor)

I bought mine in 2014 with the original Fazor drivers. Then in 2016 I sent it to Audeze to replace the drivers with the lastest/revised version.

Fit & Comfort

The HD580 are smaller, lighter, and better ventilated. They stay in place as I move my head around. I can wear them all day without any discomfort.

The LCD-2F are bigger, heavier, and less ventilated. They stay in place as long as my head is upright but if I bend my head forward & down, they try to fall off. They are comfortable, but after 2-3 hours the weight (especially on the headband) begins to drag.

In this category the HD580 wins.

Efficiency and Impedance

The HD580 are rated at 330 ohms, but their impedance ranges from 300 through most frequencies, rising to a peak of 600 ohms at 100 Hz. Voltage sensitivity is on the low side at 0.17 V for 90 dB SPL. A phone can’t drive them properly, you’ll need a headphone amp. And if that headphone amp (or phone) has a high output impedance, it will boost tones near the impedance peak (around 100 Hz) making the headphones sound warmer.

The LCD-2F are 70 ohms at all frequencies; being planar magnetic, their impedance vs. frequency curve is flat. Voltage sensitivity is a bit higher than the HD580 at 0.11 V for 90 dB SPL. They play 3-4 dB louder than the HD580 at the same volume setting (voltage). A phone can almost but not quite drive them properly, you’ll need a headphone amp. The frequency response of these headphones will not be affected by the amp’s (or phone’s) output impedance.

Overall, the LCD-2F are easier to drive than the HD580, and you may get acceptable results driving them from a phone, but you’ll need a headphone amp to get the most out of either.

Sound Quality

HD580

  • Bass: rolled off below 80 Hz
  • Midrange: smooth and linear
  • Treble: rolled off above 10 kHz
  • Distortion very low, but high (5%) in the bass
  • Voicing: a slight brassy/boxy coloration

LCD-2F

  • Bass: smooth and linear to subsonic
  • Midrange: smooth and linear
  • Treble: dip at 4 kHz
  • Distortion very low throughout (even in the bass)
  • Voicing: open, transparent uncolored

Summary

The LCD-2F has near-perfect ruler flat response from subsonic through the upper mids (to around 2 kHz). In the treble, it has the Audeze “house sound” with a dip around 4 kHz, though compared with the rest of the LCD models it has the smallest dip and is the most neutral. If you don’t EQ this dip, the sound is a bit soft — yet not dark, as the extreme treble above 10 kHz is not attenuated.

The HD580 has a more linear, neutral response through the treble, though it rolls off both the lowest bass and the highest treble. The HD580 also needs EQ to lift the bass below 100 Hz, but when you do, the bass sounds wooly or soft as distortion becomes audible.

Overall, these are 2 of the best headphones money can buy in terms of sound quality. Of course you can spend a lot more, but you can’t really get much better sound. However, the LCD-2F is a little better:

  • Wider frequency response extends to extreme top & bottom octaves that the HD580 rolls off (below 40 Hz, above 10 kHz)
  • Lower distortion, especially in the bass
  • Perfect ruler-flat response from sub-bass through upper mids
  • Open, transparent, uncolored voicing

That said, the differences are small enough that you need really good recordings and a quiet listening environment to hear it. And the HD580 is less expensive, and more comfortable. So it is the value king: 90% of the sound quality for 20% of the price.

Firefox and Audio Streaming

I use my desktop computer as an audio source for music listening. Listening to high quality (lossless) music over the browser, I’ve explored different browsers and how they deal with audio. This is on Ubuntu 18 Linux with Pulseaudio. I’ve set up the audio to avoid resampling as much as possible.

I tried about 10 different browsers on Ubuntu. Every one but Firefox resamples audio to some fixed rate, either 44.1 or 48 kbps. Firefox is the only one that passes audio through unmolested. Or, at least it used to. Primephonic is a classical music streaming service that passes audio uncompressed at whatever rate the albums were recorded (from 44.1 to 192 kHz).  I could listen to different albums and watch Pulseaudio change the sampling rate to match whatever rate each was recorded. At least until some time in Feb 2021, when Firefox’s behavior changed.

Here’s a summary of the changes:

Firefox now ignores the audio stream’s native rate and attempts to stream it at the highest rate the system will support. This means it will resample the audio rather than play it at its native rate.

If Pulseaudio’s avoid-resampling is set to true, then that rate will always be the highest rate the system supports. For example, with my Juli@ sound card it is 192 kHz. Otherwise (avoid-resampling set to false) that rate is the highest rate Pulseaudio is configured to use. That is either default-sample-rate or alternate-sample-rate, whichever is higher.

So in order to listen to music on Firefox without resampling, you must:

  • Set both of Pulseaudio’s rates to the native rate of the stream you are playing.
  • Set Pulseaudio avoid-resampling to false.

Essentially, you are forcing the system to play all audio at a single rate that exactly matches the audio you are playing.

And indeed, the irony is that in order to avoid resampling, you must set avoid-resampling to false!

Incidentally, why the irony? I can only speculate. Cubeb, the audio engine in Firefox, asks Pulseaudio what is its highest sampling rate. If Pulseaudio is avoiding resampling, then it reports its highest rate to be the highest rate the audio card supports. But if Pulseaudio is resampling, then it reports its highest rate as whatever rate it is resampling everything into. Seems logical. But it ironically leads the reverse of the intended behavior. The root of the problem is cubeb. It should pass audio to the system at its native rate, and let the system deal with it. Cubeb is being too smart by half, trying to deal with that itself.

High Res Audio on Ubuntu: Part 3

Once we’ve got it all set up, we want to test it while playing audio. It’s the only way to know for sure it is working as expected. To do this, we’ll be using the Linux Pulseaudio command-line tool pacmd.

If you jumped directly to this page, you may want to read part 1 and part 2.

Once you’ve tested your setup, possibly made adjustments, and confirmed they are working, you may want to read about streaming audio from a browser.

Basic Audio Device Info

To start, enter this command:

pacmd list-sinks

A “sink” is an audio output device. Even if you only have 1 sound card in your system, it may support multiple sinks. And you may have multiple cards. So you may see a lot of output here.

Let’s use grep to shrink the output to only the fields most useful to us:

pacmd list-sinks | grep -e 'sample spec:' -e 'channel' -e 'buffer' -e 'latency:' -e 'name:' -e 'alsa\.card'

On my system, it returns this:

name: <alsa_output.pci-0000_04_02.0.analog-stereo>
current latency: 0.00 ms
sample spec: s32le 2ch 176400Hz
channel map: front-left,front-right
fixed latency: 185.76 ms
alsa.card = "1"
alsa.card_name = "ESI Juli@"
device.buffering.buffer_size = "262144"
device.buffering.fragment_size = "70560"

This tells you I have an ESI Juli@ sound card that is currently set to 176.4 kHz sampling and 32-bit signed. My Pulseaudio configuration uses sample rates of 176400 and 192000, so this is the default sample rate. This is 4x oversampled for normal CD quality (44.1 kHz) and 4x oversampled for normal DVD quality (48 kHz).

Now I play an audio file that happens to be sampled at 96 kHz. While it’s playing I run the above command again and it returns this:

name: <alsa_output.pci-0000_04_02.0.analog-stereo>
current latency: 170.65 ms
sample spec: s32le 2ch 192000Hz
channel map: front-left,front-right
fixed latency: 185.76 ms
alsa.card = "1"
alsa.card_name = "ESI Juli@"
device.buffering.buffer_size = "262144"
device.buffering.fragment_size = "70560"

You can see that Pulseaudio has changed the sample rate to 192 kHz. Why? I have “avoid resampling” enabled, so it should play at the audio file’s native rate of 96 kHz. But Pulseaudio will never use a sample rate lower than what you configure. Since it can’t use 96 kHz, it uses the next best thing, which is an integer multiple of the native rate. That is why it switches to 192 kHz.

Resampling

The above command showed us the current state of the audio device. We can also use pacmd to get the current state of any audio being sent to or processed by that device.

First, ensure no audio is playing on your system and then enter this command:

pacmd list-sink-inputs

You should see this response:

0 sink input(s) available.

Now, try the prior command again:

pacmd list-sinks| grep -e 'sample spec:' -e 'channel' -e 'buffer' -e 'latency:' -e 'name:' -e 'alsa\.card'

You will see something like this:

name: <alsa_output.pci-0000_04_02.0.analog-stereo>
current latency: 0.00 ms
sample spec: s32le 2ch 192000Hz
channel map: front-left,front-right
fixed latency: 185.76 ms
alsa.card = "1"
alsa.card_name = "ESI Juli@"
device.buffering.buffer_size = "262144"
device.buffering.fragment_size = "70560"

This tells you that the audio card is in a certain state, but there is no data or input being sent to that card.

Now play an audio file of any kind, and while it’s playing, repeat the above commands. In my case, I played a CD file (44.1 kHz, 16-bit) and get the following:

First, the card itself:

pacmd list-sinks| grep -e 'sample spec:' -e 'channel' -e 'buffer' -e 'latency:' -e 'name:' -e 'alsa\.card'

This returns:

name: <alsa_output.pci-0000_04_02.0.analog-stereo>
current latency: 185.75 ms
sample spec: s32le 2ch 176400Hz
channel map: front-left,front-right
fixed latency: 185.76 ms
alsa.card = "1"
alsa.card_name = "ESI Juli@"
device.buffering.buffer_size = "262144"
device.buffering.fragment_size = "70560"

You can see the card switched to 176.4 kHz sampling, because the source is 44.1 kHz and it wants to use an integer multiple for resampling.

Now let’s check the status of the audio being sent to the device:

pacmd list-sink-inputs

Now you see a bunch of output. As above, let’s use grep to filter it down to the essentials we care about:

pacmd list-sink-inputs | grep -e 'sample spec:' -e 'resample method:' -e 'application\.name'

Now we see something like this:

sample spec: float32le 2ch 44100Hz
resample method: soxr-vhq
application.name = "VLC media player (LibVLC 3.0.8)"

Here we see that the source is coming from VLC (my media player), sampled at 44.1 kHz and the system is resampling it using the soxr-vhq method.

Now let’s play an audio file that happens to exactly match one of our system’s sampling rates (in my case, 176.4 kHz or 192 kHz). And then re-run this command. We get:

sample spec: float32le 2ch 192000Hz
resample method: copy
application.name = "VLC media player (LibVLC 3.0.8)"

Look at the resample method: copy. This means Pulseaudio is not resampling the audio, but is directly copying the stream from the source to the sink without resampling it. This is an important test: it tells you when the system is resampling audio.

Conclusion

So, now we know how to test our audio settings, see how the audio card is currently configured, and also check the audio stream being played. Also, whether audio is being resampled, and if so, using what resampling method, and the source and target sample rates.

As a general guide to resampling:

  1. No resampling is always best
  2. Resampling at integer multiples is better (faster, more transparent) than fractional
  3. Up-sampling is more transparent than Down-sampling

Conclusions we can draw from this

  • Avoid resampling wherever possible
  • If you must resample, upsample by integer multiples
  • If we have 88.2 kHz, downsampling to 44.1, is better than upsampling to 96
  • If you must resample by a non-integer multiple, sample up rather than down

Meier Audio Corda Soul

The Soul is a DAC, headphone amp and preamp. It’s the best preamp I have owned and a unique piece of kit. It has the transparency of a passive attenuator and the flexibility of a DAC and active preamp. This page summarizes the info I have on it.

So what’s the deal? DACs, headphone amps and preamps have improved a lot over the past 20 years and nowadays SOTA sound quality is commodified. What’s so special about the Soul? Jan Meier incorporates both engineering and psychoacoustics into his designs. Without getting into subjective impressions, here are some its engineering features.

  • Stepped gain-volume control
    • The volume knob is a stepped attenuator that sets the analog gain ratio, instead of attenuating a fixed gain ratio.
    • Benefit: lower noise and perfect L-R channel balance, especially at low-medium volume settings
  • 100% balanced/differential both D and A
    • The Soul is fully balanced/differential from the DAC chip to the analog outputs.
    • Benefit: lower noise and distortion.
  • Dual WM8741 chips in mono mode
    • The Soul uses a pair WM8741 chips, each in mono mode, one for each channel (instead of using a single WM8741 chip in stereo mode).
    • Benefit: lower noise and distortion
  • Switching power supplies
    • The Soul has 4 separate power supplies, all switching at about 70 kHz
    • Benefit: lower noise and distortion, eliminates 50/60 Hz hum
  • Maximum oversampling at all rates
    • The Soul sets the WM8741 chip in “OSR high” mode which oversamples all data to the chip’s max rate (44.1k is 8x, 192k is 2x).
    • Benefit: lower noise & distortion.
  • FF internal feedback pre-emphasis
    • The Soul applies internal pre-emphasis to minimize noise & distortion in the frequency range where human hearing is most sensitive
    • Benefit: pyschoacoustically shaped (perceptually lower) noise & distortion
  • Top quality parts: Neutrik, Alps, Lorlin, AD797 opamps, BUF634, WM8804, Nichicon caps, etc.
    • The Soul uses top quality parts and build quality, made by Lake People in Germany.
    • Benefit: reliability, durability, longevity

 

High Res Audio on Ubuntu: Part 2

In part 1 we saw recommended settings for bit depth and sample rates, why these are recommended, how they work, and how to set them. Here, we’ll talk about glitch-free audio.

If you want to check your configuration, skip ahead to part 3. Or return to part 1.

In Ubuntu you may notice occasional audio glitches. They can be obvious or subtle. For example, here is one I encountered recently that is not quite obvious, but you can definitely hear if you are paying attention:

Clean
Dirty

The higher the resolution of the audio, the increased demand for data flow & processing, the more likely these glitches are to occur. These glitches arise from the way Pulseaudio buffers audio data and schedules interrupts for itself to process and flow that data. Many systems don’t glitch with CD quality and lower, but start to glitch at higher rates. Or they may glitch only when the PC is busy doing other work.

Fortunately, this can be configured so almost any computer can play high resolution audio glitch-free. I’ve experimented with these settings on a 15-year-old PC running Ubuntu 18 that was seriously glitchy even at CD quality, using default settings. By changing settings I got this PC to play local audio files up to 192-24, and stream audio in the browser up to 96-24. Then I applied these settings to a fast modern PC running Ubuntu 16. This PC played CD quality audio just fine with the system defaults, but glitched when playing back high resolution audio. This PC now plays back audio seamlessly at all bit rates.

There are 4 basic settings to configure. You may not need to do them all. Try each individually in turn to see if it fixes the problem.

Pulseaudio Process Priority

The Pulseaudio process normally runs at nice level -11. This gives it priority over normal system processes. But increasing its priority even more can help. That means a numerically smaller number (you’re being “less nice” to the rest of the system).

File: /etc/pulse/daemon.conf

; nice-level = -11
nice-level = -15

Comment out the default nice-level and set it a bit lower. It doesn’t seem like much, but it does make a difference.

Pulseaudio Timer Based Scheduling

A few years ago, Pulseaudio switched to timer based scheduling. This is a better way to reduce audio latency while keeping audio streams running smoothly. But Linux is not a real time operating system; it doesn’t give processes guarantees when they will get CPU time. So timer based scheduling sometimes causes buffer under-runs, which is one cause of audio glitches. The timer based scheduling system is supposed to detect when this happens and increase buffers & latency to compensate. But even if it does, you may still get occasional audio glitches as it detects and compensates.

File /etc/pulse/daemon.conf has settings for audio buffers:

; default-fragments = 4
default-fragments = 4
; default-fragment-size-msec = 25
default-fragment-size-msec = 50

The total buffer is fragment size * count, so the above example is 4 * 50 = 200 ms of audio buffer, which is 200 ms of latency. This is more than twice the default value.

Note: while the setting says milliseconds, it actually sets the buffer size in bytes. The conversion is based on the default sample rate. So if you set it to 200 ms and the default rate is 44.1 kHz, at 96 kHz it will be about 92 ms, as 200 * (44.1 / 96) = 91.875.

However, if you simply increase these values and restart Pulseaudio, nothing will change. That’s because Pulseaudio by default uses timer based scheduling, which ignores these buffer settings. For these settings to take effect — to increase the buffer size — you must disable timer based scheduling.

Open this file: /etc/pulse/default.pa

Look for this section of the file (around line 50):

### Automatically load driver modules depending on the hardware available
.ifexists module-udev-detect.so
load-module module-udev-detect
.else
### Use the static hardware detection module (for systems that lack udev support)
load-module module-detect
.endif

See the line I marked in bold face above? Add a parameter at the end, like this:

load-module module-udev-detect tsched=0

Adding this parameter and setting it to 0 disables timer based scheduling, and makes Pulseaudio use the fragment settings shown above.

Don’t go too crazy with huge audio buffers. Increase it just enough to eliminate audio glitching, and add maybe 50% more to account for system load or high sample rates. Big buffers increase latency which becomes problematic in applications like gaming and video calls.

Resampling

In part 1 we mentioned using the highest quality resampler, soxr-vhq or speex-float-10. You can use a faster, lower quality resampler like speex-float-3.

However, if it becomes necessary to make this change, then there’s no point to high resolution audio because your system is so slow it can’t handle the necessary data & processing. So if you must resort to this, you should also set sample rates back to their defaults (44100 and 48000), and set avoid-resampling to false (its default). This way, Pulseaudio will downsample higher rates to something your system can handle, and it will use a fast lower quality resampling algorithm when doing so.

The benefit is, if your system can’t handle high resolution audio, at least you can configure it to play CD quality audio glitch-free.

CPU Governor

Ubuntu’s default CPU governor is “ondemand”, which sometimes throttles back the CPU when it shouldn’t. For example, playing audio is considered a background task, and it may think the PC is not busy and throttle back the CPU, causing audio glitches.

It’s worth trying the “performance” governor instead. If it doesn’t improve things, you can easily revert back. To try this, first disable the service that always sets the “ondemand” governor, because this will override any other settings you make:

sudo update-rc.d ondemand disable

Next, install package cpufrequtils:

sudo apt install cpufrequtils

Then edit the config file: /etc/init.d/cpufrequtils

Find the commented-out section that looks like this, around line 40

# eg: ENABLE="true"
# GOVERNOR="ondemand"
# MAX_SPEED=1000
# MIN_SPEED=500

After this section, add a line like this:

ENABLE="true"
GOVERNOR="performance

Ensure to comment out or replace any existing lines that set these same settings. Then reboot.

Conclusion

Make sure to restart Pulseaudio after every config change. Use “ps” to ensure only 1 copy of the pulseaudio process is running at a time. When you find settings that work, try them under different conditions of system load to see how robust they are. Sometimes they’ll work when the system is idle then you’ll have problems when it gets busy, as other processes take computing time away from Pulseaudio.

Glitch-free audio is easier to achieve when playing back local files, than when streaming. This is because streaming presents more system load. Thus, you may find settings that work fine for playing back local files but glitch when streaming. If so, try increasing the buffer size.

Note: this method uses bigger audio buffers to ensure smooth playback. This increases latency, which can negatively impact other applications like video calling, movies, and gaming. So, experiment with different buffer sizes and uses the smallest buffers that work reliably.

Above I mentioned an alternative approach. Instead of increasing buffering, you can enable the Linux kernel "threadirqs" feature and increase the IRQ priority of the sound card. This may provide glitch-free playback without increasing latency. I have not tried this approach.

Now, we can jump to part 3, where we check how things work while playing audio.

High Res Audio on Ubuntu: Part 1

People sometimes criticize Ubuntu, more specifically, Pulseaudio and any Linux variants that use it, for not being audiophile friendly. Not surprisingly, this criticism has a thread of truth to it. Yet Ubuntu can be configured to support high quality audio.

The settings are simple, but explaining them takes space, making this a multi-part series.

Note: I made these changes on Ubuntu, though they probably work on any Linux variant that uses Pulseaudio.

Click to skip this and jump to part 2 or part 3.

Pulseaudio Versions

Pulseaudio is an audio layer on top of ALSA. One of its key benefits is enabling different apps to share the audio hardware (e.g. the sound card). ALSA works without Pulseaudio, but in this case only 1 app at a time can use the audio hardware.

Yet one of the essential parts to sharing audio is converting formats: sample rates and bit depths. Pulseaudio tends to do this all the time, even when it’s not necessary because only 1 app is using audio. This unnecessary resampling gives Pulseaudio a bad reputation among audiophiles.

Pulseaudio Resampling

In days of yore, Pulseaudio had a single sample rate and resampled everything to this rate. Since DVDs use 48000 and CDs use 44100, however you configure Pulseaudio, one or the other would always be resampled.

About 10 years ago Pulseaudio introduced the alternate-sample-rate config setting. This gave it 2 sample rates, for example the default /etc/pulse/daemon.conf file says:

default-sample-rate = 44100
alternate-sample-rate = 48000

The first is for CD, the second is for DVD, the 2 most common audio sources. This means Pulseaudio uses whichever rate provides the minimum effort / cleanest  conversion. Resampling between rates that are integer multiples is simple and transparent: less math and cleaner audio. For example, if the audio stream is at 96000, then downsampling to 48000 is cleaner and easier than to 88200; even though 88200 is numerically closer. So Pulseaudio has these defaults (44100 and 48000) for good reason, and when it must resample, it chooses the rate intelligently. Every audio rate commonly used for music and movies is one of these, or an integer multiple of it.

So the good news is this feature is really useful. The bad news is that it doesn’t always work. Here’s a super important limitation of Pulseaudio: It doesn’t change the sample rate while sounds are playing, so it can only change the rate while audio isn’t being used. So if you start playing a DVD, Pulseaudio sets the system sample rate to 48k. If you start a CD while the DVD is playing, the audio rate will remain at 48k and Pulseaudio will resample the CD’s 44.1k audio to 48k — and keep it there even if you stop the DVD and keep the CD going. The reverse happens if you start the CD first, then start the DVD while the CD is playing.

So to take advantage of the alternate sample rate, you must stop all apps from playing.

Avoiding Resampling

In version 1.11 Pulseaudio added a new config setting. In the /etc/pulse/daemon.conf file it looks like this:

avoid-resampling = true

Pulseaudio still uses the default and alternate sample rates. So this new setting controls what Pulseaudio does when it encounters an audio stream using a sample rate that is neither the default nor the alternate. If this setting is false (the default), Pulseaudio will resample the stream to one of the 2 configured rates, as described above. If this setting is true, Pulseaudio will use the stream’s native sample rate without resampling it.

Essentially, this new setting enables Pulseaudio to play every audio stream at its native rate, avoiding all resampling. The configured rates (default and alternate) become entirely optional, rather than mandatory.

However, Pulseaudio still won’t change the sampling rate while sounds are playing. And it still forces resampling of a new audio stream, if another audio stream is already playing when it starts. So this new feature to avoid resampling only works when no other audio is already playing, when we start a new audio stream.

Bit Depth and Reample Method

For bit depth, I recommend using at least s24le (signed 24-bit little endian), or s32le or float32le.  That’s because converting to larger sizes is harmless, but going the opposite way reduces resolution.

Pulseaudio supports several different methods for resampling. This command lists the available resamplers:

pulseaudio --dump-resample-methods

There is no reason not to use the highest quality: soxr-vhq. If it isn’t available on your system, use speex-float-10.

Summary

Overall, I recommend the following settings in Pulseaudio. When you make these changes to the config file, make sure to comment out the default settings you are replacing.

Version 1.8 (Ubuntu 16.04 or earlier)

/etc/pulse/daemon.conf

resample-method = soxr-vhq
default-sample-format = float32le
default-sample-rate = 44100
alternate-sample-rate = 48000

Version 1.11 (Ubuntu 18.04 or later)

Same as above, but with 1 extra line to avoid resampling.

/etc/pulse/daemon.conf

resample-method = soxr-vhq
default-sample-format = float32le
default-sample-rate = 44100
alternate-sample-rate = 48000
avoid-resampling = true

Now you’ve configured the system to set preferred sample rates, avoid resampling, and you know how to allow the system to change sampling rates. In part 2 we will set audio system buffers and priority to avoid audio playback glitches.

Digital Audio: Bit Depth vs. Resolution

It’s commonly said that digital audio’s resolution depends on the bit depth of each sample. Each bit doubles the range of amplitudes that can be stored, and a doubling of voltage is about 6 dB, so 16-bit audio is said to have 16 * 6 = 96 dB of resolution.

However, I believe that resolution is the wrong word. Here I will show that digital audio actually has virtually* infinite resolution at any bit depth. But first, let’s explore the common belief with an example.

Use REW to generate a single-tone sin wave, say 622 Hz at -114 dB. It sounds like this:

Of course you probably can’t hear it because -114 dB is very quiet. So let’s amplify it by +113 dB:

OK, that’s it. Yet experienced listeners may notice this doesn’t sound like a pure tone. It sounds a bit dirty. Let’s take a look at it:

You can see that the curve isn’t smooth. It has jagged jumps. This is called quantization distortion. We’ll get to this later. But the point is, the wave is there.

Now that we know this wave really exists, let’s take it at its original level of -114 dB and convert it to 16-bit. Here’s what that sounds like:

Nothing to hear, folks. It pure digital zeroes. No matter how high you turn it up, the only noise you’ll hear is from your sound card or amp.

Intuitively this makes sense. This wave’s peaks are too small; they never get anywhere near as loud as -96 dB, which is the smallest signal that 16-bit audio can capture. In fact, their peaks are a full 18 dB below that minimum threshold.

So, doesn’t this prove that 16-bit audio has only 96 dB of resolution? That is, it can’t capture anything below -96 dB? It seems so, but no — it doesn’t.

The reason for this is because I did the above transformations without using dither.  But dither is an essential part of digital audio. When dithered, digital audio can capture signals well below -96 dB.

Here’s that -114 dB signal converted to 16-bit, with dither:

If that is too quiet to hear, here’s the same signal boosted by +90 dB (this is loud, so turn down the volume before playing):

That noise like tape hiss is the dither. You can clearly hear the sin wave in the noise. For comparison, here’s the above non-dithered transformation, boosted to the same level with dither:

This is pure noise/hiss without any signal. Comparing it to the above, the difference is obvious.

Conclusion

Here we’ve captured a -114 dB signal with 16-bit audio, which supposedly has only 96 dB of resolution. That’s 18 dB below its supposed minimum. Yet there’s nothing special about 18 dB. If it can go 18 dB below, there’s no arbitrary limit how much lower it can go. Eventually it will get masked by the noise so you won’t hear it anymore, but that happen far below 16-bit’s oft-quoted “resolution”.

This might seem like a contradiction, but it’s not. That’s because resolution is the wrong way to think about bit depth, leading to wrong notions about what actually is limited by bit depth.

Dither is what makes this possible, so it’s an essential part of digital audio. It enables us to capture signals well below the 6 dB / bit levels that are often quoted. Dither is not about psychoacoustics, it is about physics (or math, if you prefer).

What exactly is dither? Essentially, it’s randomizing the LSB (least significant bit) of each sample. Yes “random” means noise, so this adds noise to the signal. The irony is, adding noise increases the resolution. How much noise you get by randomizing the LSB depends on how “small” the LSB is. That is, it depends on the bit depth. With 16-bit audio, the LSB is -90 to -96 dB. With 24-bit audio, the LSB is -138 to -144 dB. In this sense, higher bit depths are like better quality analog tape having less hiss (though of course even 16-bit has far less noise than any analog tape ever invented).

Alternative Explanation

So how exactly does randomizing the LSB enable the samples to detect tiny signals below the bit depth? Here’s an intuitive way to think about this: every sample’s LSB is randomized, so 0 and 1 are equally likely. But when you add a tiny signal to this, it slightly biases the outcome. When the signal swings positive, the sum of signal + random LSB is slightly biased toward 1, meaning it’s slightly more likely to be 1 than 0. When the signal swings negative, the opposite happens.

Conclusion

In summary, digital audio can capture extremely low level signals well below its bit depth. The limiting factor for the smallest encodable signal is determined not by the bit depth, but by the noise level. At some point the dither noise will mask low level signals, but this happens well below the bit depth.

Phone, Tablet Measurements

I’ve read that most mobile devices (phones and tablets) have surprisingly good audio quality from their analog headphone outputs. To test this, I decided to measure mine and found that this is not necessarily the case.

Method

I used Room EQ Wizard to generate frequency sweep files at 44 kHz and 96 kHz. Copied the files to my phone (Galaxy Note 4 SM-N910T) and tablet (Galaxy Tab S SM-T700). Connected the device’s analog headphone output to my sound card’s analog input. Played the sweep files on the device at max volume, recorded using Audacity on my PC. Then used REW to “import sweep” and analyze the files.

The results showed audible discrepancies in both frequency response and distortion. So I played the files back using 2 different apps: USB Audio Pro (in bit perfect mode, all DSP disabled), and VLC. Both measured the same.

Baseline Loopback

I made these measurements with my sound card, so its performance is the baseline. To measure that, I used RCA cables to connect its outputs directly to its inputs to measure its loopback performance.

As you can see below, the Juli@ measures quite well for a sound card. It should be audible transparent.

Loopback Frequency Response

At both sampling frequencies, frequency response is flat with less than 0.1 dB variation through the audible spectrum. Phase response and group delay are equally flat.

Loopback Distortion

First 44.1 kHz, then 96 kHz. As you can see, distortion around -96 dB with a few peaks into the -80 range at 30, 60 and 180 Hz, probably related to 60 Hz power regulation.

Device Measurements

The baseline having been set, here are how my phone & tablet measured. These are raw, uncorrected so they are relative to the baseline.

Results: Frequency Response

The frequency response is nowhere near flat, with deviations plenty big enough to hear.

The top lines (purple/blue) are the phone, bottom lines (brown/teal) are the tablet. 44 kHz and 96 kHz are right on top of each other, so the sampling rate didn’t make any difference.

These response curves are so far off from flat I thought I measured it wrong. I double checked the apps playing back the frequency sweeps (USB Audio Pro and VLC), made sure they weren’t applying any EQ. Both were set to “bit perfect” or flat, and had the same response.

Results: Distortion

The phone’s distortion rises in the low frequencies to about -50 dB. That’s nowhere near as good as I expected and worse than inexpensive dedicated DACs. But it should be below perceptible thresholds. Especially since even good headphones typically have between 1% (-40 dB) and 10% (-20 dB) distortion in the bass.

The tablet’s distortion is significantly higher: -20 dB in the lows and about -40 in the mids and treble. This close to perceptible thresholds and may be audible. It’s dominated by 3rd harmonic.

Conclusion

The take-away here is to bust the myth that phones & tables produce decent sound quality from their headphone jacks; their main limitation is they have only enough power to drive sensitive IEMs, not full size headphones. They certainly do have this power limitation, but their sound quality may be compromised even when driving easy loads. Of course, other phones and tables may perform better than the ones I measured.

Frequency response varies by around 6 dB which is not only audible, but obvious. My old cassette tape deck had flatter frequency response! Distortion is “OK” but I’d like to see lower.

However, the phone or tablet can still be used as a musical source. All of the above limitations are in the built-in DAC and headphone amp. Instead, you can use an app like USB Audio Player to stream the musical data bits out its USB port to a dedicated DAC and headphone amp. This bypasses the above distortions. For portable listening you could use a USB dongle; some of them have surprisingly good measurements, far superior to what I saw above. For desktop/home listening you have a lot more options, using any DAC having a USB input.

Corda Soul Measurements

I was curious about my Corda Soul, so I measured a few things. My measurement setup is pretty basic, which limits what I can measure.

Setup

This PC has a Juli@ XTE sound card. It’s a great sound card, but it’s not professional test equipment. But it does have balanced inputs & outputs. So here’s the setup:

Source: PC playing test signals through USB output
Test Device: Corda Soul, USB input, Analog output (balanced XLR)
Measurement: PC sound card, Analog input (balanced TRS)

Baseline Loopback

I made these measurements with my sound card, so its performance is the baseline. To measure that, I used TRS cables to connect its balanced outputs directly to its inputs to measure its loopback performance.

As you can see below, the Juli@ measures quite well for a sound card. It should be audibly transparent.

Loopback Frequency Response

At both sampling frequencies, frequency response is flat with less than 0.1 dB variation through the audible spectrum. Phase response and group delay are equally flat.

Loopback Distortion

The Juli@’s distortion was the same at 44.1 and 96 kHz sampling. So I’ll show the graph for 96, measured with a -1 dB digital signal:

We can see 60 Hz power at -86 dB and its harmonics nearly as strong. Overall, this is good performance for a sound card (especially one nearly 10 years old) and should be audibly transparent. The baseline now completed, let’s look at the Corda Soul.

Frequency Response

I expected to see perfectly flat response, but it wasn’t. At 96 kHz sampling with the filter in the “sharp” position, the Soul shows slow rolloff, down 0.5 dB at 20 kHz.

I measured the Soul’s frequency response at different volume settings. Why? Because it has 2 unique design features that might make its response vary with volume.

  1. Its unique volume control
  2. Its frequency-shaped gain-feedback

The Soul has a uniquely designed volume control. Instead of attenuating a fixed gain ratio like most preamps do, it changes the gain ratio. It has 64 discrete positions, each applying different resistors in the gain-feedback loop. As you reduce volume from full, it has less gain and more negative feedback. Theoretically, this means lower volume settings should have lower noise and distortion, and wider bandwidth, which could impact frequency response.

The Soul’s frequency-shaped gain feedback means it digitally attenuates low frequencies before DA conversion, then it boosts them back to normal level in the final analog stage (after DA conversion and analog gain/volume control). These shaped curves are applied in separate steps, one digitally, one analog, so any imperfections in the matching of these curves should appear as variations in frequency response.

To see if the above features had any measurable impact, I tested frequency response at different volume settings:

The grey line is the sound card, for reference. I made all lines equal at about 600 Hz, which is the perceptual midrange. Note the Y scale is only 1/2 dB per division to exaggerate the differences. At lower volumes the Soul has a small lift in the bass and the treble. This is only 1 or 2 tenths of a dB, so it is inaudible. Also, it has an early “slow” rolloff in the treble that is down from 0.2 to 0.5 dB at 20 kHz, also inaudible.

At higher sampling rates (48, 88, 96 and 192), the Soul applies a slow rolloff that starts just above 20 kHz. This minimizes passband distortion. To summarize, I measured the following:

RateFilter20k (max; half)-3 dB Fr-3 dB %Fs
44.1lin-0.5; -0.221,3500.484
44.1min-4.4; -4.119,8700.450
48lin-0.5; -0.223,2800.484
48min-0.5; -0.221,6200.450
88.2lin-0.5; -0.228,3600.322
88.2min-0.5; -0.228,6700.325
96lin-0.5; -0.230,7400.320
96min-0.5; -0.231,0600.324

Note: the Soul’s output is non-inverting, so readers with EE knowledge may wonder: if the Soul’s volume knob changes the gain, how can it have less than unity gain? The Soul uses an inverting topology in the gain-feedback loop, so gain is simply Rf/Rin and can be less than unity. Its final fixed gain stage is also inverting, so it does not invert overall.

The high frequency rolloff starts a little lower sampling at 44.1 kHz with the filter in “slow” mode, due to its internal WM8741 DAC chip’s filter implementation. More on that subject here.

Noise & Distortion

Here’s a -1 dB digital signal, with Soul at max analog volume:

Here we can see the Soul’s noise floor is lower than the loopback connector. But the Soul does have an interesting distortion profile, peaking around -70 dB between 1 and 2 kHz. This is surprisingly high distortion for such an expensive and carefully engineered device. But look closer: this is dominated by 3rd harmonic with a little 5th (green). This pattern of odd harmonic distortion is sometimes seen in balanced (differentially signalled) systems, which tend to squash even harmonic distortion.

This unusual result was worth another test, so I played the same test signal through the Soul and recorded its analog output with my Tascam SSR1 instead of the sound card.

Wow – what a difference! The distortion is 10 dB lower and matches the spec for the Tascam recorder, suggesting that the Soul’s distortion is too low to measure with my equipment. Also, there is no hint of any 60 Hz or its harmonics. This is to be expected since the Soul uses a switched power supply.

This shows the limitations of using my sound card for measurement. The only way I’ll get an idea of the Soul’s distortion is comparative, not absolute.

Soul vs. JDS Atom

I happen to have a JDS Atom headphone amp, which is one of the best (lowest noise & distortion) that Amir has measured at ASR. Subjectively, the Atom is a great sounding amp, a little “giant killer”. It’s as good as amps in the kilobuck price range. My favorite aspect of the Atom is how well it performs as you turn down the volume. Its SNR at 50 mV is 92 dB, which is phenomenally high. This is important because SNR is usually measured at full-scale max volume. But nobody ever listens that loud, so this is an example of measurements that are pointless because they don’t reflect actual listening conditions. When you turn the volume down to actual listening levels, the SNR in most amps typically drops by 30 to 40 dB.

So let’s get a comparative measurement at actual listening levels. I measured the Atom and the Soul at a typical listening level with my LCD-2F headphones, which is the 10:00 knob position on both (low gain on the Atom).

Here is the Soul at the 10:00 knob position (about 15 clicks up from the min):

Here is the JDS Atom (low gain, 10:00 position):

While my sound card’s own distortion dominates both graphs, we can still see that the Soul has lower noise, and about the same distortion, as the JDS Atom. REW says the Soul’s noise is about 8 dB lower than the Atom, which would put the Soul’s 50 mV SNR at 100 dB, higher than anything measured at ASR.

In summary, the Soul’s performance looks “good” for distortion and “great” for noise. Due to the limitations of my test method, I can’t say anything more detailed.

Headphone Notch Filters

Many headphones have a resonance causing a bump in frequency response between 6 and 12 kHz. The Soul has a notch filter to correct this. The manual says it ranges from 6 to 11 kHz, each is -6 dB, Q=2.0. Specifically, the frequencies should be spaced 6.3% apart which is 1/11 of an octave, or slightly further apart than a musical half-step.

Here’s how they measured. The grey line is the frequency response with all controls disabled.

Here’s a closer in look:

Each measures spot-on to what the Soul’s manual says: in frequency, amplitude and width.

Tone Controls

The Soul has 4 tone controls. Meier customized mine to be equally spaced in octaves. That is, the corner frequencies should be 80, 320, 1,250 and 5,000 Hz. All 4 are shelf controls; the bottom two are low pass, the top two are high pass. Each control has 5 clicks up and 5 clicks down, each click should be 0.8 dB. I measured each at click positions -5, -3, +3, and +5.

Note: I measured these with a digital frequency sweep at full scale / 0 dB. This should cause digital clipping when the tone controls are set in the positive range. But due to Meier’s “FF” or frequency shaped feedback, the lower frequency controls don’t clip. That is, “FF” is reducing low frequencies more than 4 dB, which is the tone control range. More on this later.

In each of the following graphs, the vertical marker is at the corner frequency.

Knob 1, low bass.

Knob 2, mid bass

Knob 3, mid treble

Aha! In the above we finally see clipping, so we get some idea of the shape of the FF response curve. To compensate, I lowered the frequency sweep to -6 dB:

Knob 4, high treble

You can see that the lowest position attenuates a lot more. Let’s zoom out a bit to see the full curve:

What we see here is that the lowest position on knob 4 triggers the CD redbook de-emphasis curve, which is a gradual cut that starts at 1 kHz and becomes -10 dB at 20 kHz. This feature was rarely used, but if you have any old CDs using it, and they sound too bright, it means your playback equipment failed to detect it. The Soul enables you to apply the proper de-emphasis manually.

Here are all the tone control knobs seen at once

You can see they are spaced symmetrically. Also, their combined effects are cumulative, which enables a lot of flexibility when setting them. Because they are shelf controls, you won’t get amplitude ripples when combining them.

Crossfeed

The Soul has DSP to narrow (for headphones), and widen (for speakers), the stereo image. This is a common feature for headphone amps, having several different implementations. Meier’s is one of the best: it reduces the “blobs in my head” effect that headphones can have, especially with recordings that have instruments hard-panned fully L or R. And it does this without any perceptual sonic side effects like changes to frequency response, which is what sets it apart from others.

I measured the Soul’s frequency response in all 10 modes (5 narrow, 5 wide), plus its frequency response with all DSP disabled. As you can see below, all 11 curves are exactly the same, even with the Y scale zoomed in to 0.1 dB per division.

For example, the crossfeed in the Headroom amps from 15-20 years ago attenuated mids & treble due to comb filter effects from their inter-channel time delay. These amps had a gentle high pass filter to compensate for this. Meier’s crossfeed is free of these effects.

This doesn’t necessarily mean the crossfeed will be perceptually transparent. Measuring the same doesn’t imply that it sounds the same, because crossfeed is mixing some L into R and vice versa, with time shifts. Percepetually, this may make it sound like the FR has changed, to some people.

Meier FF

The Corda Soul uses Meier’s Frequency Adaptive Feedback. I’ve written about this here and here. Essentially, it shapes the frequency response to attenuate low frequencies in order to “unload” the digital and analog stages of the DAC and preamp, and brings the bass level back to normal for the final output stage, so the overall frequency response remains flat. This improves the midrange & treble where our hearing perception is most sensitive.

Meier customized my Soul’s firmware to make some changes I requested. These changes are:

  • Auto-Mute: the Soul auto-mutes whenever the digital input signal drops below a threshold for more than a brief time. This prevents the outputs from carrying a DC offset. The threshold is just above digital zero, so digital dither won’t prevent auto-mute from triggering. Auto-Mute is a standard Soul feature, not something Meier did just for me.
    • Extend the auto-mute delay
      • The original delay at 44 kHz was only a couple of seconds. This caused the Soul to auto-mute, then turn back on, on some CDs that had between-track silence. When doing this, the Soul emitted an audible “click”.
      • The new delay is about 20 seconds at 44 kHz, so this never happens anymore.
    • Disable auto-mute entirely
      • The Soul has a 3-way gain switch: high, medium, low. It’s implemented digitally. I never used the high position, so on my Soul, this switch position disables auto-mute entirely (mine has no high gain mode).
      • The medium and low settings are unchanged.
    • Silent auto-mute
      • The Soul emitted an audible click when auto-mute triggered. Meier changed my firmware so this does not happen; the auto-mute is completely silent in both ways, coming on and off.
  • Tone control changes
    • Space the corner frequencies at equal octave intervals (80, 320, 1250, 5000).

After doing these customizations, Meier sent me the firmware code so I can keep a backup copy, in case my Soul ever needs maintenance. From this code, I have the actual frequency response curve he uses for FF. However, Meier prefers to keep this confidential, so I do not publish it here. Suffice to say, like the rest of the measurements above, it is truth in advertising. The implementation is exactly what he says it is.

DACs and Digital Filters, Pushing the Limits

I’ve discussed this topic before, here and here. A recent discussion at ASR led me to think about this further, devise some practical examples, and gain a deeper understanding, which I share here.

44-16 is a Tough Nut to Crack

It all started with the digital filters of the WM8741, which my DAC uses (article linked above). We tend to think of CD audio as being “perfect” for all practical purposes. It certainly is higher quality than lossless streaming, and perceptually transparent for most people. Yet at 44.1 kHz, none of the WM8741’s 5 filters was perfect from an engineering perspective. The closest were filters #3 and #5, which it labels “sharp linear phase” and “slow linear phase”, respectively.

Filter #3 has perfectly flat frequency response up to 20,021 Hz (0.454 fs at 44,100 kHz sampling) and no phase distortion. Problem is, it is too weak. At Nyquist (22,050) it is attenuated only 6.43 dB and the stopband (-110 dB) is 24,079 Hz (0.546 fs at 44,100 kHz sampling). The stopband being above Nyquist, it could allow high frequency noise to leak through.

Filter #5 is fully attenuated by Nyquist – the stopband (-110 dB) is 22,050 Hz. And it has no phase distortion. But the passband only goes up to 18,390 Hz, so it begins to attenuate below 20 kHz.

Neither of these filters is perfect, each is a compromise. Why is that? The problem is, the CD standard of 44.1 kHz sampling is so low, it forces a filter transition band that is very narrow (20,000 to 22,050; only 0.03 octaves, less than 1 musical half-step). Even with modern hardware, it’s hard to implement digital filters that are correct from an engineering perspective and run in real-time, with these constraints. Something’s got to give: frequency response, phase response, or Nyquist attenuation.

Note that at 48 kHz, the WM8741’s filter is perfect. Fully attenuated at Nyquist, with no attenuation or phase shift below 20 kHz. So while 44.1 kHz may not be quite sufficient for implementing perfect real-time filters, it’s almost sufficient. It only takes just a little more “room” to make it perfect. By “room” I mean a wider filter transition band.

So which of these filters, #3 or #5, is better? At first I thought filter #5 was better because I considered full attenuation at Nyquist to be the most important feature of any digital reconstruction filter. Few people (not me) can hear above 18 kHz, so that is a small price to pay for full attenuation. But on further thought, I believe that filter #3 is better. To explain why, I’ll start with aliasing.

Aliasing

Most audiophiles have heard of aliasing and have some idea what it means. Yet surprisingly few have a solid grasp on the math behind what it actually is. I was one of them, so I did a little exploring to rectify that.

The Nyquist-Shannon theorem says if we sample at least twice as fast as the highest frequency we want to capture, our sampling points capture the wave with mathematical perfection. The Whittaker Shannon formula provides a method to perfectly reconstruct the analog wave from the digital sampling points. In both cases, limiting the bandwidth to frequencies below half the sampling rate (the Nyquist limit) is critical.

Note: the Whittaker-Shannon interpolation formula provides mathematically perfect reconstruction, but it is not the only way to reconstruct the analog wave. It requires summing an infinite series for every sampling point, and even when the series is truncated it is too computationally expensive to be practical for real-time decoding. Two common methods that DACs use are delta-sigma and R2R, which provide similar results. One can think of these as engineering compromises: mathematically imperfect, but requiring fewer computations.

For any frequency (below Nyquist) we encode digitally into sampling points, an alias is a different frequency (above Nyquist) that passes through the exact same sampling points. We can derive a mathematical relationship between frequencies and their aliases. Intuitively, each frequency and its alias are reflected across Nyquist. Put differently, they are equidistant from Nyquist, or that Nyquist is always the arithmetic average of a frequency and its alias.

At CD sampling at 44,100 Hz, Nyquist is 22,050 Hz, so we can encode any frequency below this. Examples:

  • The alias of 18,000 Hz is 22,050 + (22,050 – 18,000) = 26,100 Hz. That is: 18,000 and 26,100 are each 4,050 away from 22,050: one below it, one above it.
  • The alias of 1 kHz is 43,100 Hz; each is 21,050 away from Nyquist
  • The alias of 100 Hz is 44,000 Hz; each is 21,950 away from Nyquist

A picture’s worth a thousand words. In the following graphs, I use small numbers to keep it all simple, but it all extends to any sampling frequency. The entire X axis is 1 second, and we sample at 10 Hz, so Nyquist is 5 Hz.

Here is a 3 Hz wave.

At 10 Hz sampling, the alias of this 3Hz wave is 7 Hz, in red below.

Now recall what exactly it means to say that these 2 waves are aliases of each other at 10 Hz sampling: it means either of these waves can perfectly match the same sampling points.

We can see this below:

Hmmm… is that not obvious? OK try this:

The green shows the points where these waves intersect. Of course, intersecting means they are equal. Observe that these intersection points are perfectly evenly spaced in time. If you sampled either of these waves at these points, you would get the exact same thing. Both waves perfectly fit the sampling points. That is what aliasing means.

Note: the astute reader may notice that the above 2 waves intersect more often than the points noted in green. For purposes of digital sampling and reconstruction, it is sufficient that they pass through the same sampling points, and it's irrelevant whether they intersect more often than that.

Now suppose all you have are these sampling points, and you must construct the analog wave. You could construct either one! So the solution is ambiguous: how do you know which is the correct one — meaning the one that was recorded and encoded?

Recall the primary rule of digital recording: you must filter the analog wave to remove all frequencies above Nyquist. The same rule applies when reconstructing the wave from the sampling points. Alias pairs are always symmetrically centered around Nyquist; one above, one below. Thus, filtering to only frequencies below Nyquist eliminates the ambiguity during reconstruction.

A Simple Yet Clever Trick

One conclusion we can draw from the above is that frequencies close to Nyquist have aliases close to Nyquist. Grokking the fullness of this symmetry leads to a simple, yet clever trick when implementing digital reconstruction filters.

As we’ve seen above, the filter’s stopband should be no higher than Nyquist. But squashing the signal from full scale at 20,000 Hz to negative infinity (say -100 dB) at 22,050 Hz will cause passband artifacts, given real-time hardware limitations.

Yet consider what happens if we break the rules and shift the filter stopband a little above Nyquist. Remember how aliases reflect across Nyquist? We want the top of our passband to be 20 kHz, and Nyquist is 22,050. The difference is 2,050 Hz. Add that to Nyquist and we have 24,100 Hz. This is the alias of 20 kHz, when sampled at 44.1 kHz. What if we make this the filter stopband?

Any frequency below 20 kHz will have an alias above 24,100 Hz, so it will be fully attenuated. Conversely, any frequency between Nyquist and the stopband will have an alias above 20 kHz. And we stretched our filter transition twice as wide, making a gentler slope, easier to implement.

Thus, our digital filter will be imperfect from a math or engineering perspective, but perceptually transparent. It may leak some frequencies above Nyquist, which is by definition noise or distortion (call it “junk”). But all this “junk” and its aliases must be all above 20 kHz which is inaudible.

In this case, we shifted the filter stopband just a bit above Nyquist, to widen its transition band. We took advantage of aliasing symmetry, or the fact that frequencies near Nyquist have their aliases near Nyquist.

Of course, TANSTAAFL and this is no exception. This filter may leak some supersonic junk from 20 kHz to 24 kHz. This is inaudible in itself, but when it passes through analog circuits (preamps, power amps, speakers), harmonic and intermodulation distortion will create artifacts in the passband. However, this filter transition band from 20 to 24 kHz is strongly attenuated and most music has little or no energy up there to begin with. So pragmatically speaking, it should not be a problem. Even so, one can see why Wolfson’s engineers provided filter #5 as an alternative – being fully attenuated at Nyquist, it cannot leak any supersonic junk. So the engineers building devices that use the WM8741 can choose which filter makes the best compromise for their needs.

The WM8741 Uses this Trick

Now let’s take another look at the WM8741’s filter #3, at 44.1 kHz sampling. The passband goes up to .454 * fs, which is 20,021 Hz. The stopband is .546 * fs, which is 24,079 Hz. The range between them is the transition band.

Notice anything interesting about these numbers? The transition band is perfectly centered around Nyquist! By sampling frequency ratio, it’s .046 below and .046 above. By frequency, it’s 2,029 below and 2,029 above. Any frequency below 20,021 will alias above 24,049, so aliases of all passband frequencies are fully attenuated. This is the filter we just described above!

BTW, I don’t think this trick is unique to the WM8741. At ASR, reviews of various DACs show their “sharp, linear phase” digital filters down only 6 dB at Nyquist (22,050 Hz), and their stopband around 24 kHz. So it seems like common engineering practice, creative rule-breaking to stretch the limits and provide the best implementation possible given the constraints of 44.1 kHz sampling. Now I know why, and so do you!

If audio standardized on a higher sampling frequency (even only slightly higher like 48 kHz which is already used for DVD), or as DAC chips gain more processing power, these engineering compromises would become unnecessary.