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Does a 4 million taps FIR filter sound better than a 16K one? Let's find out.

pkane

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Claim
A claim is frequently made that DAC digital filters with a lot of taps can make a significant difference in sound quality. Some software packages and even hardware manufacturers are touting the benefits of large FIR filters, often with millions of taps, supposedly because these produce a more natural, smoother, analog sound or improve "time domain" accuracy, whatever that means. Some of these are sold at large premiums, supposedly because of the complexity of implementing large filters.

Test
Let's use DeltaWave software to find out the real story. I'll use a null test to produce a difference between a music file generated with two different size filters, and then measure the differences in frequency and time domain. For audibility testing, we'll also listen to it. Let's see if there's something to these claims!

The music file I'll be using is one some you may recognize as one used in other null tests on another forum:

http://www.mediafire.com/file/5hg6wl6ygql7217/Original2.wav/file

Since DeltaWave can generate and apply various size FIR filters, from 1k to 16M (yes, 16 million) taps, I decided to compare a 16k filter to a 4M one.

The Original2.wav music file is 24/44.1k, about 2 minutes. I'll place both filters with a cutoff at 21,150Hz. A shorter filter will have a gentler slope than the 4M one. The 4M one is a brickwall filter, as it drops the signal by nearly 300dB within a 20Hz transition band.

Applying FIR filters is just a simple setting in DeltaWave, so I used each filter on the original music file, and then saved the results as 64-bit floating point WAV. I then loaded these up in DeltaWave to compute the difference. Below are the results.

Results
First, the spectrum comparison. The only difference is visible right around the transition band (white line is obviously the 16k filter, blue is the 4M taps filter). I zoomed in on that area to show it better:
1661482737405.png



Spectrum of the difference file (null file) generated by subtracting the two filtered files... not much difference here, except past the cutoff where we already know the two filters are different:
1661482815543.png


Here's the phase difference between the two files (indicative of timing differences or group delay).

Note the scale on the left is 1x10^-7 degrees (0.0000001)! Nothing to see here... as one would expect with a linear FIR filter:
1661482904863.png


Let's check out the time-domain differences. Below is the actual waveform plot of the null file. Except for some sharp transients that have frequencies that extend past the filter cutoff, everything else is below -120dB! And even the sharp transients don't exceed -112dB, so way below audibility, considering that they are above 21kHz:

1661482988019.png


Here's the RMS average of the entire null file in time domain. Note that it's -229dBA, and -124.44dBFS. In other words, way below any thresholds of audibility, A-weighted or not:

1661483275853.png


Let's take a look at the difference spectrogram, maybe something will become apparent there... No difference at all except above the filter cutoff frequency:
1661483148853.png



And finally, here's the actual difference file: https://app.box.com/s/dde7ua0x668ismhebxpzxr57gh33u0jn

The file is a 32-bit FP WAV, mono to save space/size, about a 39MB download. Feel free to listen to see what the differences sound like between a 16k and 4M-size FIR filters. Personally, I can't hear anything even after raising the level by a whopping 100dB!

Conclusion
There's no audible benefit to all those heroic extra taps in a 4M-sized FIR filter. Don't believe me? Listen for yourself.
 

pvehling

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These custom filters on "hardware" are also written in software for the FPGA to decode, so you're paying for the development time and the analogue out implementation of a specific hardware in the end. It's up to what people can, or will, pay for that custom implementation in the end. Toss in a fancy story and scientific rhetoric and people will believe any magic, especially if they pay upwards of $15k for that story.

I'm not opposed to custom integrations - it's cool to see people doing interesting things in the audio world, but it also seems like people would rather have dopamine hits than actually listen to the music they love. I'm more interested in proper mastering techniques than gimmicks.

It's like American whiskey bottle labels - it's 90% "magic" stories about pretentious hogwash that is certainly not historically accurate.. but if the story seems magical, then open those wallets and buy it! But don't tell the people the $50 bottle is the same juice as the $25 one, even from the same distiller, aged the same amount of time.
 
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fieldcar

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Conclusion
There's no audible benefit to all those heroic extra taps in a 4M-sized FIR filter. Don't believe me? Listen for yourself.
While I certainly appreciate your efforts, a large majority of the people that you are trying to reach are stubborn and unwilling to consider truly testing their ears. They insist on long term auditory memory of things far lesser than 0.1% deviation. Fantasy and emotion cloud their judgement. Though, if you make one of those lost souls think, just for a second, then it was worth every moment you've spent today with your post.

I will part with the famous klippel listening test as a cherry on top.
 

Blumlein 88

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Your test here is not adequate to answer the question. What if you use PCM digital to create MoFi LP's. Then can analog listeners hear the difference in the 16k and 4 million tap filters while spinning some vinyl without knowing anything happened along the way onto the vinyl disk?:p
 

solderdude

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Conclusion
There's no audible benefit to all those heroic extra taps in a 4M-sized FIR filter. Don't believe me? Listen for yourself.

But... you did not include a button to inject 'magic™' (which can be toggled and is indicated by a different color ball on the screen).
This is exactly what R Watts did... his filter algo has 'a magic™ ingredient' only known to Rob and your filter is lacking this.

Besides you HAVE to listen sighted and knowing it does sound different... and the sweetspot is 1M taps, any higher or lower and the magic is removed again. That's why no difference in your test but a clear audible difference to Chord believers.
 
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kongwee

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I assume at line level, what happen being amplified like 1 watt?
 

seashell

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I don't really care what people do with filters and what kind of filter they use, but I don't feel the best comparison or utilization of a 4M vs 16K tap FIR for audio is to spend all those extra taps decreasing the width of the transition region to an already excessive stop band attenuation level (~-225dB attenuation relative to pass band?) in what appears to be an equiripple design. Of course you're not going to see (or hear) hardly and difference as your pass and stop bands look identical for the two filters. So really you're showing there's not much information in the transition region.

So first I suggest you raise your stop band attention level to something nearer to the limit of audibility, maybe -130dB relative to the pass band. I'm sure others here know the right number for threshold of audibility. Then you can likely get less ripple in your 16K filter for the same transition region bandwidth.

Then when you move to 4M taps spend all the extra power to flatten the ripple rather than narrow the transition region. Heck with so many taps why not drop equiripple and try a maximally flat pass band filter? You can probably still reach a reasonable transition band and a stop band attenuation below audibility even with increased ripple in the stop band.

Of course this also in no way addresses the time domain argument you threw out at the beginning. That's typically made as a comparsion of FIR vs IIR filters because IIR filters are not linear phase whereas you can create linear phase and thus constant group delay using FIR filters. I see the time domain argument mostly in room correction, with some people advocating using the phase design control of FIR filters to actually correct the overall room response phase.

I've not seen a consensus on if people can hear the relative group delay spread from non-linear phases typically encountered in audio systems and I'm not qualified in anyway to answer that myself.
 

Sokel

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Yes,but what about as purists who like NOS like the Topping's D70s (burnt for at least 200 hours as I read)?:p
That should be the test,none to 16M :facepalm:

(to those about to take the guns off,it's only a joke,I have to say it despite the smilies)
 
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nyxnyxnyx

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thanks for sharing your conclusion. you seem to know a lot about audio, do you have a background or career in this field?
 

AudioSceptic

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Claim
A claim is frequently made that DAC digital filters with a lot of taps can make a significant difference in sound quality. Some software packages and even hardware manufacturers are touting the benefits of large FIR filters, often with millions of taps, supposedly because these produce a more natural, smoother, analog sound or improve "time domain" accuracy, whatever that means. Some of these are sold at large premiums, supposedly because of the complexity of implementing large filters.

Test
Let's use DeltaWave software to find out the real story. I'll use a null test to produce a difference between a music file generated with two different size filters, and then measure the differences in frequency and time domain. For audibility testing, we'll also listen to it. Let's see if there's something to these claims!

The music file I'll be using is one some you may recognize as one used in other null tests on another forum:

http://www.mediafire.com/file/5hg6wl6ygql7217/Original2.wav/file

Since DeltaWave can generate and apply various size FIR filters, from 1k to 16M (yes, 16 million) taps, I decided to compare a 16k filter to a 4M one.

The Original2.wav music file is 24/44.1k, about 2 minutes. I'll place both filters with a cutoff at 21,150Hz. A shorter filter will have a gentler slope than the 4M one. The 4M one is a brickwall filter, as it drops the signal by nearly 300dB within a 20Hz transition band.

Applying FIR filters is just a simple setting in DeltaWave, so I used each filter on the original music file, and then saved the results as 64-bit floating point WAV. I then loaded these up in DeltaWave to compute the difference. Below are the results.

Results
First, the spectrum comparison. The only difference is visible right around the transition band (white line is obviously the 16k filter, blue is the 4M taps filter). I zoomed in on that area to show it better:
View attachment 226655


Spectrum of the difference file (null file) generated by subtracting the two filtered files... not much difference here, except past the cutoff where we already know the two filters are different:
View attachment 226656

Here's the phase difference between the two files (indicative of timing differences or group delay).

Note the scale on the left is 1x10^-7 degrees (0.0000001)! Nothing to see here... as one would expect with a linear FIR filter:
View attachment 226657

Let's check out the time-domain differences. Below is the actual waveform plot of the null file. Except for some sharp transients that have frequencies that extend past the filter cutoff, everything else is below -120dB! And even the sharp transients don't exceed -112dB, so way below audibility, considering that they are above 21kHz:

View attachment 226658

Here's the RMS average of the entire null file in time domain. Note that it's -229dBA, and -124.44dBFS. In other words, way below any thresholds of audibility, A-weighted or not:

View attachment 226661

Let's take a look at the difference spectrogram, maybe something will become apparent there... No difference at all except above the filter cutoff frequency:
View attachment 226660


And finally, here's the actual difference file: https://app.box.com/s/dde7ua0x668ismhebxpzxr57gh33u0jn

The file is a 32-bit FP WAV, mono to save space/size, about a 39MB download. Feel free to listen to see what the differences sound like between a 16k and 4M-size FIR filters. Personally, I can't hear anything even after raising the level by a whopping 100dB!

Conclusion
There's no audible benefit to all those heroic extra taps in a 4M-sized FIR filter. Don't believe me? Listen for yourself.
What an analysis! It's interesting that a mere 16k taps can achieve complete attenuation within such a narrow band. I wonder, what do 1/2/4/8 k taps look like at this scale?

Edit: is there a simple formula for calculating the slope and passband of a filter according to the number of taps?
 
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PeteL

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Are the filters labeled "linear phase" in typical AK4493 or ES9038 chips are actual real FIR filters? and if so is it documented (or "evaluated") how many taps are implemented?
 

pma

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Hi Paul,

Great test! The only think I doubt is that there can be any audible output with headphones and thus the effect of the test. Of course it will be inaudible, with standard quality of headphones and good headphone amplifiers.

I can imagine a scenario where the type of digital filter may become audible, and this will be not because of the filter used, but the power amplifier used. Below please see the output of the DacMagicPlus DAC playing a 21kHz sine (-1dBFS) with sampling frequency of 44.1kHz. The analog output is digitized at 96kHz/24bit with E1DA Cosmos ADC. 3 digital filters are used:
- Linear phase
- Minimum phase
- Sharp

We can see that both the Linear phase filter and Minimum phase filter create a mirror image at 23.1kHz. This tone itself is of course inaudible. But when it goes through a poor power amplifier, like almost all tube amplifiers or some solid state amplifiers with high IMD distortion, these 2 tones, 21kHz and 23.1kHz, will create a very audible 2.1kHz tone, though both tones were inaudible for the normal human population. This of course may happen only for the signal frequencies near to Fs/2 and depending on digital filter steepness. However, the effect cannot be generally excluded.
One can also see an amplitude drop of the Sharp filter at 21kHz fundamental frequency.

DM+_21kHz_linphase.png


DM+_21kHz_minphase.png


DM+_21kHz_sharp.png
 
OP
pkane

pkane

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Hi Paul,

Great test! The only think I doubt is that there can be any audible output with headphones and thus the effect of the test. Of course it will be inaudible, with standard quality of headphones and good headphone amplifiers.

I can imagine a scenario where the type of digital filter may become audible, and this will be not because of the filter used, but the power amplifier used. Below please see the output of the DacMagicPlus DAC playing a 21kHz sine (-1dBFS) with sampling frequency of 44.1kHz. The analog output is digitized at 96kHz/24bit with E1DA Cosmos ADC. 3 digital filters are used:
- Linear phase
- Minimum phase
- Sharp

We can see that both the Linear phase filter and Minimum phase filter create a mirror image at 23.1kHz. This tone itself is of course inaudible. But when it goes through a poor power amplifier, like almost all tube amplifiers or some solid state amplifiers with high IMD distortion, these 2 tones, 21kHz and 23.1kHz, will create a very audible 2.1kHz tone, though both tones were inaudible for the normal human population. This of course may happen only for the signal frequencies near to Fs/2 and depending on digital filter steepness. However, the effect cannot be generally excluded.
One can also see an amplitude drop of the Sharp filter at 21kHz fundamental frequency.

View attachment 226700

View attachment 226701

View attachment 226702
Hi Pavel,

Sure, it's not audible. It's not audible even when I increase the volume by 100dB :)

There are some DACs (and certainly many "audiophile" DAC filters) that assume there will be very little to no energy at or above the filter cutoff. They make the filter too slow or too gentle resulting in images of any large amplitude spikes that occur past the cutoff. Not an issue in most cases, as normal music recordings usually don't contain that much energy past 20kHz. There's no substitute for proper design, though it obviously doesn't require these multi-milllion tap filters to work well.
 

PeteL

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Hi Pavel,

Sure, it's not audible. It's not audible even when I increase the volume by 100dB :)

There are some DACs (and certainly many "audiophile" DAC filters) that assume there will be very little to no energy at or above the filter cutoff. They make the filter too slow or too gentle resulting in images of any large amplitude spikes that occur past the cutoff. Not an issue in most cases, as normal music recordings usually don't contain that much energy past 20kHz. There's no substitute for proper design, though it obviously doesn't require these multi-milllion tap filters to work well.
But Pavel was talking about 2.1 kHz generated from intermodulations of that 21k by poor amplifiers. I am not sure how, or if there is a rationale for that, I'd like some explanations, but he was not talking about what you measured being audible or energy past 20k. Not saying that would be audible or not but he is talking about a totally different test conditions than yours, 100 dB gain applied or not.
 
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pkane

pkane

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But Pavel was talking about 2.1 kHz generated from intermodulations of that 21k by poor amplifiers. I am not sure how, or if there is a rationale for that, I'd like some explanations, but he was not talking about what you measured being audible or energy past 20k. Not saying that would be audible or not but he is talking about a totally different test conditions than yours, 100 dB gain applied or not.
21kHz signal at 2.46v, right? A proper filter will cut off any images. A poor one will not. An amplifier can't produce IMD from a non-existent energy at the input.
 
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