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

PeteL

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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.
I agree with all that, just saying that PMA is talking about 2.1k, not 21k, and I don't know how he get's this figure.
 
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pkane

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I agree with all that, just saying that PMA is talking about 2.1k, not 21k, and I don't know how he get's this figure.
In his example, 21kHz and 23.1kHz tones intermodulate, one of the products is 23.1k-21k = 2.1kHz
 

DanielT

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What is taps in an FIR filter?

Very possible I missed something.:)


Edit:
Aha:
"Tap – A FIR "tap" is simply a coefficient/delay pair. The number of FIR taps, (often designated as "N") is an indication of 1) the amount of memory required to implement the filter, 2) the number of calculations required, and 3) the amount of "filtering" the filter can do; in effect, more taps means more stopband attenuation, less ripple, narrower filters, etc."

 
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danadam

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What is taps in an FIR filter?

Aha:
"Tap – A FIR "tap" is simply a coefficient/delay pair. The number of FIR taps, (often designated as "N") is an indication of 1) the amount of memory required to implement the filter, 2) the number of calculations required, and 3) the amount of "filtering" the filter can do; in effect, more taps means more stopband attenuation, less ripple, narrower filters, etc."
Also here mansr explains:
 

phoenixdogfan

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Also has implications for things like DSP. aCCOURATE and Audiolense are claimed to be superior to Dirac in some quarters because they employ linear phase filters while Dirac uses mixed phase. While all of them are expensive, the Dirac seems far simpler to set up and its filters result in less latency which is an importnt consderation when employing them in home theater applications.
 

Dathzo

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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.
Good stuff, thanks for taking the time and post this @pkane !
I would expect that after a certain number of taps, audible differences become indiscernible. Audiolense and Acourate can generate filters up to 132k taps, and from your results, there is no benefit of such number vs. 16k. The question is, when is the cutoff? Minidsp can implement filters up to 4k taps I think. This is lower than the 16k you tested. Would it be a difference between 4K and 16k? Any perspective there?
Thanks again.-
 
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pkane

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Good stuff, thanks for taking the time and post this @pkane !
I would expect that after a certain number of taps, audible differences become indiscernible. Audiolense and Acourate can generate filters up to 132k taps, and from your results, there is no benefit of such number vs. 16k. The question is, when is the cutoff? Minidsp can implement filters up to 4k taps I think. This is lower than the 16k you tested. Would it be a difference between 4K and 16k? Any perspective there?
Thanks again.-

Probably not fair to compare complex DSP products that attempt to correct complex frequency and timing issues to a simple low-pass reconstruction filter used in DACs.
 

Dathzo

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Probably not fair to compare complex DSP products that attempt to correct complex frequency and timing issues to a simple low-pass reconstruction filter used in DACs.
Fair enough, thanks for the quick reaction
 

Cbdb2

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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
In properly mastered music (44.1khz) there won't be any signal above 20khz.
 

pma

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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!
3 digital filters are used:
- Linear phase
- Minimum phase
- Sharp

Paul, I think that an appropriate music material must be used to compare the filters, and it has to contain fast transients. I have prepared test files using the Minimum phase filter and the Sharp filters, as mentioned before. The files may be downloaded from


and the zip file contains the Deltawave difference as well. The differences in transients are not tiny, as you may verify yourself, if you are interested.

filter_delta.png


filter_pkmetric.png


and for @Cbdb2 , we stay below 20kHz. Still, differences are not tiny.

1661536307599.png


Edit: added Foobar ABX result. Different ringing on a clash is clearly audible.

Code:
foo_abx 2.0.2 report
foobar2000 v1.4.8
2022-08-27 09:14:04

File A: Filter_2.wav
SHA1: 63938cf0e897b0b7e310e1ec7dac6ff19ae7e554
File B: Filter_3.wav
SHA1: dcc96356ea37cb2b8851813ccb18bda438b69344

Output:
ASIO : Topping USB Audio Device
Crossfading: NO

09:14:04 : Test started.
09:15:59 : 00/01
09:16:11 : 00/02
09:16:19 : 01/03
09:16:30 : 01/04
09:16:39 : 02/05
09:16:50 : 02/06
09:17:01 : 03/07
09:17:12 : 03/08
09:17:25 : 04/09
09:17:33 : 05/10
09:17:56 : 06/11
09:18:03 : 07/12
09:18:17 : 08/13
09:18:25 : 09/14
09:18:40 : 10/15
09:19:09 : 11/16
09:19:09 : Test finished.

 ----------
Total: 11/16
Probability that you were guessing: 10.5%

 -- signature --
c91010571e3c2f5ab78764ab82fc5658b915f048

Edited, the previous ABX result was from files that were not linked
 
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Spkrdctr

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All this talk of Taps made me think of BEER! Seriously though, as I have said at least 50 times on these amazing threads, in the end 90% of what is talked about endlessly and determines awesome performance from ok performance is NOT AUDIBLE. But, it is nice to have someone come along and once again with graphs and data say the same thing. ASR is the only place on the internet where real down to earth audio topics are discussed and analyzed in detail. So nice for Amir and others to cut through the mountains of marketing BS. Thank you to all of the members who do the work to help other audio enthusiasts gain critical knowledge. I think I am an ASR addict. Best drug ever as it is free!
 

fpitas

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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
The obvious answer: only if they use the warmest tube amps.
 
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pkane

pkane

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Paul, I think that an appropriate music material must be used to compare the filters, and it has to contain fast transients. I have prepared test files using the Minimum phase filter and the Sharp filters, as mentioned before. The files may be downloaded from


and the zip file contains the Deltawave difference as well. The differences in transients are not tiny, as you may verify yourself, if you are interested.

View attachment 226765

View attachment 226766

and for @Cbdb2 , we stay below 20kHz. Still, differences are not tiny.

View attachment 226768

Of course, different filter types will have a different impulse response. And I'm not at all surprised that some DACs out there may have really poor, leaky filters, that may also be poorly implemented, or implemented for different purpose than accuracy (for example, low latency).

Transients will contain higher frequencies. So it's not surprising that a poor, gentle, or poorly placed reconstruction filter may not be able to handle these properly. A minimum phase filter will have a different response than a linear phase one, an IIR filter will have a different response than a FIR.
 

doug2761

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Thanks for the analysis and the post. Can you help me to put this in the context of the tap length of contemporary DAC chips? Looking at the ESS 9038Q2M data sheet, linked here, It doesn't seem to disclose the number of taps in the primary filter. If I'm correct, this is the DAC chip in the SMSL D0100.
 

Blumlein 88

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Thanks for the analysis and the post. Can you help me to put this in the context of the tap length of contemporary DAC chips? Looking at the ESS 9038Q2M data sheet, linked here, It doesn't seem to disclose the number of taps in the primary filter. If I'm correct, this is the DAC chip in the SMSL D0100.
Most of your current DAC chips are probably 64 to 256 taps.
 
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