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

[Tks]

hey @pkane I know this has nothing to do with audibility but if you could..

I'd be really interested if you could deduce some semblance of what the processing overhead differences would be (maybe run the tap count until your PC or whatever starts to bog down, or until you reach the software cap).

 

[GWolfman]

Thanks!

Even looking at the spectrum graph there's only measurable differences in a narrow 70Hz band around 21.5kHz. Doubt anyone can pick out different pure tones in that small bandwidth and frequency, let alone multi tone sounds (e.g., music)!

 

[GWolfman]

Maybe it'd be an interesting test to see if any audible difference between the extreme low end (1k) and your selected 4M taps.

 

[pma]

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.

FYI, below are the responses in the frequency domain and time domain of the DM+ filters (linear phase, minimum phase, sharp). The sharp filter is in fact the linear phase filter with Fc shift a bit to lower frequency. My point (and I am not sure that it was understood) is that you cannot only look at amplitude frequency response, without viewing phase response or impulse/square response. You just do not see the whole transfer function from the amplitude frequency response only. You will not see the difference between the linear phase and minimum phase filters in frequency domain amplitude response only. And, to find possible audible differences between the filters, one has to use an appropriate signal that is able to discover it.

Generally, the intention of this thread was good, but as usually, a bit simplified. It is not enough to laugh at audiophile claims, deeper analysis is needed.

 

[tecnogadget]

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.

I think the benefits of Acourate and Audiolense is that using high tap FIR filters you get a lot more correction at low frequencies (where you want to EQ do its magic). As far as I know, everything that runs Dirac and its not a PC uses very few taps because of lack of processing power and it only corrects a few bands below 100Hz…
As for the PC VST version, they are very opaque for such details…

 

[pkane]

FYI, below are the responses in the frequency domain and time domain of the DM+ filters (linear phase, minimum phase, sharp). The sharp filter is in fact the linear phase filter with Fc shift a bit to lower frequency. My point (and I am not sure that it was understood) is that you cannot only look at amplitude frequency response, without viewing phase response or impulse/square response. You just do not see the whole transfer function from the amplitude frequency response only. You will not see the difference between the linear phase and minimum phase filters in frequency domain amplitude response only. And, to find possible audible differences between the filters, one has to use an appropriate signal that is able to discover it.

Generally, the intention of this thread was good, but as usually, a bit simplified. It is not enough to laugh at audiophile claims, deeper analysis is needed.

Pavel, I appreciate the additional details, but this was specifically about linear phase FIR filters and was addressing claims about those. Phase response was not only assumed to be linear but was also shown to be linear in the OP.

By the way, DeltaWave implements minimum phase filters, as well as a maximally flat IIR filter, should any one want to run additional tests with those. But I guarantee that there will be greater differences there, since time performance of those filters (phase response) will not be linear.

 

[RandomEar]

FYI, below are the responses in the frequency domain and time domain of the DM+ filters (linear phase, minimum phase, sharp). The sharp filter is in fact the linear phase filter with Fc shift a bit to lower frequency. My point (and I am not sure that it was understood) is that you cannot only look at amplitude frequency response, without viewing phase response or impulse/square response. You just do not see the whole transfer function from the amplitude frequency response only. You will not see the difference between the linear phase and minimum phase filters in frequency domain amplitude response only. And, to find possible audible differences between the filters, one has to use an appropriate signal that is able to discover it.

Generally, the intention of this thread was good, but as usually, a bit simplified. It is not enough to laugh at audiophile claims, deeper analysis is needed.

You aren't wrong. But the phase response isn't determined by the number of filter taps, it's simply a design choice. Thereby, comparing two linear phase filters with a (vastly) different number of taps is still a valid comparison.

Also, I haven't seen any evidence that well designed linear- and minimum phase filters with the same frequency response actually sound different at all. It's possible, I just haven't seen the evidence. Therefore, even if two filters with a different tap number and different phase response were compared here and the result was that they sounded identical - why would that be a problem?

 

[pkane]

hey @pkane I know this has nothing to do with audibility but if you could..

I'd be really interested if you could deduce some semblance of what the processing overhead differences would be (maybe run the tap count until your PC or whatever starts to bog down, or until you reach the software cap).

Not sure I can do that, since FFT implementations vary, some use additional accelerators offered by the CPU, others can also use GPU. 4M taps should not be a problem for a normal, consumer-grade PC with no GPU acceleration. In computational complexity, the FIR filter is applied using FFTs which require an order of N*log(N) computations where N is the size of the FFT. As the filter size increases, the number of computations will increase approximately as N*log(N).

 

[voodooless]

@pkane is the calculation done in single or double precision?

 

[pkane]

@pkane is the calculation done in single or double precision?

All double precision, and files were saved as 64-bit floating point before analysis.

 

[gnarly]

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.

So true.
True to the degree that maybe the tread title could be better narrowed to:
'Does a 4 million taps anti-aliasing low pass FIR filter for a DAC sound better than a 16K one?'

As a DSP product used for altering the magnitude and phase of the audio stream, will have a frequency resolution determined by the number of taps and the sample rate.
For alterations, more taps increase the frequency resolution, while higher sampling rates decrease it.
So alterations depend on the amount of time the FIR filter has available to accomplish them, which is simply taps/sampling rate.
( I know you know all that; writing to maybe help others following along...)

Thanks for your work! Comes as no surprise. That said, verifications are always nice !

​

 

[Chromatischism]

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.

I think the benefits of Acourate and Audiolense is that using high tap FIR filters you get a lot more correction at low frequencies (where you want to EQ do its magic). As far as I know, everything that runs Dirac and its not a PC uses very few taps because of lack of processing power and it only corrects a few bands below 100Hz…
As for the PC VST version, they are very opaque for such details…

I am unsure of the resolution of Dirac filters, but Audyssey uses the equivalent of 16,000 taps per channel. I think Dirac would be very similar.

 

[xnor]

From a DSP point of view, length of the filter does not say anything about its quality. In fact, longer (linear phase) FIR filters can be detrimental to audio quality if any of the FR deviations are in the audible range due to pre-ringing.

Btw, just saying "N taps" is meaningless in resampling filters if you don't specify at which sampling frequency.

For example, a low pass centered at 22.05 kHz may have ~500 taps at 2x 44100 Hz, but ~16000 taps at 64x. The same filter.

Generally, here's what an increased number of taps (at the same sampling rate) gives you: higher attenuation, a steeper filter, increased group delay.

On attenuation: it's pretty easy to get magnitudes beyond what electronics let alone electromechanical systems could ever achieve.
For example, for the 2x filter above the difference going from -120 dB to -144 dB to -180 dB are about +40 and +60 taps.

On steepness (transition width): steeper also means more ringing. Luckily, this doesn't matter at about 20 kHz.

On increased group delay: this can become a real problem. 16k at 64x 44.1 kHz results in a delay of 2.8ms, but 4 M would result in a delay of ~700 ms.

 

[Chromatischism]

I've read that group delay and pre-ringing are side effects (intentional, unsure of audibility) of the Dirac mixed-phase approach using all-pass filters to adjust phase, but didn't think that was the case in a purely FIR-based system like Audyssey that does not correct phase. True or false?

 

[Head_Unit]

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?

They can only hear it when the weather is nice, it was a good day at work, and they are relaxing with some special $50 whisky as rebottled by @pvehling...and whether the vinyl was pressed from African or European oil.

 

[Head_Unit]

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.

What if you had no filter at all? Would that really be a problem at 44/48/etc sampling rate? Has anyone ever tried to check this? How...by measuring digital files on a workstation before playback? I guess I have seen some analysis showing ultrasonics but I don't recall the levels and I think that was DSD come to think of it.

 

[pkane]

What if you had no filter at all? Would that really be a problem at 44/48/etc sampling rate? Has anyone ever tried to check this? How...by measuring digital files on a workstation before playback? I guess I have seen some analysis showing ultrasonics but I don't recall the levels and I think that was DSD come to think of it.

Yes, it can be a problem, especially at lower sampling rates, like 44.1 or 48kHz. There are enough "audiophile" DACs out there with what they call a NOS mode, without a digital filter. This results in out of band images reflecting into the audible range. Plus, the absence of a reconstruction filter results in other issues that may be audible, like additional distortions. Some audiophiles rectify this by upsampling and/or pre-filtering PCM data in software, before it's sent to the DAC.

Nyquist-Shannon sampling theorem requires a proper reconstruction filter, otherwise you don't get the an accurate reconstruction of the original, sampled signal.

 

[Lbstyling]

Taps may not make a difference, but IIR and FIR linear or Min phase filters do.

Try rephase on a time aligned dual concentric driver like the KEF reference range and tell me I'm wrong.

 

[Tks]

Not sure I can do that, since FFT implementations vary, some use additional accelerators offered by the CPU, others can also use GPU. 4M taps should not be a problem for a normal, consumer-grade PC with no GPU acceleration. In computational complexity, the FIR filter is applied using FFTs which require an order of N*log(N) computations where N is the size of the FFT. As the filter size increases, the number of computations will increase approximately as N*log(N).

I've never seen filtering get GPU accelerated. Now I'm curious about that.

 

[xnor]

I've read that group delay and pre-ringing are side effects (intentional, unsure of audibility) of the Dirac mixed-phase approach using all-pass filters to adjust phase, but didn't think that was the case in a purely FIR-based system like Audyssey that does not correct phase. True or false?

It's not a side effect. All these things are inextricably linked.
In a min phase system, you get all of the filter's output after the input impulse.
In a linear phase system, the filter delays the impulse and produces symmetric output before and after the input impulse.
Mixed-phase is just that, a mix of the two (or even of max phase).

FIR just means that the filter is stored literally as a sampled impulse response. Filtering happens through convolution (which can be implemented as trivially as multiplying each tap aka sample of the reversed FIR with the input signal, adding them up producing an output sample and then shifting the FIR one sample ahead, repeat the same for the next output sample).

The cool thing about it is that you can design arbitrary linear filters, that is with arbitrary frequency response (magnitude and phase).