Since you have referenced Mr Putzeys, have you heard the Mola Mola Tambaqui ?
Yes, but I'm not very familiar with it. I've read that it is based on Bruno's own PWM design.
Reconstruction/Image-Band Filter Investigation Outline
Introduction
First thing. While I have some functional knowledge, I am not a digital filter design expert. There are engineers who study and design digital filters for a professional living, which I do not. For those of you who may be expert, please feel free to correct any substantive errors which you may spot.
I hope we can avoid the vast mathematical foundation of FIR filter design as much as possible in an attempt to not leave anyone feeling excluded from the discussion. For those of you who may have been hoping to see an FIR filter design tutorial, this is not that. There are plenty of excellent such resources easily found via Google for that.
The outline takes an larger initial view of image-band suppression, not only utilizing digital OS filters. Acoustical filtering is primarily what prompted me to launch this thread, as it is always in effect, and seems it should make NOS and OS sound essentially identical. Analog filtering is where, as I understand the history, the Sony CD playback units began with their 16-bit DAC. Essentially, NOS plus a sharp active analog reconstruction filter. While Phillips, I've read, began with a 4xOS 14-bit DAC, in order to achieve 16-bit performance. Perhaps, the best solution will turn out to be a full-circle return to Sony's original approach. Who knows? Finally, we come the FIR digital OS interpolation-filtering, where DSP techniques take the lead, and where image-band suppression solutions become much more complex.
B) RECONSTRUCTION/IMAGE-BAND HANDLING
==============================================================================================
1. Acoustic Filters:
a) Human hearing provides greater than -50 dB pf suppression at 20KHz than at 1KHz for males over age 40. Significantly less loss, however, for ears younger than age 40.
b) Tweeter roll-off, but often not exceeding 10dB until 30KHz or greater. Still, it increases the ear's already substantial roll-off by several dB. Fullrange dynamic driver treble roll-off is typically more rapid than for a dedicated tweeter. Particularly, with off-axis listening.
KEY OBSERVATIONS: Acoustic suppression may reach levels which can fairly be considered as providing 'reconstruction' of the original signal, for human listening purposes. These filtering effects can not be bypassed. The filtering mechanisms are always 'operational', whether or not the DAC is NOS. Even so, NOS exhibits a different subjective character than with OS applied to the task of signal reconstruction. This is the root mystery, for me.
2. Analog Filters:
a) Low-order filters (3rd order, and lower) provide relatively insignificant suppression of most of the first image-band. Which extends from as low as 22KHz up to 44.1KHz.
b) High-order analog filters can offer significant suppression of the lower part of the 1st image-band. At roughly -20dB down @25KHz in the modeling I've done with a 7th order passive low-pass filter which utilized pole-zero pairs such as Abraxalito has done with his phiDAC passive reconstruction filters. . Which, theoretically, is insufficient suppression for CD. Meaning, does not suppress the images to a stop-band level beneath one LSB (Least Significant Bit) of 16-bits, around -96dB. Compared to typical FIR digital filters, high-order analog filters are not linear-phase. Although, they can offer relatively flat phase response until moving above 5KHz with the 7th order Abraxalito type pole-zero passive filter which I have modeled.
KEY OBSERVATIONS: I have a little bit of practical experience with low-order analog reconstruction filters, but heard no difference than without any added filter. Regarding high-order analog filters, I would like us to gain the subjective assessments of those utilizing 5th order or higher analog reconstruction filtered DACs. Especially, regarding, in what ways it sounds different to you than OS digital interpolation-filter DACs you have owned. This assessment must be of a DAC without any OS digital interpolation-filter in operation. Essentially, a NOS DAC with an entirely analog, high-order output filter. Similar to Sony's original CD-player. This is something which those of you who have built Abraxalito's phiDAC can provide valuable input.
3. Digital Filters (FIR Oversampling Interpolation-Filters):
a) Windowed-SINC filters. The SINC function is a mathematical function defining the perfect low-pass reconstruction filter impulse-response. It is where the term, brick-wall filter originates, as it appears to allow NO frequency above the filter cut-off to pass through the filter. Of course, it is not perfect in that task, just much, much better than analog filter.
Windowed-SINC FIR filter's can often be characteristically identified via filter frequency-response graphs, by a very short, but exponentially increasing oscillation in frequency-response peak amplitude just before the filter cut-off slope edge. This is easily seen within filter graphs contained in the PMD-100 and PMD-200 interpolation-filter chip data sheets. I note, anecdotally, that the PMD filters were typically judged as having the best sounding OS digital filter at the time. The mathematical SINC function impulse-response features an decaying oscillation which never actually comes to rest. It goes on, infinitely. For a linear-phase filter utilizing the SINC function, not only does it continue infinitely in to the future, it also begins infinitely in the past! That is not an problem in mathematics, but is, obviously, a problem for a physical processing engine. Therefore, the perfect SINC function must be made imperfect in some way for use in practical digital FIR filters. One way to make it imperfect is to simply chop off the function oscillation, called truncation. Truncation introduces undesired artifacts to the filter, however. 'Windowing', is the practical alternative to truncation, and simply involves smoothing the decaying oscillations to zero according to some formula, instead of simply chopping the ends of the function to a stop.
Windowed-SINC filters are the most processing inefficient, being the least elegant and the most brute force. They take no 'short-cuts' to save processing time or chip hardware cost in order to keep up with the high processing load of a lengthy SINC-function impulse-response. The longer is the filter's SINC function impulse-response, the more accurate will be the reconstructed signal. Even so, the reconstructed signal will always be somewhat imperfect, as the SINC impulse-response is infinite, while the filter processing construct is finite by definition (FIR = Finite Impulse Response). Processing artifacts due to a non-infinite impulse-response are reduced by 'windowing' (smoothing) the two decaying, otherwise truncated, ends of the SINC impulse-response. This type of digital filtering is much more practical to implement via off-line processing of a track (file), which is NOT currently being played than it is for the real-time playback of a track.
b) Parks-McClellan/Remez design method FIR filters. Minimizes the peak amplitude error of the filter's frequency response. Equiripple characteristic then results, as very small repeating ripples of uniform amplitude, within the filter's passband frequency-response. These are typically shown in the data sheets of audio DAC chips featuring integrated digital OS filters, which is to say, about all of them. It turns out that those ripples in the frequency-domain equate to signal echoes within the time-domain. While the audible significance of these echoes is debatable, their objective existence is not. They are simply the Fourier transform of the tiny uniform frequency response ripples appearing across the pass-band.
c) Half-band FIR implementation. This is a highly efficient, in terms of computations required to operate the filter, design. Processing load is essentially half that required by a Windowed-SINC filter of similar performance. Digital processing engines, such as FIR filters, can be computationally intensive. One way to address these computation intensive tasks is to dedicate more hardware to the effort. More hardware equals greater chip cost. Therefore, the DAC chip manufacturers have(had?) strong incentive to utilize design implementations which minimized chip hardware. Chip hardware, (meaning, on-chip logic gates) used to be costly. The result was/is the nearly universal (within dedicated hardware) half-band filter design. Chip hardware, especially for digital circuitry, is much less costly to produce today. Yet, half-band filter design persist as, seemingly, the only means for implementing an OS FIR filter, even among newly released DAC chips.
While performance efficiency is one matter, performance at the intended task is something else, it turns out. The half-band filter is one of the greatest violators of the sampling theorem, due to the processing corners which are cut in order for it to provide increased efficiency, which it does. It just plainly violates the Nyquist limit, however, allowing some aliasing in ADC use (it's worst offense, IMHO), and some image-band intrusion in DAC use. The subjective effect of it's DAC use is not clear to me. It may be responsible for the wider soundstage I hear via OS, for instance. In any case, the half-band filter is primarily chosen for it's low cost as an on-chip FIR filter, while it's performance is evidently deemed as adequate by it's sellers.
KEY OBSERVATIONS: It would seem that acoustical filtering plus high-order analog filtering taken together, hold the finger which would point to whether one or more of the FIR digital OS interpolation-filter design/implementations is the culprit we seek. However, before jumping to assign responsibility for the sometimes disappointing OS sound there, I would first like us to confirm whether a high-order analog reconstruction filter still allows the best aspects of NOS remain, and further, whether it makes the worst aspects of OS disappear. Assuming that we are able to eliminate the analog filter as harming NOS, and possibly even may combining the best of NOS and OS sound, we can then focus directly on the various FIR filter designs/implementations, and develop tests to reveal which appear responsible for the undesirable aspects of OS sound.
I've already mentioned above that the PMD filter chips had the reputation of delivering the 'best' subjective character at their time. While I don't believe I've seen the following notion specified, I strongly suspect that they utilized a Windowed-SINC interpolation-filter, judging from the filter graphs shown in their data sheets depicting classic Windowed-SINC band edge behavior. I seem to recall that the subjectively well regarded SoX upsampling utility within Foobar also utilizes a Windowed-SINC filter. Someone, please correct me about that if I'm mistaken. While these examples suggest to me that there may be a correlation between Windowed-SINC FIR interpolation-filters an the subjective sound character, that alone does not establish cause-and-effect between the two. That would require some experiments to fully determine.
Introduction
First thing. While I have some functional knowledge, I am not a digital filter design expert. There are engineers who study and design digital filters for a professional living, which I do not. For those of you who may be expert, please feel free to correct any substantive errors which you may spot.
I hope we can avoid the vast mathematical foundation of FIR filter design as much as possible in an attempt to not leave anyone feeling excluded from the discussion. For those of you who may have been hoping to see an FIR filter design tutorial, this is not that. There are plenty of excellent such resources easily found via Google for that.
The outline takes an larger initial view of image-band suppression, not only utilizing digital OS filters. Acoustical filtering is primarily what prompted me to launch this thread, as it is always in effect, and seems it should make NOS and OS sound essentially identical. Analog filtering is where, as I understand the history, the Sony CD playback units began with their 16-bit DAC. Essentially, NOS plus a sharp active analog reconstruction filter. While Phillips, I've read, began with a 4xOS 14-bit DAC, in order to achieve 16-bit performance. Perhaps, the best solution will turn out to be a full-circle return to Sony's original approach. Who knows? Finally, we come the FIR digital OS interpolation-filtering, where DSP techniques take the lead, and where image-band suppression solutions become much more complex.
B) RECONSTRUCTION/IMAGE-BAND HANDLING
==============================================================================================
1. Acoustic Filters:
a) Human hearing provides greater than -50 dB pf suppression at 20KHz than at 1KHz for males over age 40. Significantly less loss, however, for ears younger than age 40.
b) Tweeter roll-off, but often not exceeding 10dB until 30KHz or greater. Still, it increases the ear's already substantial roll-off by several dB. Fullrange dynamic driver treble roll-off is typically more rapid than for a dedicated tweeter. Particularly, with off-axis listening.
KEY OBSERVATIONS: Acoustic suppression may reach levels which can fairly be considered as providing 'reconstruction' of the original signal, for human listening purposes. These filtering effects can not be bypassed. The filtering mechanisms are always 'operational', whether or not the DAC is NOS. Even so, NOS exhibits a different subjective character than with OS applied to the task of signal reconstruction. This is the root mystery, for me.
2. Analog Filters:
a) Low-order filters (3rd order, and lower) provide relatively insignificant suppression of most of the first image-band. Which extends from as low as 22KHz up to 44.1KHz.
b) High-order analog filters can offer significant suppression of the lower part of the 1st image-band. At roughly -20dB down @25KHz in the modeling I've done with a 7th order passive low-pass filter which utilized pole-zero pairs such as Abraxalito has done with his phiDAC passive reconstruction filters. . Which, theoretically, is insufficient suppression for CD. Meaning, does not suppress the images to a stop-band level beneath one LSB (Least Significant Bit) of 16-bits, around -96dB. Compared to typical FIR digital filters, high-order analog filters are not linear-phase. Although, they can offer relatively flat phase response until moving above 5KHz with the 7th order Abraxalito type pole-zero passive filter which I have modeled.
KEY OBSERVATIONS: I have a little bit of practical experience with low-order analog reconstruction filters, but heard no difference than without any added filter. Regarding high-order analog filters, I would like us to gain the subjective assessments of those utilizing 5th order or higher analog reconstruction filtered DACs. Especially, regarding, in what ways it sounds different to you than OS digital interpolation-filter DACs you have owned. This assessment must be of a DAC without any OS digital interpolation-filter in operation. Essentially, a NOS DAC with an entirely analog, high-order output filter. Similar to Sony's original CD-player. This is something which those of you who have built Abraxalito's phiDAC can provide valuable input.
3. Digital Filters (FIR Oversampling Interpolation-Filters):
a) Windowed-SINC filters. The SINC function is a mathematical function defining the perfect low-pass reconstruction filter impulse-response. It is where the term, brick-wall filter originates, as it appears to allow NO frequency above the filter cut-off to pass through the filter. Of course, it is not perfect in that task, just much, much better than analog filter.
Windowed-SINC FIR filter's can often be characteristically identified via filter frequency-response graphs, by a very short, but exponentially increasing oscillation in frequency-response peak amplitude just before the filter cut-off slope edge. This is easily seen within filter graphs contained in the PMD-100 and PMD-200 interpolation-filter chip data sheets. I note, anecdotally, that the PMD filters were typically judged as having the best sounding OS digital filter at the time. The mathematical SINC function impulse-response features an decaying oscillation which never actually comes to rest. It goes on, infinitely. For a linear-phase filter utilizing the SINC function, not only does it continue infinitely in to the future, it also begins infinitely in the past! That is not an problem in mathematics, but is, obviously, a problem for a physical processing engine. Therefore, the perfect SINC function must be made imperfect in some way for use in practical digital FIR filters. One way to make it imperfect is to simply chop off the function oscillation, called truncation. Truncation introduces undesired artifacts to the filter, however. 'Windowing', is the practical alternative to truncation, and simply involves smoothing the decaying oscillations to zero according to some formula, instead of simply chopping the ends of the function to a stop.
Windowed-SINC filters are the most processing inefficient, being the least elegant and the most brute force. They take no 'short-cuts' to save processing time or chip hardware cost in order to keep up with the high processing load of a lengthy SINC-function impulse-response. The longer is the filter's SINC function impulse-response, the more accurate will be the reconstructed signal. Even so, the reconstructed signal will always be somewhat imperfect, as the SINC impulse-response is infinite, while the filter processing construct is finite by definition (FIR = Finite Impulse Response). Processing artifacts due to a non-infinite impulse-response are reduced by 'windowing' (smoothing) the two decaying, otherwise truncated, ends of the SINC impulse-response. This type of digital filtering is much more practical to implement via off-line processing of a track (file), which is NOT currently being played than it is for the real-time playback of a track.
b) Parks-McClellan/Remez design method FIR filters. Minimizes the peak amplitude error of the filter's frequency response. Equiripple characteristic then results, as very small repeating ripples of uniform amplitude, within the filter's passband frequency-response. These are typically shown in the data sheets of audio DAC chips featuring integrated digital OS filters, which is to say, about all of them. It turns out that those ripples in the frequency-domain equate to signal echoes within the time-domain. While the audible significance of these echoes is debatable, their objective existence is not. They are simply the Fourier transform of the tiny uniform frequency response ripples appearing across the pass-band.
c) Half-band FIR implementation. This is a highly efficient, in terms of computations required to operate the filter, design. Processing load is essentially half that required by a Windowed-SINC filter of similar performance. Digital processing engines, such as FIR filters, can be computationally intensive. One way to address these computation intensive tasks is to dedicate more hardware to the effort. More hardware equals greater chip cost. Therefore, the DAC chip manufacturers have(had?) strong incentive to utilize design implementations which minimized chip hardware. Chip hardware, (meaning, on-chip logic gates) used to be costly. The result was/is the nearly universal (within dedicated hardware) half-band filter design. Chip hardware, especially for digital circuitry, is much less costly to produce today. Yet, half-band filter design persist as, seemingly, the only means for implementing an OS FIR filter, even among newly released DAC chips.
While performance efficiency is one matter, performance at the intended task is something else, it turns out. The half-band filter is one of the greatest violators of the sampling theorem, due to the processing corners which are cut in order for it to provide increased efficiency, which it does. It just plainly violates the Nyquist limit, however, allowing some aliasing in ADC use (it's worst offense, IMHO), and some image-band intrusion in DAC use. The subjective effect of it's DAC use is not clear to me. It may be responsible for the wider soundstage I hear via OS, for instance. In any case, the half-band filter is primarily chosen for it's low cost as an on-chip FIR filter, while it's performance is evidently deemed as adequate by it's sellers.
KEY OBSERVATIONS: It would seem that acoustical filtering plus high-order analog filtering taken together, hold the finger which would point to whether one or more of the FIR digital OS interpolation-filter design/implementations is the culprit we seek. However, before jumping to assign responsibility for the sometimes disappointing OS sound there, I would first like us to confirm whether a high-order analog reconstruction filter still allows the best aspects of NOS remain, and further, whether it makes the worst aspects of OS disappear. Assuming that we are able to eliminate the analog filter as harming NOS, and possibly even may combining the best of NOS and OS sound, we can then focus directly on the various FIR filter designs/implementations, and develop tests to reveal which appear responsible for the undesirable aspects of OS sound.
I've already mentioned above that the PMD filter chips had the reputation of delivering the 'best' subjective character at their time. While I don't believe I've seen the following notion specified, I strongly suspect that they utilized a Windowed-SINC interpolation-filter, judging from the filter graphs shown in their data sheets depicting classic Windowed-SINC band edge behavior. I seem to recall that the subjectively well regarded SoX upsampling utility within Foobar also utilizes a Windowed-SINC filter. Someone, please correct me about that if I'm mistaken. While these examples suggest to me that there may be a correlation between Windowed-SINC FIR interpolation-filters an the subjective sound character, that alone does not establish cause-and-effect between the two. That would require some experiments to fully determine.
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Doesn't a windowed sinc, assuming the sinc cuts off at the Nyquist frequency, behave exactly as a half- band filter? The windowing in the time domain will smear out the response in the frequency domain, so you get a transition band that starts below and ends above the Nyquist frequency. A solution is to slightly reduce the cut-off frequency of the original sinc-shaped impulse response.
I believe that a Windowed-SINC filter set to a -6.02dB cut-off at Nyquist will behave like a half-band SINC implementation does. It would be open to aliasing/leaving a bit of the first image-band unsuppressed. Windowing of the filter impulse-response will produce some spreading of the transition-band, but that can be countered by by narrowing it again by increasing the length of the filter's impulse-response kernel. The major performance difference between the two appears to be that, while a Windowed-SINC filter can be set to cut-off at any frequency below Nyquist, half-band filters always cut-off exactly at Nyquist.
No matter what length of filter kernel is utilized to narrow the transition-band, the half-band filter will always be down only -6.02dB at Nyquist. Which means that it exhibits a stop-band that doesn't begin until after Nyquist. Even if ever so shortly after. Which, of course, is a mechanism for aliasing/imaging to potentially intrude. The opportunity for such intrusion depending on the narrowness of the filter's transition-band. A full convolution (meaning, not half-band) Windowed-SINC filter can be set so that the stop-band fully begins at, or prior to Nyquist.
Attached, is the chapter on Windowed-SINC filters, from Steven Smith's excellent introductory DSP book, published in 1999. His entire book, I you haven't read it, is outstanding in the clarity of it's presentation on DSP technology. All of the chapters are available as PDFs, and free for downloading at the Analog Devices website.
https:/www.analog.com/en/education/education-library/scientists_engineers_guide.html
Good tip, Marcel, I didn't know that. I've wondered how companies, such as Schiitt Audio in the U.S., produced such filters. Which they refer to as 'closed-form' filters.
Hans,
I believe that Windowed-SINC (non-Equiripple) filters do feature a perfectly flat pass-band. Except for a exponentially peaking, but short, oscillating amplitude of the pass-band frequency-response, just prior to the start of the transition-band. I suspect this stems from the discontinuity formed by Windowing of the impulse-response tails. The oscillating amplitude of the pass-band frequency-response would be worse if the SINC impulse-response were simply truncated.
FWIW -
Attached, is an (I don't know the date it was published) subjective assessment comparing three OS digital FIR filter ICs. Which are the Pacific-Microsonics PMD-100 and PMD-200, along with the Burr-Brown DF-1704. I believe that the PMD chips both feature Windowed-SINC filter design, while the Burr-Brown features a Half-band Equiripple design - which was ubiquitous then, and remains so today.
Attached, is an (I don't know the date it was published) subjective assessment comparing three OS digital FIR filter ICs. Which are the Pacific-Microsonics PMD-100 and PMD-200, along with the Burr-Brown DF-1704. I believe that the PMD chips both feature Windowed-SINC filter design, while the Burr-Brown features a Half-band Equiripple design - which was ubiquitous then, and remains so today.
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Correct link to Steven Smith's excellent DSP book:
The Scientist & Engineer's Guide to Digital Signal Processing, 1999 | Education | Analog Devices
The Scientist & Engineer's Guide to Digital Signal Processing, 1999 | Education | Analog Devices
Kostas,
You have a very interesting looking equipment set-up. Looks to be quite a serious platform. I'm not surprised, however, that no measurement jumped out to you as significant when searching with your test instruments. I rather suspect that what we are seeking to find will not prove to be obvious, even should we know exactly what parameter(s) to watch.
So that I'm clear, regarding your tweeter experiment report, are you saying that you STILL DID HEAR the subjective differences which characterize the sound of NOS versus OS playback, with the tweeters disconnected?
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Actually halfband filters have the same property, see
HALF-BAND FIR FILTERS | Chapter Five. Finite Impulse Response Filters
In the example they show, h[k] is zero for all odd values of k except the one in the middle, which is one. That means that when you take a discrete-time signal, insert zeros between each pair of samples to double the sample rate and then pass it through this filter, you will see one of the original sample values at the output whenever the inserted zeros get multiplied by the even coefficients and the samples that stem from the original signal get multiplied by the odd coefficients.
It's actually equivalent to time multiplexing between a delayed version of the original signal and an interpolated m + 1/2 sample delayed version, see posts #301 and #304 of https://www.diyaudio.com/forums/dig...a-sigma-interpolation-dac-31.html#post6539266 (Although the title suggests otherwise, it's a thread about unconventional ways to reconstruct a digital signal.)
Besides subjective perception of its performance, I feel quite confident when it comes for comparisons in my system. So, to summarize, without the tweeters I can't hear any difference. Or to use my favorite expression, I can't "see" anything... I pay more attention to the soundstage orientation than the nuances. That said, I dislike distortion as well. With the tweeters on, I feel there is something but not at the very high frequencies. To me it looks like the harmonics of the mid band projecting to the lower treble. When I find some time I will take a measurement with mid band white noise.
"Yes, but I'm not very familiar with it. I've read that it is based on Bruno's own PWM design."
rfbrw, the above response of mine, taken from post #342, was orignally intended for you. I just now, realized that it was accidentally misdirected to Lampie519. My apologies.
The amp left and right channel phase response should be identical. Sometimes this factor can fall through the cracks. Not to mention the differences in tweeter specifications. Even the interconnects can influence the overall phase response - if one cable was not terminated properly: the way the shield is terminated to pin 1 (X 4 XLR connectors). All are very important with what you are doing (which I applaud!).
Ken,
Look at fig 16-1 in your attachment of posting #349.
No such peaking with a properly windowed sinc before the start of the passband.
But depending on the window you may get what you describe.
Hans
You get a large ripple at the end of the passband and the start of the stopband when you try to find FIR coefficients by just doing an inverse DFT on the frequency response you would like to have, especially when you don't make a smooth transition from passband to stopband in the target frequency response. I used to do that on my VIC-20 home computer in the late 1980's. Smoothing the transition helped a lot.
Figure 16-2 of post #349 shows that all the mentioned windowed sinc filters have ripples in the stopband. I wonder if there aren't any matching ripples in the passband that are just too small to see on this scale. At least they are there with the rectangular window of figure 16-1, second plot on the right side.
Does anyone know the answer?
Figure 16-2 of post #349 shows that all the mentioned windowed sinc filters have ripples in the stopband. I wonder if there aren't any matching ripples in the passband that are just too small to see on this scale. At least they are there with the rectangular window of figure 16-1, second plot on the right side.
Does anyone know the answer?