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Analog Delta-Sigma interpolation DAC
Analog Delta-Sigma interpolation DAC
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Old 18th February 2021, 08:35 PM   #301
U130421 is offline U130421  Antarctica
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Quote:
Originally Posted by MarcelvdG View Post
Isn't that a standard two times interpolating filter, that is, a combination of inserting zeros and brick-wall low-pass filtering? Instead of a windowed sinc, you can also use the Parks-McClellan program (based on the Remez exchange algorithm) to find a finite impulse response that approximates the ideal sinc.
sinc hamming.JPG
No zero stuffing. Instead of sinc interpolation of very high samples, it is Hamming windowed.
All I find from Park McClellan is FIR filter design, any reference for the sinc?

Last edited by U130421; 18th February 2021 at 08:41 PM.
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Old 18th February 2021, 08:44 PM   #302
Hans Polak is offline Hans Polak  Netherlands
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Sorry Hayk, it is for 100% zero stuffing with one zero.
No question about that, believe me.
Exactly what I did with 3 zero’s.

Hans

P.s. with such a short filter you will get miserable results.

Last edited by Hans Polak; 18th February 2021 at 08:48 PM.
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Old 18th February 2021, 08:51 PM   #303
U130421 is offline U130421  Antarctica
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Another one with Kaiser window.
Windowed Sinc Interpolation | Physical Audio Signal Processing
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Old 18th February 2021, 10:10 PM   #304
MarcelvdG is offline MarcelvdG  Netherlands
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I think you are both right, actually.

The filter from post #301 could be one of the two polyphase decompositions of a two times interpolating 32-tap FIR filter (two times oversampling filter), the other polyphase decomposition is then a group of zeros, a one and another group of zeros.

Real interpolating filters are never made of an oversampler that inserts zeros and then a low-pass filter. In practice these two steps are intertwined because it is more computationally efficient.

If you would first insert zeros and then pass it though a normal filter, for each output sample, half the filter coefficients would be multiplied by zero. You can save half the multiplications by leaving out those coefficients. You then end up with a filter of half the length that uses two different coefficient sets for the odd and even output samples, so in fact it becomes a time variant filter. For some reason those coefficient (sub-)sets are know as polyphase decompositions.

In this specific case, one of the two polyphase decompositions has only one one and a bunch of zeros as its coefficients, so you can actually time multiplex between a delayed version of the input signal and the output signal of the filter of post #301. That way you need only a quarter of the multiplications.
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Old 18th February 2021, 10:40 PM   #305
MarcelvdG is offline MarcelvdG  Netherlands
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Regarding Parks-McClellan, all design methods for linear-phase FIR low-pass filters lead to some finite-length approximation of a sinc. The Parks-McClellan approximation leads to an equiripple frequency response in the pass and the stop band.

As an example, attached is the impulse response of a 128-tap Parks-McClellan filter with a pass band up to 0.22675 fs, stop band from 0.27325 fs onwards, 12778 times as large error in the pass band as in the stop band. The picture with the discrete points is the correct plot, the other one has nonexistent line segments added for clarity.
Attached Images
File Type: png IMPULSE_McClellan128.png (18.3 KB, 71 views)
File Type: png IMPULSE_McClellan128_wlp.png (33.9 KB, 72 views)
Attached Files
File Type: txt IMPULSE_McClellan128TIachtig.TXT (3.5 KB, 2 views)
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Old 19th February 2021, 06:08 AM   #306
MarcelvdG is offline MarcelvdG  Netherlands
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Maybe they used a standard two times oversampling digital filter for the circuit of post #258 and sent the odd words to one DAC and the even words to the other DAC, with 1/88200 s delay between them. Or they just made a half cycle delay filter like the one from post #301 to feed one of the DACs, still with 1/88200 s shift between the DACs. That way they can have a good suppression of the first two images and still claim it is a non-oversampling DAC without steep analogue filter.
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Old 19th February 2021, 08:55 AM   #307
Hans Polak is offline Hans Polak  Netherlands
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There are all kind of tricks to reduce the amount of multiplications when calculation resources are restricted, but at the end if more samples come out then came in, it boils mostly down to be a smart derivative of zero stuffing and straight convolution, tricks that may or may not result in a loss of sound quality.

So when enough processing power available, why bother ?
Over the last years since processing power is abundant, even music programmes like JRiver can do the convolution whith your self fabricated Fir filter coefficients.

With a 1000 point Fir and 4 times upsampling, 44e6 multiplications have to be done per second, which even a fast Intel processor can achieve.
A graphic NVidia card can do at least 100 times more than that.

There is a clear development with DACís having all sorts of different filters, and DSPís or FGPAís can do the job with ease.
So I think the challenge is nowadays not to have the smartest algorithm but to have the best sounding filter that can beat the supposed clarity of NOS.

Hans

P.s. I have never read a test in Stereophile of a NOS Dac that beats all the oversamplers, so what to think of that ??
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Old 19th February 2021, 10:10 AM   #308
Hans Polak is offline Hans Polak  Netherlands
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I simulated the Accuphase solution and added 8 time shifted samples of a NOS Dac.
All the supersonic images are still there, but as can be seen, compared to the Sinc of a single sample NOS Dac in Red, these images are suppressed quite a bit depending on their frequency, so it is effectively in some way.
But an analogue filter will still be needed to correct the loss of level at the high end side of the audio range, caused by the Sinc.

Hans
.
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File Type: jpg 8 samples.jpg (405.1 KB, 57 views)
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Old 19th February 2021, 10:36 AM   #309
MarcelvdG is offline MarcelvdG  Netherlands
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Quote:
Originally Posted by Hans Polak View Post
There are all kind of tricks to reduce the amount of multiplications when calculation resources are restricted, but at the end if more samples come out then came in, it boils mostly down to be a smart derivative of zero stuffing and straight convolution, tricks that may or may not result in a loss of sound quality.
It seems unlikely to me that adding a bunch of zeros is going to improve the sound quality.

Quote:
Originally Posted by Hans Polak View Post
With a 1000 point Fir and 4 times upsampling, 44e6 multiplications have to be done per second, which even a fast Intel processor can achieve.
Actually 176.4 million multiplications per second are needed when you don't use polyphase decompositions: 1000 times 4 times 44.1 kHz. Of those 176.4 million multiplications, 132.2 million will be multiplications with the stuffed zeros.
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Old 19th February 2021, 12:24 PM   #310
Hans Polak is offline Hans Polak  Netherlands
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Marcel,
Right, adding zeroís donít improve things, but it helps to understand the process, because thatís basically whatís it all about.
The execution how to do it is up to the designer and as long as no shortcuts are taken that are harmful, thatís o.k.

The solution with two Dacís and only oddís in between being processed is absolutely better as adding two time shifted samples, but it doesnít seem the best way to follow because the whole chain from beginning to end differs from the even channel adding extra noise.

We agree on the calculations: 176M-132M are exactly the 44Mflops that I mentioned.

Hans
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