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18th February 2021, 08:35 PM  #301  
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Quote:
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. 

18th February 2021, 08:44 PM  #302 
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Join Date: Mar 2005
Location: Blaricum

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. 
18th February 2021, 08:51 PM  #303 
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Another one with Kaiser window.
Windowed Sinc Interpolation  Physical Audio Signal Processing 
18th February 2021, 10:10 PM  #304 
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Join Date: Mar 2003
Location: Haarlem, the Netherlands

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 32tap 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 lowpass 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. 
18th February 2021, 10:40 PM  #305 
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Location: Haarlem, the Netherlands

Regarding ParksMcClellan, all design methods for linearphase FIR lowpass filters lead to some finitelength approximation of a sinc. The ParksMcClellan approximation leads to an equiripple frequency response in the pass and the stop band.
As an example, attached is the impulse response of a 128tap ParksMcClellan 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. 
19th February 2021, 06:08 AM  #306 
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Location: Haarlem, the Netherlands

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 nonoversampling DAC without steep analogue filter.

19th February 2021, 08:55 AM  #307 
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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 DAC’s having all sorts of different filters, and DSP’s or FGPA’s 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 ?? 
19th February 2021, 10:10 AM  #308 
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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 . 
19th February 2021, 10:36 AM  #309  
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Quote:
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. 

19th February 2021, 12:24 PM  #310 
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Marcel,
Right, adding zero’s don’t improve things, but it helps to understand the process, because that’s basically what’s 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, that’s o.k. The solution with two Dac’s and only odd’s in between being processed is absolutely better as adding two time shifted samples, but it doesn’t 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: 176M132M are exactly the 44Mflops that I mentioned. Hans 
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