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Analog Delta-Sigma interpolation DAC
Analog Delta-Sigma interpolation DAC
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Old 18th February 2021, 08:28 AM   #291
Hans Polak is offline Hans Polak  Netherlands
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Quote:
Originally Posted by kokoriantz View Post
The FIR filter after zeros added , cuts above what frequency?
My 512 point Fir filter was a low pass filter with a transition band from 20Khz to 22.05Khz.

Hans
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Old 18th February 2021, 09:05 AM   #292
Hans Polak is offline Hans Polak  Netherlands
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I also did the test with the two time shifted sample streams, because I had my doubts about the removed first mirror at 24.1Khz, and indeed, it's not the case.

See image below of two added samples time shifted 10usec sampled at 50Khz.
The 30Khz first image is still there, alive and kicking.

If you prefer, I could repeat this with 44.1k instead of 50K.

Hans
.
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File Type: jpg Two Shifted.jpg (412.1 KB, 51 views)
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Old 18th February 2021, 10:04 AM   #293
Hans Polak is offline Hans Polak  Netherlands
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I tried to fit a Sinc envelope around the two time shifted signals.
On one hand the original one at Fs 50Khz should still be there and at the same time since the sample width has halved, a Sinc with it's first zero at 100Khz was expected.

Well, it seems to be a bit of both, as becomes clear in the image below for the two 10usec time shifted and added samples.
The Sinc with it's first zero at 50kHz touches the spectrum at 20K, 80K, 120K, 180K etc, while the Sinc with it's first zero at 100Khz, touches at 30k, 70K, 130K, 170K etc.
A very complex envelope !

The right image is for exactly the same sample but now on it's own without a second time shifted sample.
In this case the Sinc with its first zero at 50Khz fits perfectly.

Hans
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File Type: jpg Two Shifted1 sinc.jpg (499.6 KB, 46 views)

Last edited by Hans Polak; 18th February 2021 at 10:06 AM.
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Old 18th February 2021, 10:28 AM   #294
U130421 is offline U130421  Antarctica
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I am referring to post 258 non oversampling dac to be a hoax that they could by two DACs shift the 24khz image to much higher frequencies. Your way is always by filtering the image 30khz by a brick wall and not by shifting.
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Old 18th February 2021, 11:16 AM   #295
U130421 is offline U130421  Antarctica
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I am looking a way to interpolate digitally the midpoint between two samples by sinc/Hamming window. for 20khz, I have 10 cycles for 1 beat 2khz, as each cycle is 3 samples, I need 30 samples to interpolate the midpoints. It will output a true 2xoversampled. Explained here http://www.audiomisc.co.uk/ArchiveMa...Upsampling.pdf
As sinc function is symmetrical, I need 15 constants representing sinx/x * Hamming variable to apply on each sample and sum to obtain the value of the midpoint. Maybe such interpolator does already exist.

Last edited by U130421; 18th February 2021 at 11:22 AM.
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Old 18th February 2021, 12:13 PM   #296
Hans Polak is offline Hans Polak  Netherlands
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Quote:
Originally Posted by kokoriantz View Post
I am referring to post 258 non oversampling dac to be a hoax that they could by two DACs shift the 24khz image to much higher frequencies.
Yes, I agree. For shifting a frequency you will need a multiplier and not an adder.

Hans
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Old 18th February 2021, 01:18 PM   #297
Hans Polak is offline Hans Polak  Netherlands
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Iíll have to read the article, but sinc convolution in the time domain is the same as brick wall in the frequency domain.
In fact what I saw in a quick glimpse is exacly like the Fir filter that I used.
But I increased Fs a factor 4.

Hans
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Old 18th February 2021, 01:40 PM   #298
Hans Polak is offline Hans Polak  Netherlands
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Here are at the left the filter coefficients of my FIR, and when taking it's FFT , you get the FR.

Hans

P.S. I used two in series to get twice the damping.
Not the best way, but good enough for the test.
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File Type: jpg Fir Filter.jpg (337.4 KB, 41 views)

Last edited by Hans Polak; 18th February 2021 at 01:44 PM.
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Old 18th February 2021, 03:27 PM   #299
MarcelvdG is offline MarcelvdG  Netherlands
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Join Date: Mar 2003
Location: Haarlem, the Netherlands
Quote:
Originally Posted by kokoriantz View Post
I am looking a way to interpolate digitally the midpoint between two samples by sinc/Hamming window. for 20khz, I have 10 cycles for 1 beat 2khz, as each cycle is 3 samples, I need 30 samples to interpolate the midpoints. It will output a true 2xoversampled. Explained here http://www.audiomisc.co.uk/ArchiveMa...Upsampling.pdf
As sinc function is symmetrical, I need 15 constants representing sinx/x * Hamming variable to apply on each sample and sum to obtain the value of the midpoint. Maybe such interpolator does already exist.
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.
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Old 18th February 2021, 03:51 PM   #300
Hans Polak is offline Hans Polak  Netherlands
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Yes, Marcel you ate right.
The guy inserted one zero after each sample instead of the three that I did.
For some strange reason he did not mention this zero stuffing.
So indeed, it is exactly what I did in the previous simulations.

How to find the coefficients for your FIR filter is up to the designer, but it has to be long enough and the calculation has to be accurate.
What I mentioned earlier is that you will need a fast DSP to do the math.

Hans
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