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Analog Delta-Sigma interpolation DAC
Analog Delta-Sigma interpolation DAC
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Old 28th February 2021, 06:08 AM   #401
U130421 is offline U130421  Antarctica
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20 samples didn't make anything better, the image is at -28db. It looks the 30 samples is the best.
20samples.JPG
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Old 28th February 2021, 06:40 AM   #402
Hans Polak is offline Hans Polak  Netherlands
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With 30 point plus sophisticated post interpolation you have found a very nice optimum.
You canít escape physics, when you improve on one aspect, you wil lose somewhere else.

Hans
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Old 28th February 2021, 10:32 AM   #403
U130421 is offline U130421  Antarctica
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I will try to interpolate the midpoints of the derivatives, by this the sinc ringingings get subjected to delta sigma filter. After all I am interpolating the cubic spline of the derivatives and no more that of the data.
I will also use the heterodyne to add instead of filtering the 68k-88khz images.
There is still lot to do.
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Old 28th February 2021, 12:49 PM   #404
Hans Polak is offline Hans Polak  Netherlands
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I tried a 36point Blackman Harris window while not using the outer 4 points because they were practically zero, so filter length stayed still the same as before.
Below, at the left Blackman Harris in Red t and the Hamming with 0,45% gain at the right in Blue.

FR is now a bit smoother around 20Khz, but stopband is much deeper that the Hamming window with 0,45% gain.
Suppression at 24.1Khz is a bit less, but to be realistic, at this frequency the spectral content of music is quite a bit lower, see second image.

Hans
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File Type: jpg Blackman Harris.jpg (586.4 KB, 69 views)
File Type: jpg Frequency content.jpg (283.7 KB, 69 views)
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Old 28th February 2021, 06:11 PM   #405
Hans Polak is offline Hans Polak  Netherlands
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Correction: I did discard the 6 outer point, not 4.
They were resp 0,00000, 0,00002 and -0,00008.
So not really much lost.

Hans
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Old 28th February 2021, 10:16 PM   #406
U130421 is offline U130421  Antarctica
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Is this the formula you used?
bh.JPG
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Old 1st March 2021, 03:16 AM   #407
U130421 is offline U130421  Antarctica
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I am now interpolating the delta. It gets -3db at 20khz instead of -1.2db, but the transient is faster.
delta vs data.JPG
Attached Images
File Type: jpg impulse diffe.JPG (76.0 KB, 63 views)
File Type: jpg deta spec.JPG (112.3 KB, 60 views)
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File Type: asc sinc hamming delta interpolator cubic spline.asc (50.2 KB, 0 views)
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Old 1st March 2021, 06:05 AM   #408
MarcelvdG is offline MarcelvdG  Netherlands
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An advantage that very short filters, very long filters and minimum-phase filters have in common is their reduction of the passband-ripple-related pre-echo. That's something else than the ultrasonic pre-ringing. Using very short filters reduces the time between the pre-echo and the main signal, very long filters reduce the level of the pre-echo and minimum-phase filters simply haven't got a pre-echo. See the attachment for an explanation about the relation between passband ripple and pre-echo.
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File Type: pdf preechoes.pdf (85.4 KB, 10 views)
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Old 1st March 2021, 08:19 AM   #409
Hans Polak is offline Hans Polak  Netherlands
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Quote:
Originally Posted by kokoriantz View Post
Is this the formula you used?
Attachment 927313
That's the one, although my formula had N instead of N-1.
Here are the values that I used:

0.63382, -0.20393, 0.11397, -0.07312, 0.04922, -0.03352, 0.02267, -0.01505
0.00970, -0.00603, 0.00359, -0,00202, 0.00106, -0.00051, 0.00022

And I discarded the last three -0.00008, 0.00002, -0.00000.

Hans
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Old 1st March 2021, 10:34 AM   #410
Hans Polak is offline Hans Polak  Netherlands
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Quote:
Originally Posted by MarcelvdG View Post
An advantage that very short filters, very long filters and minimum-phase filters have in common is their reduction of the passband-ripple-related pre-echo. That's something else than the ultrasonic pre-ringing. Using very short filters reduces the time between the pre-echo and the main signal, very long filters reduce the level of the pre-echo and minimum-phase filters simply haven't got a pre-echo. See the attachment for an explanation about the relation between passband ripple and pre-echo.
Marcel,
Interesting paper, but it produces more questions than answers.

1. A filter with an impulse response consisting of a pre-echo, a main response and a post-echo produces exactly this kind of equidistant ripple response.
That is, when the echoes occur a time T before and after the main signal and have a magnitude α.


This pre- and post-echo definition here is here confusing.
At some places it looks as if echo is referring to pre- and post-ringing. At other places it almost seems as if he is referring with this echo to the ripple in the pass band.
And what exactly is the parameter α, is this the magnitude of the ripple in the passband or from the pre- and post-ringing, or is it even the deviation from the zero crossing points in the impulse response ?
If from post- and pre-ringing, how does one define the magnitude α of a decaying signal ?


2. Cascade the filter under test with an ideal continuous-time low-pass filter with cut-off frequency fmax.
As we are interested in what happens below fmax, this doesn't affect the part of interest.
When the passband is perfectly flat, the impulse response of the combined filter now has a sin(2πfmaxt)/(2πfmaxt) shape.


An ideal continuous-time low-pass filter with cut-off frequency fmax, already has a sin(2πfmaxt)/(2πfmaxt) shape.
So why should the cascade of filters now also have this shape?



3. Sample the impulse response of the combined filter with a sample rate of 2 fmax and ensure that the samples fall on the zero crossings of the sin(2πfmaxt)/(2πfmaxt) function.
Ideally, this produces only one nonzero sample, the one related to the main response.
Any other peaks or sin(x)/x shaped ripples are due to the imperfect passband response of the filter under test.


In Hayk’s application all samples at 2fmax are zero except one, so no ripple in the passband ?


4. Step 1 can be done mathematically by calculating the convolution of the impulse responses of the filter under test and the ideal filter. .

The convolution of the step response of both cascaded filters boils down to cut off everything from the filter under test above fmax in the frequency domain
When doing an IFFT of the cascaded FR, we get a somewhat modified impulse response.
By looking at distances 1/2fmax, the deviations from zero are now supposed to have a direct relation to the ripple in the passband, is that what is meant here ?
If so, a rather confusing route IMO was taken to get to this point.

Hans

Last edited by Hans Polak; 1st March 2021 at 10:40 AM.
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