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Analog Delta-Sigma interpolation DAC
Analog Delta-Sigma interpolation DAC
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Old 1st March 2021, 03:27 PM   #411
MarcelvdG is offline MarcelvdG  Netherlands
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Quote:
Originally Posted by Hans Polak View Post
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 ?
This refers to a hypothetical filter with an impulse response consisting of only three peaks, one with magnitude alpha, one with magnitude 1 and one with magnitude alpha, so it has no ringing. This hypothetical filter is only used to model the passband ripple.

Quote:
Originally Posted by Hans Polak View Post
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?
Because the cascade is still an ideal low-pass filter, and an ideal low-pass filter has a sinc impulse response.

Quote:
Originally Posted by Hans Polak View Post
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 Haykís application all samples at 2fmax are zero except one, so no ripple in the passband ?
That would be the consequence, yes. Do you see a passband ripple or only monotonic roll-off? Any signs of echoes?

Quote:
Originally Posted by Hans Polak View Post
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
Yes. I'm trying to find a relation between the pre- and post-echoes and the passband ripple without needing to assume that the filter is a cascade of a hypothetical low-pass with perfectly flat passband and a hypothetical filter that causes the passband ripple, but has perfectly equal distances between the ripples.
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Old 1st March 2021, 05:15 PM   #412
MarcelvdG is offline MarcelvdG  Netherlands
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I'm actually not sure if my third answer is correct, as I don't know what the impulse response of a cascade of Hayk's filter and an ideal filter looks like.
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Old 1st March 2021, 05:34 PM   #413
Hans Polak is offline Hans Polak  Netherlands
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If any ripple in the passband of Hayk's setup, they must be very small, at least unvisible in the image below up to 10Khz when using a Blackman Harris window.

Hans
Attached Images
File Type: jpg Pass Ripple.jpg (229.0 KB, 69 views)
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Old 1st March 2021, 07:30 PM   #414
MarcelvdG is offline MarcelvdG  Netherlands
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That could be an advantage of windowed sinc filters over Parks-McClellan filters then - although you can easily realize a filter with +/-0.000017 dB passband ripple with Jim McClellan's program.
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Old 1st March 2021, 08:46 PM   #415
Hans Polak is offline Hans Polak  Netherlands
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Thatís almost noise
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Old 1st March 2021, 11:35 PM   #416
U130421 is offline U130421  Antarctica
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While you are considering my interpolator as filter, I am trying to filter out nothing. For that, I tried the heterodyne to decrease the images 68k-88khz.
I succeeded for 20khz,
heterodyn.JPG
but for global it is not so effective, with and without.
with heterodyn.JPG
To clean up the output from spikes, I added S/H on the derivatives outputs.

Last edited by U130421; 1st March 2021 at 11:51 PM.
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Old 2nd March 2021, 06:30 AM   #417
U130421 is offline U130421  Antarctica
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I interpolate for the second time, first the data, second the delta. May be I have an error, as I get longer post ringing and rippled passband.
4os.JPG
pulse4os.JPG
Attached Files
File Type: asc sinc hamming interpolator x4 cubic spline.asc (45.5 KB, 0 views)
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Old 2nd March 2021, 07:19 AM   #418
U130421 is offline U130421  Antarctica
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I had an error.
no error.JPG
no error pulse.JPG
Attached Files
File Type: asc sinc hamming interpolator x4 cubic spline.asc (45.5 KB, 1 views)
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Old 2nd March 2021, 07:52 AM   #419
U130421 is offline U130421  Antarctica
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No doubt Blackman-Harris is by far superior.
blackman harris.JPG
Attached Files
File Type: asc sinc blackman-Harris interpolator x4 cubic spline.asc (45.5 KB, 2 views)

Last edited by U130421; 2nd March 2021 at 07:55 AM.
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Old 2nd March 2021, 09:40 AM   #420
Hans Polak is offline Hans Polak  Netherlands
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Nice result, and smart to replace the three adders at the end by one delay line plus adder at the start of the filter line.

Hans
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