Analog Delta-Sigma interpolation DAC

[Hans Polak]

Originally Posted by MarcelvdG

I expect that the pre- and post-ringing will be determined by the filter with the narrowest bandwidth, so it will stay around 22050 Hz no matter which of the two solutions is chosen. At least with ideal filters, the two solutions would be completely equivalent.

Marcel,
Two filters in series, the second one working at twice the speed, but both having the same set of coefficients that Hayk used now.
When leaving a section signal rings at Fs/2, true ?
So the first section will ring at 22.05khz and the second at 44.1Khz.
How could this result in a combined ringing only at 22.05Khz ?

Hans

[MarcelvdG]

Because there is nothing exciting the second filter's ringing.

At the output of the first filter, you have a signal band from 0 to 22.05 kHz, from 66.15 kHz to 110.25 kHz and copies every 88.2 kHz. How is that going to excite ringing at or just above 44.1 kHz?

[kokoriantz]

Giving extra gain of 0.45% to midpoints, the 24khz image vanishes.
dissapear.JPG
I am now looking to interpolate the sinc looking only the 30 succeeding samples to avoid pre ringing.

[Hans Polak]

Originally Posted by MarcelvdG

Because there is nothing exciting the second filter's ringing?

When interpolating three points in parallel instead of one at Fs, three polyphase filters are needed.
But when using only one and placing a second identical segment working at 2Fs behind the first, there are only two filters in action.
You might be true, but I have a problem understanding how these two versions can produce the same result with only 2/3 of the amount of multiplications.

Hans

P.s. But at the end the result is in both cases that there are three interpolated points.
So your thesis can’t be that far off. Funny problem.

[Hans Polak]

Originally Posted by kokoriantz

Giving extra gain of 0.45% to midpoints, the 24khz image vanishes.
Attachment 926216
I am now looking to interpolate the sinc looking only the 30 succeeding samples to avoid pre ringing.

Wow, that’s the nicest image you have produced so far !

Hans

[MarcelvdG]

Originally Posted by Hans Polak

When interpolating three points in parallel instead of one at Fs, three polyphase filters are needed.
But when using only one and placing a second identical segment working at 2Fs behind the first, there are only two filters in action.
You might be true, but I have a problem understanding how these two versions can produce the same result with only 2/3 of the amount of multiplications.

Hans

P.s. But at the end the result is in both cases that there are three interpolated points.
So your thesis can’t be that far off. Funny problem.

Not counting the trivial filters that only delay the signal by an integer number of samples, you indeed need three versus two filters, but when the second filter in the cascade has to work at twice the speed, the number of multiplications stays roughly constant. You could get away with a shorter filter for the second stage by giving it a larger transition band, then you do reduce the required number of multiplications.

Interpolation by large factors is usually done with a chain of interpolating filters, the filters getting simpler and simpler as you go further down the chain. The last couple of stages are often CIC filters, which just have adders, subtractors and registers and no multipliers at all.

[Hans Polak]

Marcel,
Yes, with two filters in series, the second filter has to produce two interpolations versus only one for the first filter.
So in effect three convolutions have to be calculated in series between two original samples, exactly the same as with three parallel filters.
So the amount of multiplications is the same in both cases, par. or serie.

Hans

Nice trick to make filters simpler down the chain.

[kokoriantz]

I found an alternative sinc interpolation that doesn't have ringings.
modif sinc.JPG
The formula is too complicated for me to understand.
modified sinc.JPG
Interpolation: Find good approximation from given samples
I will try to decipher by trial and error, or may be my son (PhD), too busy, can do it.

[Hans Polak]

Interesting, never seen this before in a DAC.
Let your son pay attention, I'll do the same.
Anxious to see what the FFT of this impulse response will show.

Hans