Optimal FIR filter into Analog (IIR) filter for SDM

[ahmad.mar]

Hi all,

for my sigma delta modulator I have a mathematically optimized filter impulse response (of finite length), which I need to implement as an analog filter
from system point of view it could be directly implemented as an FIR filter, but since the number of taps is relatively large (~100) that does not make a lot of sense.

do you know any way to match the optimized response into any regular analog (active) filter e.g. Butterworth or SC-filter

I tried to convert this response into the frequency domain (which has a low-pass characteristics), and then design a filter that matches the same specifications
but that does not bring the same performance

your help or comment is highly appreciated

 

[FvM]

The question doesn't seem to make much sense. An important advantage of the oversampling involved with SDM ADC and DAC is to avoid high order analog filters and perform all precise filtering in the digital domain. You might want to explain your considerations.

 

[ahmad.mar]

thanks for your comment,..
well what is intended is to build a SDM DAC, so the filtering is needed in the analog domain ...
The high number of taps for the FIR comes from the optimization study, and represents the number of samples for sdm (OSR).
but still the optimized response represents characteristics similar to a third order low pass , so the filter does not need to be of a high order

 

[FvM]

In this case, instead of thinking in FIR terms, why don't you simply consider the analog filter specification (cut-off frequency, maximum pass-band error/ripple, stop band frequency, required stop band attenuation). It will lead you directly to a filter design. An "optimal" filter approach might end up in a Chebyshev prototype, usually people try to get along with more simple filter designs, may be passive RC ones.

 

[ahmad.mar]

sorry, one more additional info is about the "optimal" filter. the impulse response for that filter is obtained through a mathematical optimization of the filter response for a defined number of samples, which is the period for the SDM as an incremental modulator, after which a rest for the whole DAC is taking place.

so, I do not see a direct approach to get the analog filter specifications as you mentioned, and that is my main issue here!

 

[FvM]

The simple idea is that the SDM DAC reconstruction filter has no effect in the signal passband, possibly except for a small amplitude droop to be corrected in the digital domain. If your design requires a higher order filter, than a Bessel filter might be appropriate. Review Chapter 12 Analog Circuit Design for DS DACs in Norsworthy/Schreier/Temes Delta-Sigma Converters, Theory, Design and Applications.

If you have have strict requirements about the phase respectively time domain response, you can still compensate the exact filter transfer function on the digital side.