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Decimator Design for sigma delta converter

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steadymind

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i am trying to design a decimator for sigma delta converter for audio. my decimation factor is 128. from material i found i decided on a CIC filter for first stage (decimation of 64) and a half band FIR as second.

so the CIC filter has 3 parameters - decimation factor , no of delay elements and the number of sections. i know the decimation factor but how do i determine number of differential delay elements and the number of stages.

sampling freq = 5.6448M , fin = 0-20khz, how do i design the filter to get me 80dB of stop band attenuation ?
 

You didn't tell the intended pass band characteristic and stop band cut-off frequency. If you mean a steep cut-off beyond 22 kHz, it won't work without a high order FIR filter. Both CIC and halfband or rather smooth filters. Often a FIR compensation filter is applied to achieve a more "rectangular" frequency characteristic.

CIC frequency characteristic can be easily calculated, because it's simply (sin(x)/x)^n.
 

FvM said:
You didn't tell the intended pass band characteristic and stop band cut-off frequency. If you mean a steep cut-off beyond 22 kHz, it won't work without a high order FIR filter. Both CIC and halfband or rather smooth filters. Often a FIR compensation filter is applied to achieve a more "rectangular" frequency characteristic.
Click to expand...

the pass band is 0-20KHz, and the stop band for the first CIC filter to be at 66KHz, to allow for decimation factor of 64 and intermediate sampling freq of 88kHz . is this correct ? i would try to implement a FIR to get a more rectangular repsonse.

CIC frequency characteristic can be easily calculated, because it's simply (sin(x)/x)^n.
Click to expand...

is n in (sin(x)/x)^n the order of the sinc filter. is the order same as the number of stages in CIC filter ?
 

Yes in sin(x)/x raised n, n is the number of stages. This corresponds to the operation principle of CIC decimator. 1st order CIC is a simple boxcar averager, having the well-known sin(x)/x frequency characteristic.
 
@wonbef

can u explain ur statement or point me to some reference for this
 

I think, that you can answer the question yourself. Besides frequency decimation, that can be achieved by a first order CIC, the main purpose of a decimation filter is attenuation of aliasing signal components. By defining a cut-off frequency and a stop band attenuation, you get the required filter order. It's discussed in Hogenauers classical paper An economical class of digital filters for decimation and interpolation and many text books, e.g. U. Meyer-Baese DSP with FPGA.
 

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