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Noise aliasing with CIC filter

Started by flutekick 5 years ago3 replieslatest reply 5 years ago595 views

Hi,

Would the amount of noise aliasing/folding back into signal band change as we change decimation ratio of the CIC filter. (Assume the input has white noise)

In other words, is the area under curve of CIC filter response which would fold back after decimation same for different decimation ratios?

Thanks,

Krishna

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Reply by lishalironOctober 19, 2017
Increasing the number of stages improves the alias rejection, meaning, enhancing the NULLs area, and increases the pass-band droop.

The NULL areas is computed with 

H(z)=|sin(pi*L*f)/sin(pi*f/N)|^k ~ |LN*sin(pi*L*f)/pi*L*f|^k 

(for 0=<f=<1/L)

You'll have a null in each multiply of f=1/L while L is the diff. delay.

Check out Hogenauer's article, "Economical Class of Digital Filters for Decimation and Interpolation", for more useful information about the CIC parameters.

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Reply by Tim WescottOctober 19, 2017

I'm not entirely sure what you're trying to say here, because with a constant input sample rate, changing the decimation ratio changes the output sampling rate.  (Or visa-versa, for a constant output sampling rate).

For an N-stage CIC filter, the slope of the amplitude response coming out of the null will always be N*20dB/decade with respect to the difference frequency (meaning, it'll be proportional to \(\left(f-f_0\right)^{-N}\)).

I would suggest doing the math.  Feel free to ask for help if it confounds you.

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Reply by andrewstanfordjasonOctober 19, 2017

I wrote a quick and dirty numerical test, cic python, i get:

Decimation ratio: 2 SNR: 7.65218361275dB

Decimation ratio: 3 SNR: 4.10244607988dB

Decimation ratio: 4 SNR: 2.32488423661dB

Decimation ratio: 5 SNR: 1.17873242654dB

Decimation ratio: 6 SNR: 0.342327100825dB

Decimation ratio: 7 SNR: -0.284212311663dB

where the SNR is the ratio of sum of pass band to the sum of the stop band. Excuse mistakes, but it seems to me the answer is: yes.