ASN10 - Frequency response of low pass filters
Problem Statement
Use Octave (or Mathlab or Silab) to plot the frequency response of low pass filters with cut off frequencies of 1/32T, 1/8T, and 1/4T and compare how many coeffficients are needed with an eye to answer the question “Is it less calculation to decimate and then filter, or better to put the filter in the pre-decimation filter?”
Response
In octave I creating various plots of frequency responses varying cutoff frequency 1/4T, 1/8T, 1/32T, and number of filter coefficients 10 and 100. Analyzing the plots, my answer to the question is that it is better to decimate then apply the filter. Below I have posted two images to support my answer. The first image frequency response cutoff frequency is 1/4T with 100 filter coefficients and the second image coefficents are reduced to 10. The Third image frequency response cutoff frequency 1/32T with 10 filter coefficients. The frequency response of Image 1 is well defined and with slighlty less noise compared to Image 2. With frequency of 1/4T the number of coefficients are not as crucial as compared to having a faster frequency. For instance, the response of Image 3 with cutoff at 1/32T has a much larger signal to noise ratio and is obvious that more filter coefficients are needed to reduce noise.
