Question

Design a multirate system that converts a 300 Hz sinusoid sampled at 1000 samples/second to 450 Hz sinusoid without any aliasing.

Answer 1

So the amount by which the frequency has to be changed

This means we have to upsample by L = 9 and the downsample by M = 20. The clock diagram will be

To avoid aliasing

The filter is a low pass filter with a cut off frequency of

So the filter H(z) is a low pass filter with a cut off frequency of rad/sample

The magnitude of the filter should be L in the pass band.

So the filter frequency response will be

This filter can be IIR or FIR

Let us design a FIR filter of order 7

Using MATLAB

W = hamming(7);
b = 9*fir1(6,1/20,W)

This will give a filter as