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3. find the transferfunction gz of the fir filter yn ...

# Question: find the transferfunction gz of the fir filter yn ...

###### Question details

Find the transfer-function G(z) of the FIR filter

y[n] = (1/(M+1))Sum x[n-1] where sum is the sum from i=0 to M

Obtain its zeros and frequency response. You may use the fact that if |x|<1 then

SUMx^j = (1-x^(M+1))/(1-x) sum from j=0 to M

A comb filter is formed by taking the z transfer-function of the FIR filter of the above equation and replacing z by z^H, where H is a positive integer. Find the transfer-function, zeros and frequency response of this filter.

Give a clearly labelled sketch of the filter in the case of M=3 and H=3