A simple averaging filter is defined as yn  1

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N xn  1  ...  xn  N

This is clearly an FIR Filter.

a) Let N  4. Determine the transfer function, its zeros and poles;

b) Determine a general form for zeros and poles for any N;

c) By comparing yn and yn  1 determine a recursive implementation. Also the transfer func-

tion, together with its zeros and poles of the recursive implementation. Looking at this example, can

we say that "any" recursive filter is IIR?​