Determine the frequency response of the following causal IIR LTIsystem, where |a| < 1
y[n] = x[n] + a * y[n-L]
Determine the maximum and minimum values of the magnitude response.How many peaks occur in the magnitude response in the frequencyrange from zero to 2π? What are the locations of the peak and dips?
Convert to the z - domain and find transfer function H(z) =Y(z)/X(z)
y(z) = x(z) + a * y(z) * z-L so H(z) = 1 /(1 - a * z-L)
The frequency response H(ejw) = 1 / ( 1 - a *e-jwL)