The impulse response of a linear phase FIR and LTI system is given as h(n)={1, -1/2, 2, -1/2, 1}. a) Calculate the frequency response of the system with DFT. Give the amplitude and phase responses and the group delay.
The impulse response of a linear phase FIR and LTI system is given as h(n)={1, -1/2, 2, -1/2, 1}.
a) Calculate the frequency response of the system with DFT. Give the amplitude and phase responses and the group delay.
b) Let h'(n)={1, -1/2, 2, -1/2, 1, 0} be the periodic form of h(n) with N=6. Give the DFS coefficients of h'(n). Compare the computational load for DFT and FFT algorithms. (The calculation load for DFT is N2,
For FFT, N is calculated as log2 N)
c) The input sign x(n)={1, 2} is applied to the system in (a). Calculate the 5-point circular convolution of x(n) and h(n) in the time or frequency domain: c(n) = x(n) *5 h(n)
d) Now calculate the output y(n) of the system first by linear convolution: y1(n) = x(n) * h(n), then by circular convolution of 6 points, in the time or frequency domain: y2(n) = x(n) *6 h(n). Compare the results.
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