H,(2) Fourier Series (FS) is one of the design method of FIR filters. It can be summarized as follows: a) Sketch the ideal frequency response required H, (2). -2c Where, i denotes of ideal. b) Find the impulse response of the filter hi[n]. Proof that : h_i [n] = 2fe sinc(2f. n) c) Truncate the impulse response ( hi[n] ) to be from -N:N. That is the filter will be length finite (2N+1 samples). Denote the new impulse response by ht [n], where t denotes of truncated. d) Shift ht[n] by N samples. State why?. Denote the new impulse response by ht s[n] where, t_s denotes for truncation and shift. e) Find the frequency response H, ,2) corresponding to ht s[n]. f) Increase N until having the required specification. Apply the above steps to design a FIR low-pass filter with cut-off frequency Qc=0.4r. Write a Matlab program to : a) Sketch hi [n] versus n. Select a proper range of n. b) Sketch ht [n] versus n With N =3 c) Find and sketch the magnitude and phase of Hi(2). d) Sketch ht s [n]= ht [n-N] versus n. e) Find and sketch the magnitude and phase of Ht s (2). State the effect on the shift process on both the magnitude and phase characteristics. f) Sketch H s(N) versus 2 for N=3, 7, and 9 on the same graph. Write your comments. g) Modify he s [n] to perform as a high pass filter. h) Repeat step (f) for the case of high pass filter.