H,(2) Fourier Series (FS) is one of the design method of FIR filters. It can be...

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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. 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.

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