Please help me with this FIR filter problem a Consider the 7

Please help me with this FIR filter problem

(a) Consider the 7-point FIR filter: h_1[n] = {1.25,0.5, -2.1,0, -2.1, 0.5,1.25} (i) Sketch the impulse response, and determine if the filter is linear-phase. If so, which category of linear-phase FIR filters does it correspond to (Type 1-4)? (ii) Sketch the direct form and transpose filter structures for h_1[n]. (iii) Based on your answer to part (i), exploit symmetry to reduce the number of multiplier elements in the structure. (iv) Draw a cascade-filter structure for h_1[n] consisting of three first/second-order sections. To factorize H_1(z), you may use the roots command in MATLAB. (b) Now consider the 6-point FIR filter: h_2[n] = { 1, - 2,3, - 3,2, - 1 } Repeat steps (i)-(iv) from part (a).

Solution

clear all;

close all;

%x=[1 2 3 4]

x=input(\'enter the input sequence\');

n=input(\'enter the lenth of DFT\');

subplot(4,1,1);

stem(x);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'input signal\');

y=fft(x,n);

subplot(4,1,2);

stem(y);

xlabel(\'frequency\');

ylabel(\'amplitude\');

title(\'discrete fourier transform\');

z=abs(y);

subplot(4,1,3);

stem(z);

xlabel(\'frequency\');

ylabel(\'magnitude\');

u=angle(y);

subplot(4,1,4);

stem(u);

xlabel(\'frequency\');

ylabel(\'phase plot\');

gtext(\'kl university\')

output :

enter the input sequence[1 2 3 4]

enter the lenth of DFT16