Question

For the causal filter below x(п) y(n) -2j0 1 -0.8e 2j0 Write the difference equation(show the equation clearly and define coefficients) а. b. Give and plot the frequency response magnitude (show the equation clearly) Compute and plot the impulse response using MATLAB Use MATLAB to determine steady state response due to x(n)=u(n) c. d. Write a MATLAB program to compute and plot the frequency response of the overall system. Give plots in dB and the program e.

Answer 1

(ulK e -2Jn 23n 1-082 Hite Let Hle) H(e). H2le Hledn) Hle 1-8 C23 1n 2 domain put e 2Jn J2 1 H12) 1 82 Hence Ye)2thens for m of Nh) X2) 2 tans form of h YR-HI2) X(2) (27 inverse ztans form

b 1-823n Hed))megnitude 11-8 2304) Hie)) /LCost2 sin2.a) 2 1- 1-64 1-6 Cos(2)

(C) impulse response

Commands >> n I-2:15]; >> x= (n0);%impulse input >> b= [1];a= [1 0 -0.8]; h=filter (b,a,x) ;%impulse response >> stem (n,h); » xlabel('n') ;ylabel('h'); >>

Show Data Cursor Figure 1: xlabel('n'),ylabel ('h); 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -2 2 10 12 14 16 Co st
(d)

Files MATLAB Drive impuls2.m 1 n [0:50] 2 x-1.*(n>-0);%input b-[1] a= [1 0 -0.8]; 4 y=filter(b,a, x); 5 stem (n, y); 6

from plot steady state response is 5

Show Data Cursor Figure 1: impuls2 5 4.5 4 3.5 2.5 2 1,5 10 0.5 50 40 45 35 30 25 20 10 15 5 0