Question

CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is x(n) = (0.95)u(n), calculate an expression for y(n) analytically and plot it for 0 <n<99. (b) If the input to the system is x(n) = u(n), calculate an expression for y(n) analytically and plot it for 0 <n< 99. (c) Is this system BIBO stable?

Answer 1

4)

4) fon)= [2 3 a Hmuiin) - uCO2) = [1] y (n) = [1 3 3

MATLAB script:

clc;close all;clear all;

n1=0:1:2;

h=[1 2 1];%Impulse response

n2=0:1:10;

x=(n2>=0)-(n2>=2);%Input

m=min(n1)+min(n2):1:max(n1)+max(n2);

y=conv(x,h);%output

figure;

stem(m,y);xlabel('n');ylabel('y(n)');title('y(n) =x(n)*h(n)');grid;ylim([0,5])

y(n) =x(n)*h(n) y(n) 1 2 4 6 8 10

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5)

© (0.95) a) Xeo)=6.95) "uLs) ; hosszucs) yo = 3x) Ren_c) - K 20 KEconti For nzo . yen = 6-60.95) = 2001–0.9560.95)) T-0.95 yen 120 - 1960.95)"7ues) e C9zuch) ; RCD) z ucs) y cm = ☆ Coci) = nil for nzo - I yen) = 6+1) un

y(n) =20-(19(0.95)) magaseemaDEPARRIERSPORT TRENDEDEOman y(n) ABOARDA00000 "0 20 4 0 60 80 100

001 08 09 0 0 OZ EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE y(n) (u)n(I+4)= (u)A

c)

No.the system is unstable

sum of the absolute value of the impulse response = infinity.

Hence the system is not BIBO stable.