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# Answer to Question #281799 in Electrical Engineering for Mig

Question #281799
Find the impulse response h[n] for a causal LTI discrete-time systems satisfying the given
difference equations and indicate whether the system is a FIR or an IIR system.
y[n] = x[n] + 1/2 x[n - 1] + 2x [n - 2] + 4x[n - 3] - x[n - 5]
1
Expert's answer
2021-12-22T12:01:02-0500
close all,
clear all,
clc,
%y[n] = x[n] + 1/2 x[n - 1] + 2x [n - 2] + 4x[n - 3] - x[n - 5]
y=[];
x=0:1:10;
for n=1:1:length(x)
if(n<6),
y(n)=0;
else
y(n) =  x(n) + (1/2)*x(n-1) + 2*x(n-2) + 4*x(n-3) - x(n-5);
end
end
scrsz = get(0,'ScreenSize');
Dim=0;
figure('Position',[scrsz(1)+Dim, scrsz(2)+Dim,scrsz(3)-20,scrsz(4)-100]);
subplot(1,2,1);
plot(x,y);
grid on,
xlabel('--- x --->');
ylabel('y[n] = x[n] + 1/2 x[n - 1] + 2x [n - 2] + 4x[n - 3] - x[n - 5]');
title('Plot: y[n] = x[n] + 1/2 x[n - 1] + 2x [n - 2] + 4x[n - 3] - x[n - 5]','FontSize',20);

subplot(1,2,2);
impz(y);
grid on,



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