Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Time-domain Analysis
h[n]=1.5 h[n-1] -0.85 h[n-2] + δ[n]
Let n=0, 1, 2, 3,…
h[0]=0-0+1=1
h[1]=1.5 ´1-0 -0=1.5
h[2]=1.5´1.5-0.85´1+0=1.4
h[3]=1.5´1.4-0.85´1.5+0 =0.825
...
Therefore, the impulse response h[n]=[1, 1.5, 1.4, 0.825, …].
↑
Generally for the difference equation:
y[ n]
= a1 y[
n −1]
+ a2
y[
n − 2] + a3
y[
n − 3] + ... + b1
x[
n −1]
+ b2
x[
n − 2] + b3
x[
n − 3] + ...
The impulse response can evaluated by the special equation with the simple unit impulse input:
h[ n]
= a1 h[
n −1]
+ a2h[
n − 2] + ... + b1d [ n −1]
+ b2d[
n − 2] + ...
(3.10)
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