Question

Prove that x[n]*h[n]=h[n]*x[n] where * reprsents the convolution opertaion

Answer 1

4 Convolution
Recommended
Problems
P4.1
This problem is a simple example of the use of superposition. Suppose that a dis-
crete-time linear system has outputs y[n] for the given inputs x[n] as shown in Fig-
ure P4.1-1.
Input x[n] Outputy [n]
III xn] yi[n]
0 0 n 0 n
-1 0 1 2 -2 -1 0 1 2
x2[n] 1 2[n]
0 0 n 0 0 n -1 0 1 2 3 -1 0 1 2 3
2 1
1 X3 [n] y3[n]
.-. n -n
-1 0 1 2 3 -1 0 1 2
Figure P4.1-1
Determine the response y4 [n] when the input is as shown in Figure P4.1-2.
I x4[n]
-1 012 0 2 3
-1
Figure P4.1-2
(a) Express x 4[n] as a linear combination of x 1[n], x 2[n], and x 3[n].
(b) Using the fact that the system is linear, determine y 4[n], the response to x 4[n].
(c) From the input-outpu