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Solve the following fourier using
written 5.3 years ago by | • modified 5.3 years ago |
Subject : Signals & Systems
Topic :Fourier Series.
Difficulty: Medium
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written 5.3 years ago by | • modified 5.3 years ago |
Subject : Signals & Systems
Topic :Fourier Series.
Difficulty: Medium
written 5.3 years ago by |
Given: x[n] = (1/3)^n u[n]
h[n] = (1/2)^n u[n]
Therefore, y[n] = x[n]*h[n] ------------ 1
y[n] = ∑_(k= -∞)^∞〖x[k] h[n-k]〗 -------------- 2
Using the formula, ∑_(k= 0)^N〖 a^k= (1-a^(N+1))/(1-a) 〗
y[n] = (1/2)^n (1-(2/3)^(n+1))/(1- 2/3)
∴y[n] =〖3(1/2)〗^n [1- (2/3)^(n+1)]