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ECE250 Signals and Systems Assignment 3 solved

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Programming Problems (10 points)

[CO3] Q1.
1. Given a discrete-time signal x[n]:
[6 Points]
π‘₯[𝑛] = {
1 π‘“π‘œπ‘Ÿ βˆ’ 𝑁1 ≀ 𝑛 ≀ 𝑁1, 𝑁1 = 2
0 π‘“π‘œπ‘Ÿ 𝑁1 < |𝑛| ≀
(Nβˆ’1)
2
Compute the Fourier series for the following cases and give the inference.
(a) N =4N1 + 1
(b) N =8N1 + 1
(c) N =10N1 + 1
[CO3] Q2. A periodic function is defined by:
[4 Points]
f(x) = x + Ο€, -Ο€ ≀ x < Ο€
f(x + 2Ο€) = f(x)
(a) Sketch the graph of f(x) for three periods.
(b) Find the Fourier series of f(x) on the interval βˆ’Ο€ < x < Ο€.
Hint: To simulate continuous signals use appropriate discretization (wherever required).