ECE250: Signals and Systems Assignment 3

Description

Programming Problems (10 points)
[CO3] Q1.
1. Given a discrete-time signal x[n]:
[6 Points]
𝑥[𝑛] = {
1 𝑓𝑜𝑟 − 𝑁1 ≤ 𝑛 ≤ 𝑁1, 𝑁1 = 2
0 𝑓𝑜𝑟 𝑁1 < |𝑛| ≤
(N−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 + π, -π ≤ x < π
f(x + 2π) = f(x)
(a) Sketch the graph of f(x) for three periods.
(b) Find the Fourier series of f(x) on the interval −π < x < π.
Hint: To simulate continuous signals use appropriate discretization (wherever required).