## Description

## Programming Problems (10 points)

[CO4] Q1. Let X(jω) be the Fourier transform of the signal x(t) given in Fig.2.

(a) Determine and Plot the frequency domain signal X(jω). [1 Point]

Figure 2: Q1

(b) Plot the magnitude spectrum of the frequency domain signal X(jω).[1 Point]

(c) Plot the phase spectrum of the frequency domain signal X(jω). [1 Point]

(d) Plot the inverse Fourier transform of real part of {X(jω)}. [1 Point]

ECE250: Signals and Systems

[CO4] Q2. Let x[n] be a discrete-time signal with Fourier Transform X(e

jω), which is the given Fig.3. Plot the

frequency response, magnitude spectrum and phase spectrum of w[n] = x[n]p[n], for these p[n]

Figure 3: Q2

(a) p[n] = cos(πn) [2 Points]

(b) p[n] = sin(πn/2) [2 Points]

(c) p[n] = ∑ 𝛿(𝑛 − 2𝑘)

∞

𝑘=−∞

[2 Points]