Signal Processing

Part 1: Implementing Convolution Function From Scratch

Here is a plot of the result of the convolution between x and y with both the built-in and Scratch functions.

$x = [2,-2,7,-3,2,4,-6,1]$

$y = [5,2,4,-6,5,1,-8,0,7,2,9]$

Part 2: Analysis of an LTI System

Adding Noise and Echo to a Reading of Persian Poetry.

Sampling

This Audio was read at 44,100Hz using imread( ) function. The plot below represents the audio signal with respect to time.

Adding Echo

In order to create an echo effect, a new signal is defined as follows.

$y[n] = x[n] + \alpha x[n-n_0]$

For a desired 1-second delay, we set the delay parameter as $n_0 = F_s = 44100$, and the attenuation factor as $\alpha = 0.9$, ensuring that the echo signal retains 81% of the energy present in the original signal.

Below is a plot showing the echo signal.

Adding Noise

The noisy signal is generated by adding the echo signal to a noise signal, where the noise has a maximum amplitude of 10% of the maximum amplitude of the echo signal. The noise is generated using the randn( ) function.

Below is a plot showing the noisy signal.

Course Description

• Course: Signals and Systems [ECE 538]
• Semester: Spring 2022
• Institution: School of Electrical & Computer Engineering, College of Engineering, University of Tehran
• Instructor: Dr. Akhavan
• Contributors: Fardin Abbasi, Iman Rasouli-Parto, Parsa Sattari