Lab 4
Convolution of Discrete-Time Sequences
Submitted By: Muhammad Maab Nawaz
FA21-EEE-021
Submitted To: Dr Fawad Zaman
Submission Date: 23/09/2023
In Lab (4)
Post Lab (6)
Total (10)
Data Presentation
Data Analysis
Writing Style
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Lab 4: Convolution of Discrete-Time Sequences - Signal Processing and Filtering, Schemes and Mind Maps of Mathematics
A lab report on the topic of convolution of discrete-time sequences in the context of signal processing and filtering. The report covers the concepts of even and odd components, convolution, and its applications in filtering, system analysis, image processing, and machine learning. Matlab code snippets and explanations for decomposing sequences and convolving sequences with negative time values.
Typology: Schemes and Mind Maps
2022/2023
1 / 6
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Lab 4: Convolution of Discrete-Time Sequences - Signal Processing and Filtering and more Schemes and Mind Maps Mathematics in PDF only on Docsity!
Lab 4
Convolution of Discrete-Time Sequences
Submitted By: Muhammad Maab Nawaz FA21-EEE- 021 Submitted To: Dr Fawad Zaman Submission Date: 2 3 /0 9 /
In Lab (4) Post Lab (6) Total (10)
Data Presentation Data Analysis Writing Style
Introduction: Introduction to MATLAB: Introduction: By the end of this lab, we will have learnt how to breakdown signals into even and odd components as well as how to extract output from an LTI system by convolving the input signal x[n] with the impulse response h[n]. This will increase their understanding of how the LTI system works. Information about the lab: In this lab, we covered a variety of concepts connected to the splitting of signals into even and odd components as well as convolution and its application. A third signal is created via convolution, a mathematical procedure that merges two discrete-time signals. The convolution of two scaled signals is equivalent to the scaled convolution of the original signals since it is a linear operation. Convolution is also a time-invariant procedure, which means that a change in time has no impact on how two signals are combined. Applications: In signal processing, convolution has a wide range of uses, including:
- Filtering: Signals can be filtered using convolution to reduce noise or highlight specific frequency components.
- System analysis: The response of a system to an input signal can be examined using convolution.
- Image processing: Convolution can be utilized for a number of images processing tasks, including edge detection, sharpening, and blurring.
- Convolution is a key component of many machines learning techniques, including convolutional neural networks. Numerous uses exist for the decomposition of signals into even and odd components, including:
- Signal analysis: The frequency content of a signal can be examined using the even and odd components of the signal.
- Signal processing: Different outcomes can be obtained by processing a signal's even and odd components separately. For instance, a signal's even component can be filtered to reduce noise, and its odd component can be filtered to highlight frequency components.
- Feature extraction: It is possible to extract features from a signal that can be employed in machine learning algorithms by separating it’s even and odd components. Here are some instances of how signals can be decomposed into even and odd components and then convolution :
- Convolution filters can be used in image processing to blur pictures. To do this, the image is convolved with a low-pass frequency response filter kernel.
- When adjusting an audio signal, a convolution filter can be utilized. Convoluting the audio signal with a filter kernel that has the desired frequency response accomplishes this.
- Machine learning: For image classification, convolutional neural networks (CNNs) are a form of machine learning algorithm. Convolution filters are employed by CNNs to extract characteristics from images that can be applied to image classification. .
The MATLAB function conv_m() convolves two sequences, l and m, that have values for t < 0. The MATLAB function conv_m() convolves two sequences, l and m, that have values for t < 0. Convolution is a mathematical operation that combines two sequences to produce a third sequence. The output sequence is the sum of the products of the elements of the two input sequences at corresponding indices. The conv_m() function works by first padding the input sequences with zeros. This is necessary because the conv() function, which is used to perform the convolution, assumes that the input sequences start at t = 0. Once the input sequences have been padded, the conv() function is used to convolve them. Finally, the padding is removed from the output sequence. TASK# 3 function [ y ] = conv_m( x,h,n1,n2 ) % This function convolves two sequences, x and h, that have values for t < 0. % Define the length of the output sequence n = n1(1) + n2(1) : n1(end) + n2(end); % Convolve the input sequences y = conv(x,h); % Plot the output sequence stem(n,y,linewidth=3); end PART 1 clc; close all; clear all; n1=0:2; n2=0:3; x=[1 2 3]; h=[2 3 4 5]; conv_m( x,h,n1,n2 )
PART 2 n=0:2; x=[1 2 1]; subplot(3,1,1); stem(n,x,linewidth=3); h=[1 1 1]; subplot(3,1,2); stem(n,h,linewidth=3); y=conv(x,h); subplot(3,1,3); a=0:4; stem(a,y,linewidth=3);