Convolution of 1D Signal using MATLAB

The aim of this experiment is to understand the concept of convolution and how to perform

convolution of 1D signals using MATLAB. This includes learning the convolution operation, its

mathematical representation, and its practical applications.

Answer 1

[Shubham]

Hi Manipal,

Convolution is a fundamental mathematical operation used in signal processing, image processing, and various other fields. It combines two sequences (signals) to produce a third sequence, representing how the shape of one is modified by the other. In practical terms, convolution is used for tasks like filtering, signal analysis, and system response characterization.

Understanding Convolution

Mathematical Representation

For two discrete-time signals ( x[n] ) and ( h[n] ), their convolution ( y[n] ) is defined as:

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This formula indicates that each point in the output signal ( y[n] ) is a weighted sum of points from the input signal ( x[n] ), where the weights are given by the signal ( h[n] ).

Practical Applications

• Signal Filtering: Smoothing or sharpening signals.
• Signal Analysis: Understanding how systems respond to different inputs.
• Image Processing: Blurring, edge detection, and feature extraction.

Performing Convolution in MATLAB

MATLAB provides built-in functions to perform convolution easily. Here’s a step-by-step guide to convolving two 1D signals using MATLAB:

Step-by-Step Guide

1. Create two vectors representing the signals you want to convolve.
2. MATLAB’s conv function computes the convolution of two vectors.
3. Plot the original signals and their convolution to understand the effects.

Example Code:

% Define two signals
x = [1, 2, 3, 4];  % Example input signal
h = [1, 0, -1];    % Example impulse response

% Perform convolution
y = conv(x, h);

% Plot the signals
figure;
subplot(3,1,1);
stem(x, 'filled');
title('Signal x[n]');
xlabel('n');
ylabel('x[n]');

subplot(3,1,2);
stem(h, 'filled');
title('Impulse Response h[n]');
xlabel('n');
ylabel('h[n]');

subplot(3,1,3);
stem(y, 'filled');
title('Convolution Result y[n] = x[n] * h[n]');
xlabel('n');
ylabel('y[n]');

Explanation of the Code

• We define two signals, x and h, as vectors.
• The conv function calculates the convolution of x and h.
• The stem function is used to plot discrete signals, and the results are displayed in a figure with three subplots for easy comparison.

Answer 2

[Amith]

Hi Manipal,

To perform convolutions on a 1D layer of signals, you can use the 'convolution1dLayer' function available in MATLAB release R2021b and later.

This function applies sliding convolutional filters to 1D input data. It works by moving the filters along the input, computing the dot product of the weights and the input, and then adding a bias term.

The dimension that the layer convolves over depends on the layer input:

• For time series and vector sequence input (data with three dimensions corresponding to the channels, observations, and time steps), the layer convolves over the time dimension.
• For 1-D image input (data with three dimensions corresponding to the spatial pixels, channels, and observations), the layer convolves over the spatial dimension.
• For 1-D image sequence input (data with four dimensions corresponding to the spatial pixels, channels, observations, and time steps), the layer convolves over the spatial dimension.

You can learn more about this function in the documentation linked below: https://www.mathworks.com/help/deeplearning/ref/nnet.cnn.layer.convolution1dlayer.html

Hope these resources assist you in your experiment!