Documentation.md

Introduction

What is convolution

Convolution is a mathematical operation that combines two functions to produce a third function. In the context of signal processing, convolution is often used to combine two signals, creating a new signal that represents how one signal modifies the other over time. In simpler terms, convolution involves flipping one of the functions, shifting it, and then integrating the product of the overlapping regions. This process is repeated for different shifts, producing the entire convolution result.

What is Echo

• An echo is a reflected sound wave that arrives at the listener's ears after bouncing off a surface. It occurs when sound waves encounter a barrier and are reflected back towards the source. The delayed arrival of these reflected waves creates a distinct repetition of the original sound, perceived as a distinct repetition of the original sound, often with a diminishing amplitude. Echoes are commonly experienced in environments with hard surfaces, such as mountains, buildings, or enclosed spaces, and they contribute to our perception of space and distance in the auditory environment.

Relation between Echo and convolution

Convolution produces an echo effect because it models the way sound waves interact with the environment, specifically how a sound wave reflects off surfaces and reaches the listener's ears at different times. In the context of signal processing, convolution is used to simulate the response of a system to an impulse, and this concept is applied to create an echo effect. 1. Impulse Response: In signal processing, an impulse response represents how a system reacts to an impulse signal. For an echo effect, we design an impulse response that mimics the reflection of sound waves. This impulse response typically includes delayed and attenuated versions of the original.

• Delayed Copies : The convolution process involves super imposing delayed copies of the original signal onto itself. Each delayed copy corresponds to the sound wave reaching the listener after reflecting off a surface. The delays create the perception of distance or space between the listener and the reflective surfaces.
• Attenuation : The attenuated versions of the signal in the impulse response simulate the decrease in intensity as sound waves travel and reflect. This attenuation contributes to a more natural and realistic echo effect. In summary, convolution introduces delayed and attenuated replicas of the original signal, emulating the reflective properties of surfaces in an environment. This modeling of sound wave interactions creates the auditory perception of an echo, enriching the audio experience with a sense of space.

MATLAB code explanation

The MATLAB code snippet is provided below for better

% echo effect 
try
    
    
    [y, Fs] = audioread('/path/soundname.mp3');  % Load the audio file
    h = [1, zeros(1, 0.4 * Fs), 0.5, zeros(1, 0.4 * Fs), 0.2];
    
    % Ensure both y and h are column vectors
    y = y(:);  % Convert y to a column vector
    h = h(:);  % Convert h to a column vector
    
    %sound(y, Fs);
    
    % Perform convolution
    out = conv(y, h);
    
    % Plot the convolved signal
    plot(out);
    
    % Uncomment the line below if you want to listen to the convolved signal
    sound(out, Fs);
    
catch exception 
    disp(['Error loading audio file: ' exception.message]);
end

Procedure

change the folder to the location where the audio file is stored

1,Load Audio File: [y, Fs] = audioread('/MATLAB Drive/Dsp/sound.mp3'); The code uses the audioread function to read an audio file ('sound.mp3') and assigns the audio data to the variable y and the sample rate to Fs. The user may have to change the path of the folder

2,Define Impulse Response (Echo Effect): The impulse response h is defined to simulate an echo effect. It includes a direct sound (1), a delayed sound with 0.4 seconds delay, a quieter delayed sound (0.5), and another delayed sound with 0.4 seconds delay followed by a quieter sound (0.2). After the inputs are made suitable

3, Perform Convolution: out = conv(y, h); The conv function is used to convolve the audio signal with the defined impulse response. This process combines the original signal with delayed and attenuated copies, creating the echo effect. 4, Plot and listen to the convolved(echo) signal