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Audio signal processing in MATLAB

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Introduction

Audio signal processing helps us understand and change sounds using a computer. It lets us work with music, speech, and other sounds in useful ways.

To remove noise from a recorded voice message.
To change the speed or pitch of a song.
To detect spoken words in a voice recording.
To analyze the loudness and frequency of sounds in an environment.
To create special sound effects for videos or games.
Syntax
MATLAB
y = filter(b, a, x)

% where:
% x = input audio signal (vector)
% b, a = filter coefficients (vectors)
% y = output filtered signal (vector)

This is a basic way to apply filters to audio signals in MATLAB.

Filters can help remove noise or change sound characteristics.

Examples
This smooths the noisy signal by averaging nearby points.
MATLAB
% Example 1: Simple low-pass filter
b = [0.2 0.2 0.2 0.2 0.2];
a = 1;
x = randn(1, 1000); % noisy signal
y = filter(b, a, x);
This reads a sound file and plays it back at its sample rate.
MATLAB
% Example 2: Reading and playing audio
[x, fs] = audioread('speech.wav');
sound(x, fs);
This shows the shape of the audio signal over time.
MATLAB
% Example 3: Plotting audio waveform
plot(x);
title('Audio Signal Waveform');
xlabel('Sample Number');
ylabel('Amplitude');
Sample Program

This program loads a sound, plays it, applies a low-pass filter to smooth it, plays the filtered sound, and then shows both signals on plots.

MATLAB
% Load an audio file
[x, fs] = audioread('handel.wav');

% Play original sound
sound(x, fs);
pause(length(x)/fs + 1);

% Create a simple low-pass filter
b = ones(1, 10)/10;
a = 1;

% Filter the audio signal
y = filter(b, a, x);

% Play filtered sound
sound(y, fs);

% Plot original and filtered signals
subplot(2,1,1);
plot(x);
title('Original Audio Signal');

subplot(2,1,2);
plot(y);
title('Filtered Audio Signal (Low-pass)');
OutputSuccess
Important Notes

Audio files in MATLAB are often read with audioread and played with sound.

Filters change the sound by emphasizing or reducing certain frequencies.

Plotting helps visualize how the sound wave changes before and after processing.

Summary

Audio signal processing lets us work with sounds using code.

We can read, play, filter, and visualize audio signals in MATLAB.

Filters help improve or change sounds by focusing on certain parts of the signal.

Practice

(1/5)
1. What does the MATLAB function audioread do in audio signal processing?
easy
A. It saves audio data to a file.
B. It plays the audio sound through speakers.
C. It reads an audio file and loads the sound data into MATLAB.
D. It filters the audio signal to remove noise.

Solution

  1. Step 1: Understand the purpose of audioread

    The function audioread is used to load audio data from a file into MATLAB as a vector or matrix.
  2. Step 2: Differentiate from other audio functions

    Functions like sound play audio, audiowrite saves audio, and filter processes signals. audioread only reads data.
  3. Final Answer:

    It reads an audio file and loads the sound data into MATLAB. -> Option C
  4. Quick Check:

    audioread = read audio data [OK]
Hint: Remember: 'read' means load data, not play or save [OK]
Common Mistakes:
  • Confusing audioread with sound
  • Thinking it saves audio instead of loading
  • Assuming it filters or changes the audio
2. Which of the following is the correct syntax to apply a simple low-pass filter b, a to an audio signal x in MATLAB?
easy
A. y = filter(b, a, x);
B. y = filter(x, b, a);
C. y = filter(a, b, x);
D. y = filter(x, a, b);

Solution

  1. Step 1: Recall the filter function syntax

    The MATLAB filter function syntax is y = filter(b, a, x); where b and a are filter coefficients and x is the input signal.
  2. Step 2: Identify correct argument order

    Options A, C, and D have the arguments in wrong order, which will cause errors or wrong output.
  3. Final Answer:

    y = filter(b, a, x); -> Option A
  4. Quick Check:

    filter(b, a, x) = correct syntax [OK]
Hint: Filter syntax is always filter(b, a, x) [OK]
Common Mistakes:
  • Swapping filter coefficients order
  • Putting signal before coefficients
  • Using wrong variable names
3. What will be the output size of y after running this MATLAB code?
x = randn(44100,1); % 1 second noise at 44.1kHz
b = [1 0 0.5]; a = 1;
y = filter(b, a, x);
medium
A. An error due to filter coefficients
B. A vector of size 44102x1
C. A scalar value
D. A vector of size 44100x1

Solution

  1. Step 1: Understand input and filter output length

    The input x is a 44100x1 vector. The filter function outputs a vector of the same length as input.
  2. Step 2: Check filter coefficients validity

    Coefficients b and a are valid. No error occurs. Output y matches input size.
  3. Final Answer:

    A vector of size 44100x1 -> Option D
  4. Quick Check:

    filter output length = input length [OK]
Hint: Filter output length equals input length [OK]
Common Mistakes:
  • Assuming output length changes with filter order
  • Expecting error from coefficients
  • Confusing vector with scalar output
4. Identify the error in this MATLAB code that tries to add an echo effect to an audio signal x:
delay = 5000;
echoGain = 0.6;
y = x;
y(delay:end) = y(delay:end) + echoGain * x(1:end-delay);
medium
A. The length of y(delay:end) and x(1:end-delay) do not match.
B. The variable echoGain should be greater than 1.
C. The indexing delay:end is invalid for vector y.
D. The echo effect requires a filter function, not direct addition.

Solution

  1. Step 1: Check vector lengths in addition

    The segment y(delay:end) has length length(y) - delay + 1. The segment x(1:end-delay) has length length(x) - delay. They differ by 1, causing a dimension mismatch error.
  2. Step 2: Eliminate other options

    A: Indexing is valid. B: echoGain=0.6 <1 is appropriate for decaying echo. D: Direct indexing addition works for simple echo.
  3. Final Answer:

    The length of y(delay:end) and x(1:end-delay) do not match. -> Option A
  4. Quick Check:

    len(y(delay:end))=N-d+1 vs len(x(1:end-d))=N-d [OK]
Hint: Check lengths of vectors before adding [OK]
Common Mistakes:
  • Assuming echoGain must be >1
  • Thinking filter is required for echo
  • Ignoring vector length mismatch
5. You want to create a MATLAB function that adds an echo effect to an audio signal x sampled at Fs. The echo delay is 0.3 seconds and echo gain is 0.5. Which code correctly implements this?
hard
A. function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = x; y(delaySamples+1:end) = y(delaySamples+1:end) + 0.5*x(1:end-delaySamples); end
B. function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = filter([1 zeros(1,delaySamples-1) 0.5], 1, x); end
C. function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = x + 0.5 * [zeros(delaySamples,1); x]; end
D. function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = zeros(length(x)+delaySamples,1); y(1:length(x)) = x; y(delaySamples+1:end) = y(delaySamples+1:end) + 0.5*x; end

Solution

  1. Step 1: Understand echo effect implementation

    Echo is created by adding a delayed and scaled copy of the signal to itself. Using filter with coefficients [1 zeros(1,delaySamples-1) 0.5] adds original plus delayed echo.
  2. Step 2: Evaluate each option

    function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = zeros(length(x)+delaySamples,1); y(1:length(x)) = x; y(delaySamples+1:end) = y(delaySamples+1:end) + 0.5*x; end extends length but adds full x without delay in echo part. function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = x; y(delaySamples+1:end) = y(delaySamples+1:end) + 0.5*x(1:end-delaySamples); end correctly indexes x to match lengths. function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = x + 0.5 * [zeros(delaySamples,1); x]; end adds vectors of different lengths causing error. function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = filter([1 zeros(1,delaySamples-1) 0.5], 1, x); end correctly uses filter with proper coefficients.
  3. Final Answer:

    function y = addEcho(x, Fs) delaySamples = round(0.3 * Fs); y = filter([1 zeros(1,delaySamples-1) 0.5], 1, x); end -> Option B
  4. Quick Check:

    Use filter with delayed coefficients for echo [OK]
Hint: Use filter with delayed coefficients for echo [OK]
Common Mistakes:
  • Adding vectors of different lengths directly
  • Forgetting to delay the echo signal
  • Incorrect indexing causing errors
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