How to Use conv Function in MATLAB for Convolution

In MATLAB, use the conv function to compute the convolution of two vectors or signals. The syntax is conv(a,b), where a and b are input vectors, and the output is their convolution result as a vector.

Syntax

The basic syntax of the conv function is:

• c = conv(a, b): Computes the convolution of vectors a and b.
• c = conv(a, b, shape): Computes convolution with shape option 'full', 'same', or 'valid'.

Explanation:

• a and b are input vectors (arrays) representing signals or sequences.
• c is the output vector containing the convolution result.
• shape controls the size of the output: 'full' (default) returns the complete convolution, 'same' returns the central part with the same size as a, and 'valid' returns only parts where a and b fully overlap.

matlab

c = conv(a, b)
c = conv(a, b, 'shape')

Example

This example shows how to convolve two simple vectors and display the result.

matlab

a = [1 2 3];
b = [4 5 6];
c = conv(a, b);
disp(c);

Output

4    13    28    27    18

Common Pitfalls

Common mistakes when using conv include:

• Confusing convolution with element-wise multiplication. conv combines vectors differently than multiplying elements one by one.
• Not specifying the shape argument and getting a longer output than expected.
• Using non-vector inputs or multidimensional arrays without flattening them first.

matlab

a = [1 2 3];
b = [4 5 6];

% Wrong: element-wise multiplication (not convolution)
c_wrong = a .* b;
disp(c_wrong);

% Right: convolution
c_right = conv(a, b);
disp(c_right);

Output

4    10    18
4    13    28    27    18

Quick Reference

Usage	Description
conv(a, b)	Full convolution of vectors a and b
conv(a, b, 'full')	Same as conv(a,b), full convolution
conv(a, b, 'same')	Output size same as a, center part of convolution
conv(a, b, 'valid')	Only parts where a and b fully overlap

Key Takeaways

Use conv(a, b) to compute the convolution of two vectors in MATLAB.

Specify the shape argument ('full', 'same', 'valid') to control output size.

Convolution is different from element-wise multiplication; do not confuse them.

Input vectors must be one-dimensional for conv to work correctly.

Check output size to avoid unexpected longer vectors from full convolution.