Convolution & Cross Correlation

Convolution

Convolution works in 3 modes:

1. Full: This returns the convolution at each point of overlap between kernel and signal.
2. Same: This returns the convolution such that it maintains the same size as the original signal.
3. Valid: This returns the convolution for the point where the kernel and the signal overlap completely.

The parameters for this filter are as follows:

• Mode of Operation ⇨ Can be "full", "same", "valid"
• Kernel ⇨ 1-D Array the signal is convolved with

Signal used: [2, 8, 0, 4, 1, 9, 9, 0]

Kernel used: [1, 3, 1, 3]

Code

String mode = "full"; //Can be "valid", "same"
Convolution con = new Convolution(signal, kernel);
double[] out = con.convolve("full");

Output: [2, 14, 26, 18, 37, 16, 49, 39, 36, 27, 0]

Cross-Correlation

Works in the exact same way as convolve.

The parameters for this filter are as follows:

• Mode of Operation ⇨ Can be "full", "same", "valid"
• Kernel ⇨ 1-D Array the signal is cross-correlated with

Signal used: [2, 8, 0, 4, 1, 9, 9, 0]

Kernel used: [1, 3, 1, 3]

Code

String mode = "full"; //Can be "valid", "same"
CrossCorrelation cc = new CrossCorrelation(signal, kernel);
double[] out = cc.cross_correlate("full");

Output: [6, 26, 14, 38, 15, 40, 43, 37, 36, 9, 0]