Computes the discrete convolution of two sequences.

x—A one-dimensional array.

y—A one-dimensional array.

result—A one-dimensional array containing the discrete convolution of x and y.

Direct—If set, the computation is performed using the direct method rather than the FFT method, regardless of the size of the arrays.

Periodic—If present and nonzero, a circular convolution is computed.

The function CONVOL1D computes the discrete convolution of two sequences x(k) and y(k) given by:

The values of x(n) and y(k – n) are assumed to be zero when the index is not between [0, Nx – 1] and [0, Ny – 1], respectively.

If the lengths of the sequences are small, the direct sum formula is used. Otherwise, for longer sequences the FFT is used to compute the convolution.

In this example, the convolution of x = [1, 2, 3, 2, 1] and y = [2, 2, 2] is computed.

; Define x and y.

x = [1, 2, 3, 2, 1]

y = [2, 2, 2]

PM, CONVOL1D(x, y)

This results in the following output:

2.0000000

6.0000000

12.000000

14.000000

12.000000

6.0000000

2.0000000