# CONV

## Purpose:

Computes the convolution of two series
in the time domain.

## Syntax:

CONV(series1, series2,
start, length, interval)

series1 |
- |
A series. |

series2 |
- |
A series. |

start |
- |
Optional. An integer, the starting point.
Defaults to the first point of the series. |

length |
- |
Optional.
An integer, the number of points to process. Defaults to **length(series1)**
+ **length(series2)** - **start**. |

interval |
- |
Optional. An integer, the convolution interval.
Defaults to 1. |

## Returns:

A series or table.

## Example:

conv({3, 1, 1},
{2, 1})

Yields the series {6,
5, 3, 1} producing the coefficients
of the following polynomial multiplication:

## Example:

conv(W1, reverse(W1))

yields the auto-correlation of the series
in W1.

## Example:

W1: gnorm(1000,1)

W2: rev(w1)

W3: conv(W1, W2)

W4: conv(W1, W2,
900, 200)

W3 contains the raw auto-correlation of
W1.

W4 starts calculating the convolution
when the first point in W2 reaches the 900th point of W1 (**start**
point), and continues calculating until 200 points have been processed.
The resulting series length is 200. In this example, the resulting series
is a 200 point window around the mid point of the full auto-correlation.

## Remarks:

The convolution of series x[n] and h[n] is defined as:

CONV computes convolution directly in
the time domain and is optimized for real data. Use FCONV
to perform convolution via the Fourier Transform method.

By default,
the resulting series contains **length(series1)
+ length(series2) - 1** data points.

If **start** <= 0, **start**
defaults to 1.

If **length** <= 0, **length**
defaults to **length(series1) + length(series2)
- start**

As demonstrated by the first example,
convolution is equivalent to polynomial multiplication where the terms
of the polynomials are arranged in descending powers.

See DECONV
to deconvolve two series.

## See Also:

AUTOCOR

CIRCONV

CONV2D

CROSSCOR

DECONV

FCONV

FDECONV

FFT

FILTEQ

XCORR

## References:

Oppenheim and Schafer.

Digital Signal Processing

Prentice Hall, 1975

Digital Signal Processing Committee

Programs for Digital
Signal Processing

I.E.E.E. Press, 1979