# convol

convolution

### Syntax

y = convol(h, x) [y,e1] = convol(h, x, e0)

### Arguments

- h
a vector, first input sequence ("short" one)

- x
a vector, second input sequence ( "long" one)

- e0
a vector,old tail to overlap add (not used in first call)

- y
a vector, the convolution.

- e1
new tail to overlap add (not used in last call)

### Description

Calculates the convolution `y= h*x`

of two discrete
sequences by using the fft. The convolution is defined as follows:

Overlap add method can be used.

USE OF OVERLAP ADD METHOD: For
`x = [x1, x2,..., xNm1, xN]`

First call is
`[y1, e1] = convol(h, x1);`

Subsequent calls :
`[yk, ek] = convol(h, xk, ekm1)`

; Final call :
`[yN] = convol(h, xN, eNm1);`

Finally
`y = [y1, y2,..., yNm1, yN]`

.

The algorithm based on the convolution definition is
implemented for polynomial
product: `y = convol(h, x)`

is equivalent
to `y = coeff(poly(h,'z','c') * poly(x,'z','c'))`

but
much more efficient if `x`

is a "long" array.

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