# Documentation

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# deconv

Deconvolution and polynomial division

## Syntax

`[q,r] = deconv(v,u)`

## Description

`[q,r] = deconv(v,u)` deconvolves vector `u` out of vector `v`, using long division. The quotient is returned in vector `q` and the remainder in vector `r` such that ```v = conv(u,q)+r``` .

If `u` and `v` are vectors of polynomial coefficients, convolving them is equivalent to multiplying the two polynomials, and deconvolution is polynomial division. The result of dividing `v` by `u` is quotient `q` and remainder `r`.

## Examples

If

```u = [1 2 3 4] v = [10 20 30]```

the convolution is

```c = conv(u,v) c = 10 40 100 160 170 120```

Use deconvolution to recover `v`:

```[q,r] = deconv(c,u) q = 10 20 30 r = 0 0 0 0 0 0```

This gives a quotient equal to `v` and a zero remainder.

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### Algorithms

`deconv` uses the `filter` primitive.