# deconv

Deconvolution and polynomial division

## Description

example

[q,r] = deconv(u,v) deconvolves a vector v out of a vector u using long division, and returns the quotient q and remainder r such that u = conv(v,q) + r. If u and v are vectors of polynomial coefficients, then deconvolving them is equivalent to dividing the polynomial represented by u by the polynomial represented by v.

## Examples

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Create two vectors u and v containing the coefficients of the polynomials $2{x}^{3}+7{x}^{2}+4x+9$ and ${x}^{2}+1$, respectively. Divide the first polynomial by the second by deconvolving v out of u, which results in quotient coefficients corresponding to the polynomial $2x+7$ and remainder coefficients corresponding to $2x+2$.

u = [2 7 4 9];
v = [1 0 1];
[q,r] = deconv(u,v)
q = 1×2

2     7

r = 1×4

0     0     2     2

## Input Arguments

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Input vectors, specified as either row or column vectors. u and v can be different lengths or data types.

• If one or both of u and v are of type single, then the output is also of type single. Otherwise, deconv returns type double.

• The lengths of the inputs should generally satisfy length(v) <= length(u). However, if length(v) > length(u), then deconv returns the outputs as q = 0 and r = u.

Data Types: double | single
Complex Number Support: Yes

## Output Arguments

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Quotient, returned as a row or column vector such that u = conv(v,q)+r.

Data Types: double | single

Remainder, returned as a row or column vector such that u = conv(v,q)+r.

Data Types: double | single