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Deconvolution and polynomial division


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



[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.


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Create two vectors u and v containing the coefficients of the polynomials 2x3+7x2+4x+9 and x2+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.

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

Extended Capabilities

See Also


Introduced before R2006a