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Deconvolution and polynomial division
[q,r] = deconv(v,u)
[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.
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 u:
[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.
deconv uses the filter primitive.
convmtx, conv2, and filter in the Signal Processing Toolbox, and:
conv Convolution and polynomial multiplication
residue Convert between partial fraction expansion and polynomial
coefficients