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 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.

Algorithm

deconv uses the filter primitive.