Signal Processing Toolbox

Deconvolution

Deconvolution, or polynomial division, is the inverse operation of convolution. Deconvolution is useful in recovering the input to a known filter, given the filtered output. This method is very sensitive to noise in the coefficients, however, so use caution in applying it.

The syntax for deconv is

• [q,r] = deconv(b,a)
  

where b is the polynomial dividend, a is the divisor, q is the quotient, and r is the remainder.

To try deconv, first convolve two simple vectors a and b (see Signal Processing Basics for a description of the convolution function):

• a = [1 2 3];
  b = [4 5 6];
  c = conv(a,b)
  c = 
      4   13   28   27   18
  

Now use deconv to deconvolve b from c:

• [q,r] = deconv(c,a)
  q = 
      4    5    6
  r = 
      0    0    0    0    0
  

Communications Applications

Specialized Transforms