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.

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