Here is a simple explicit example of Fourier convolution and deconvolution, for a small 9-element vector, with the vectors printed out at each stage. (You can also plot them if you want). In this example, a vector y is defined and then it is convoluted with a vector c.  But c is the wrong length, which generates a "Matrix dimensions must agree" error message, so it is zero-filled to the length of y. That produces the convoluted vector yc (with a different shape because of convolution). Finally c is deconvoluted from yc, and the original y is regenerated. 

You can modify this example by adding zeros to the original y, for example. Also, in the example c is zero-centered; try it and see what happens if you define c as shifted by one point: [0 3 2 1 0 0 0 0 0].



>> y=[0 0 0 1 1 1 0 0 0]

y =
     0     0     0     1     1     1     0     0     0

>> c=[3 2 1 0]

c =
     3     2     1     0

>> yc=ifft(fft(y).*fft(c))./sum(c);
Matrix dimensions must agree.
 
>> c=[3 2 1 0 0 0 0 0 0]

c =
       3     2     1     0     0     0     0     0     0

>> yc=ifft(fft(y).*fft(c))./sum(c)

yc =
    0.0000    0.0000      0    0.5000    0.8333    1.0000    0.5000    0.1667    0.0000

 
>> ydc=ifft(fft(yc)./fft(c)).*sum(c)

ydc =

   -0.0000       0       0    1.0000    1.0000    1.0000    0.0000    -0.0000    0.0000