使用fft进行反卷积的实现与MATLAB中的deconv函数有什么区别？

Question

I've got stuck in this code:

function [ y ] = mydeconv( c,x )
    lx=length(x);
    lc=length(c);
    %lt=lx+lc;
    c=[c zeros(1,lx)];
    x=[x zeros(1,lc)];
    y = ifft(real((fft(c)) ./(fft(x))));
end

and the result is:

mydeconv([1 2 3 3 2 1],[1 1 1])
ans =
Column 1
            NaN + 0.000000000000000i
Column 2
            NaN +               NaNi
Column 3
            NaN +               NaNi
Column 4
            NaN + 0.000000000000000i
Column 5
            NaN +               NaNi
Column 6
            NaN +               NaNi
Column 7
            NaN + 0.000000000000000i
Column 8
            NaN +               NaNi
Column 9
            NaN +               NaNi

and the result of deconv function simply is:

deconv([1 2 3 3 2 1],[1 1 1])
ans =
 1     1     1     1

In principle it should work, I can't understand what is wrong with it.

Answer 1

Since the padded vector x has a length that is a multiple of the original, you end up with zeros in the frequency domain of fft(x) . You can avoid this by choosing a different (longer) length when such zeros are observed:

function [ y ] = mydeconv( c,x )
  lx=length(x);
  lc=length(c);
  if (lc >= lx)
    lt = lc;
    while (1)
      xpadded = [x zeros(1,lt-length(x))];
      Xf = fft(xpadded);
      if (min(abs(Xf)) > 0)
        break;
      end
      lt = lt + 1;
    end
    cpadded = [c zeros(1,lt-length(c))];
    Cf = fft(cpadded);
    y = real(ifft(Cf ./ Xf));
    y = y(1:lc-lx+1);
  else
    y = [];
  end
end

Answer 2

There are two problems in your code:

Firstly, you should take real part of the IFFT output, not of individual FFTs.

Secondly, you should protect against zero-divide-by-zero cases, which are resulting in NaN in your example.

You can implement both of the above, by modifying the line computing y as follows:

y = real(ifft((eps+fft(c)) ./ (eps+fft(x))));

Note that eps is a small positive number to protect against zero-divide-by-zero cases. With this, the output is:

disp(y)
% 1.0000    1.0000    1.0000    1.0000    0.0000   -0.0000    0.0000    0.0000    0.0000