Problems with IFFT not being symmetrical I have two signals, a measurement and a reference which I have performed an FFT on.  They have both been windowed with a Hanning window, and now I would like to deconvolve these to get the impulse response.  

I have followed these steps:


Divide my reference FFT by my measurement FFT. (Point division of complex numbers).
I then take the conjugate of this resultant array. 
I then perform a forward FFT on this.
I then take the conjugate again. 
I then divide by the length to normalise the signal.


If I am to understand correctly, this should give me the symmetrical deconvolution of the two signals.  However, for my input of 1024 samples, I get the first 512 samples equal to 0, and then the second half of the samples are a little bit noisy with a definite impulse at the expected delay time. 

My measurements are actually completely electronic so should be noise free.  I can confirm that my two input FFTs are symmetrical (I am using the full FFT, not just the positive values), I am not doing any 'FFT Shift'. 

If anybody has any suggestions or hints, I would greatly appreciate it.  

Thanks
Here is an example using Matlab/Octave code. There is no need to conjugate.

x = rand(1000,1);
y = rand(1000,1);
z = conv(x,y,'full');
y2 = ifft( fft(z,1999) ./ fft(x,1999) );
norm(y - y2(1:1000)) / norm(y)

ans =

   1.5654e-13