time domain convolution not reversing frequency domain multiplication? ifft scaling isssues?

I have a input signal in time domain and a tranfer function in frequency domain. In the transmitter i take the fft of input signal multiply them and convert back to time domain. In receiver i take the conjugate of the transfer function and convoluted with the time domain signal. I am expecting my inital time domain signal at the output. I wonder if it is the problem of ifft scaling

%%%start code%%%%%%

xt=[0  1   0   0   0    1  0    1];

hf=[1.0000  -0.4879 + 0.8729i  -0.4509 + 0.8926i   0.9921 - 0.1254i  -0.2956 + 0.9553i   0.9921 - 0.1254i  -0.4509 + 0.8926i  -0.4879 + 0.8729i];

inverse_hf=conj(hf);

%transmission
temp=fft(xt).*hf;
input=ifft(temp);

%receiver
transferfunc=ifft(inverse_hf);
output=conv(input,transferfunc);

%%%%%end code%%%%
------
results from the above code 

input=[0.2242 - 0.1818i   0.1514 + 0.5814i   0.7475 - 0.5347i   0.2508 - 0.0518i   0.7475 - 0.5347i   0.1514 + 0.5814i  0.2242 - 0.1818i   0.5029 + 0.3220i];

output=[-0.0735 - 0.1371i   0.2904 - 0.0159i  -0.1254 - 0.5298i   0.0118 - 0.0056i  -0.1997 - 0.2054i   0.9651 - 0.1221i 0.0318 + 0.0608i   1.0000 + 0.0000i   0.0735 + 0.1371i   0.7096 + 0.0159i   0.1254 + 0.5298i  -0.0119 + 0.0056i 0.1997 + 0.2054i   0.0349 + 0.1221i  -0.0318 - 0.0608i];

Thanks in advance

Janu

[Honglei Chen]

Formatted the code

Answer 1

[Honglei Chen]

Looks like you are comparing the result of conv with the frequency domain multiplication? If that's the case, to achieve the same result as linear convolution carried out by conv, you need to pad the signal to correct length before you translate to frequency domain.

Also, taking conjugate of the hf does not give you an inverse filter if that's what you look for.

[janani]

Thank you so much for the reply. I have implemented a filter with inverse transfer function i observed that it is not filtering out so i thought convolution totally with inverse function should completely retrieve my signal back.

Will designing a filter with inverse transfer function help in retrieving my signal?

1. pad input signal xt with 7 zeros and then perform fft
2. pad 7 zeros with hf to match matrix size for multiplication
3. take ifft for the nearest 2^n value which is 2^4=16
4. pad inverse transfer function with 7 zeros and take ifft then conv?

is there any mistake in what i have understood so far?

[Honglei Chen]

you could just pad all sequence to the appropriate length, then multiply all three frequency representation together and then do IFFT. I just want to mention again that conj(hf) in general is not an inverse filter of hf.