Re: Numerically Computing Impulse Response from Power Frequency Response

susheemg@xxxxxxxxx wrote:
I am trying to compute the impulse response of a given channel to
include in a BER analysis. I have the power transfer function of the
channel, not the classical amplitude/phase transfer function of the
channel. Fortunately, the transfer function is symmetric, so I can
numerically calculate the impulse response as:

amp_freq_resp = sqrt(power_freq_resp);
imp_resp = ifft(amp_freq_resp);
imp_resp = real(imp_resp);

The final command simply removes the imaginary portion of the impulse
response, as it is only an effect of the IFFT calculation in MATLAB.
The square root can be used because the transfer function, so the
impulse response will be purely real.

This is where the problem arises. The power transfer function is near
Gaussian, and so is the amplitude transfer function. This would imply
that the impulse response should be near Gaussian. However, because I
am taking a finite length IFFT, the impulse response is a Gaussian
convolved with a very high frequency sinc function. So I get a
Gaussian envelope with alternating positive and negative values in my
impulse response. Of course, this sort of impuse response is terrible
for certain modulation types.

My question is, can I simply calculate the envelope of the impulse
response and use that as the impulse response in my BER analysis? If
not, is there any method that I can use to easily remove the effects
of the finite-length IFFT from the impulse response?

It sounds like you are putting your amplitudes into the wrong bins. If MatLab still works the way I remember, S(1) is the DC amplitude, S(2) and S(N) are the +/- (sampling rate)/N bins, etc.

If you are centering your power_freq_resp around S(N/2) instead of S(1) then you are telling the IFFT that you have a spectrum that's centered around 1/2 the sampling rate, which will result in an ifft that alternates.

Try recentering your power_freq_resp. If it's truly symmetrical around S(1) then the imaginary component of the ifft will be close to N * roundoff, so you can use that as a diagnostic of your shifting and measurement process.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

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