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Re: using iFFT on a Continuous Time Transfer Function

• To: mathgroup at smc.vnet.net
• Subject: [mg48673] Re: [mg48643] using iFFT on a Continuous Time Transfer Function
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Thu, 10 Jun 2004 02:43:11 -0400 (EDT)
• References: <200406090817.EAA15616@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On Jun 9, 2004, at 4:17 AM, Vin wrote:

> Hello,
>
> I know what my signal looks like in the frequency domain, because I
> have a analytic expression for that (i.e., a function of frequency). I
> don't have a time domain counterpart though, but I expect it to be a
> real valued pulse-like signal, lasting a few nanoseconds.
>
> I am wondering, can I somehow apply the IFFT to this frequency domain
> function to get a discrete time representation of the time domain
> counterpart?
>
> If so, any hints as to how to go about it?

Try InverseFourierTransform on your analytic expression.

> I have already tried sampling my frequency domain function to produce
> something like the output of a FFT, e.g., with the -ve frequency
> function values being generated from the complex conjugate of the
> positive frequency function values etc. However, when I apply the
> IFFT, I get nothing like what I expect.
>

Perhaps your expectations are not correct?  Anyway, sampling in the 
frequency domain and doing a discrete inverse Fourier Transform is not 
equivalent to sampling in the time domain.  If your function is 
bandwidth limited you can reconstruct the discrete spectrum you'd get 
if you sampled in time, see 
http://dsp7.ee.uct.ac.za/~nicolls/lectures/eee401f/05_dft.pdf for some 
pointers.  However since your signal is of finite duration it cannot be 
bandwidth limited and the best you can hope for is an approximation of 
the discrete spectrum.

Regards,

Ssezi

• References:
  • using iFFT on a Continuous Time Transfer Function
    • From: car_d_active_unit@hotmail.com (Vin)