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Re: Low pass filtering

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41755] Re: Low pass filtering
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 4 Jun 2003 08:34:38 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <bb731e$b63$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

a) ListConvolve[] will help you to implement a low pass filter   
   it call Fourier[] automatical
b) the Fourier tranform of a real signal must be symmetric, i.e.
   Fourier[signal][[i+1]]==Conjugate[Fourier[signal][[N-i]]]
   for i>1 and Length[signal]=N and you Fourier domain 
   filter must preserve this property.

Regards
  Jens

Bob Buchanan wrote:
> 
> Hello,
> 
> I have a question about recovering a filtered signal from a Fourier
> transformed input signal. I have read a time series of real sampled
> values into Mathematica. I can use Fourier[] to compute its DFT. As I
> understand the DFT, the kth value represents the "amount" of the kth
> frequency present in the original time series. To implement a simple
> low pass filter I set all the elements of the Fourier series below a
> certain threshold frequency to zero. Now I want to do the IDFT to
> recover a filtered time series containing only the low passed
> frequencies. However the IDFT I compute is not a real series, but
> contains complex entries with nontrivial imaginary parts. What about
> this filtering operation am I misunderstanding?
> 
> Thanks,
> Bob Buchanan


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