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Re: Low pass filtering

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41704] Re: Low pass filtering
  • From: "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk>
  • Date: Sat, 31 May 2003 06:07:55 -0400 (EDT)
  • References: <bb731e$b63$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In Mathematica the discrete Fourier transform is represented with the DC
term in location 1, and positive frequency terms in locations 2,3,4, and
negative frequency terms in locations -1,-2,-3 (i.e. counting from the end).
To low pass filter you must keep both positive and negative frequencies. For
instance, to keep the DC term only you keep location 1 and zero everything
else. Alternatively, to keep the DC term and the positive and negative
frequncies immediately to either side you keep locations -1,1,2 and zero
everything else. And so on...

--
Steve Luttrell
West Malvern, UK


"Bob Buchanan" <Bob.Buchanan at millersville.edu> wrote in message
news:bb731e$b63$1 at smc.vnet.net...
> 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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