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Re: Low pass filtering

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41727] Re: Low pass filtering
  • From: "\"Martin Manscher\" <"<reverse.before.and.after at to.get.e-mail.addres> rehcsnam at kd.utd.tac
  • Date: Tue, 3 Jun 2003 07:13:09 -0400 (EDT)
  • Organization: UNI-C
  • References: <bb731e$b63$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

There are at least two points you need to be aware of:

1) The Fourier terms include both an amplitude and a phase. Thus Abs[term]
is proportional to the amplitude (the normalisation might include the number
of terms; you should check this), and Arg[term] is the phase.

2) If you just set terms above a certain frequency to zero, you will get a
filter that is non-physical (I think it even violates some basic physical
laws such as causality; ask someone who know more about the topic). A
standard RC filter decreases the amplitude by 20 dB/decade, with a smooth
transition at the characteristic frequency of the filter.

Martin


"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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