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