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 >