Re: Re: Butterworth filter
- To: mathgroup at smc.vnet.net
- Subject: [mg108536] Re: [mg108507] Re: Butterworth filter
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Mon, 22 Mar 2010 02:40:09 -0500 (EST)
- References: <hnkfa8$po0$1@smc.vnet.net> <hnl0ln$6uq$1@smc.vnet.net> <201003190746.CAA08409@smc.vnet.net> <ho1uha$hoe$1@smc.vnet.net> <201003210704.CAA19585@smc.vnet.net>
On Mar 21, 2010, at 3:04 AM, Kevin J. McCann wrote:
> This is not a very good way to filter a signal. The resulting time
> series will "ring" due to the "sharp edges" in the filter. A much
> better
> way to filter the signal is with a Hamming or Hanning weighted
> bandpass
> or lowpass (whichever is appropriate) filter. This gives a much better
> response without the ring. This ringing is 13dB down from the peak,
> and
> can be significant, but with a Hamming filter the ringing is around
> 60dB
> down from the peak.
The position of the side lobes depends on the cutoff frequency, if
the passband is wide enough the ringing is negligible. At any rate
implementing a windowed low pass filter in Mathematica is still
relatively easy: Fourier the data, apply the window function of your
choice, for example;
windowedspectrum = Table[spectrum[[i]]*0.5*(1+Cos[2*Pi*i/(Length
[spectrum]-1]),{i,0,Length[spectrum]-1}]
and then inverse Fourier transform.
For other approaches to data smoothing, there are two relevant
Demonstration projects at http://demonstrations.wolfram.com/
WaveletShrinkageDenoising/ and http://demonstrations.wolfram.com/
DataSmoothing/.
>
> Kevin
>
> Sseziwa Mukasa wrote:
>>
>> Perhaps you're not getting many responses because your question is
>> somewhat unclear. A Butterworth filter is typically used for analog
>> signal processing, but your data is digitized so you'd have to use a
>> digital filter. One can digitize Butterworth filters but they don't
>> have all the properties of an analog Butterworth filter, furthermore,
>> it is trivial to implement an ideal low pass filter with superior
>> performance to a Butterworth for digitized data: Fourier transform
>> the signal, zero out all values greater than the desired cut off
>> frequency, Inverse Fourier transform to get the filtered signal.
>> Without further information about your data whether this is
>> appropriate or not, but if the goal is a low pass filter why insist
>> on a Butterworth?
>>
>
- References:
- Re: Butterworth filter
- From: Paul Floyd <root@127.0.0.1>
- Re: Butterworth filter
- From: "Kevin J. McCann" <kjm@KevinMcCann.com>
- Re: Butterworth filter