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Spectrum Filtering based on discrete convolution

  1. Jul 1, 2008 #1
    Hi, there!
    That's probably the most relevant forum thread where I can consult pros about my problem.
    Well, I'm a visual programmer and quite far of Spectra Physics to what my issue's dramatically related to. Specifically, I need to implement in C# the frequency-domain signal filtration (with a high-pass filter). Everything I've got to do is to design a proper discrete convolution method (procedure) that involves different filter models for dealing with 1D real signal.
    So, after hours of sorrow and numerous futile attempts to thoroughly realize both physical and math aspects of my puzzle I’ve grasped some theory rudiments.
    First, a convolution of two (even complex) sequences in here is defined by the following equation:
    y[k] = sum_{i=0}^{N} h*s[k-i],
    took under condition that s[k-i]=s[0], as (k-i)<0 and N=size(h)+size(s)-1. I guess, it's OK so far :-)
    Next, given the varying bandwidth (f1, f2), [f1,2 are linear frequencies] and the filter rolloff factor ‘alpha’ expressed in decibel per octave.
    I consider the discrete function h as a pulse response (i.e. inverse Fourier transform) of my band-stop filter function H representing all shape manipulation in the frequency domain, right?
    My ‘crux of the matter’ is how to find this sequence h. Whether I should first state an analytical expression of the filter (picking, for example, raised cosine filter) and then find its pulse response somehow or not?
    Thanx, in advance
     
  2. jcsd
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