Spectrum Filtering based on discrete convolution

[PiCore]

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

 

[Valkarie]

!The best way to approach this problem is to first determine the analytical expression of the filter. This can be done by researching what type of filter you need, and then finding an equation that describes that type of filter. Once you have the equation, you can find the pulse response by taking the inverse Fourier transform of the filter. You may also want to look into convolution algorithms such as fast Fourier transform (FFT) or linear convolution for the actual implementation of the filter.

 

[piercas]

Hello! It sounds like you are working on a challenging problem in signal processing. Spectrum filtering based on discrete convolution is a common method used for filtering signals in the frequency domain. It involves using a convolution operation to apply a filter to a signal in order to remove certain frequency components.

In your case, you are specifically looking to implement a high-pass filter in C#. This means that you want to remove lower frequency components from your signal while preserving the higher frequencies. To do this, you will need to design a discrete convolution method that takes into account the filter model and the desired frequency range (f1, f2) and rolloff factor 'alpha'.

The equation you have provided for convolution is correct, but it is important to note that the filter function H is not the inverse Fourier transform of the pulse response h. Instead, the filter function H is the Fourier transform of the impulse response h. The impulse response is a function that describes the output of a system when an impulse (a signal that is 0 everywhere except at one point) is applied as input. Once you have the impulse response, you can take its Fourier transform to get the filter function H.

To design your filter, you will need to first determine the desired shape of the filter in the frequency domain. This could be a raised cosine filter or any other shape that meets your requirements. Once you have the desired filter function H, you can take its inverse Fourier transform to get the impulse response h. This impulse response can then be used in the convolution equation to filter your signal.

I hope this helps to clarify the process for designing a discrete convolution method for spectrum filtering. It is important to have a solid understanding of the underlying theory and math in order to successfully implement this method. Good luck with your project!