Over the pass few weeks, I've been using Mathematica to analyze signals for the purpose of low pass filtering. Mathematica indeed has a Low Pass Filtering program in it, but I thought why not do it by brute force. Doing it by brute force can give you sense of appreciation for the LPF technique.
So here's what I did: I had a data sample of a 193 points which I called v.
I took the DFT of v.
a = Fourier[{v}, FourierParameters -> {1, 1}];
Form my low pass filtering, I set points 90 to 105 to zero.
b = ReplaceList[Take[a[[1]], {90, 105} ], {x__, __} -> 0];
Here I'm inserting those zero points back into the data.
c = Join[Take[a[[1]], 89], b, Take[a[[1]], {106, 193}]]
Then I took the inverse DFT to get back to the frequency domain.
d = InverseFourier[c, FourierParameters -> {1, 1}];
It all worked out because the imaginary points were practically zero. I eventually had to take points 6 to 184 to zero so that I could get a good enough low pass filter. Special thanks to all the people in the Wolfram Community who responed to my queries to help make his possible.
