I'm having some trouble getting the discrete transform to look as it should, but here's what I have so far (the notebook is attached).
I made a few small changes and converted to html (jupyter nbconvert filename) to make it easier to see without downloading.
I think this is close, though I haven't looked closely enough at your definitions - we should discuss.
Talk to you tomorrow.
We should do a tiny (like N=4) example with some dirt simple (like y=[1,1,0,0] or [1,-1,1,-1] or [1,1,1,1]) inputs to see if we make sense of those cases. That should make it clearer what the output k=0...(N-1) components mean.
I showed you two more notebook files: fourier.ipynb (looking at the N=4 case , plotting the basis functions, calculating the fourier coefficients as a dot products) and fourier_128_tophat (just the transform with N=128 for a "tophat" function __--__ .)
The .ipynb and .html files are attached.
last modified | size | ||
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Week1.ipynb | Wed Feb 19 2025 10:31 pm | 37K |
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Week1_jim.html | Wed Feb 19 2025 10:31 pm | 277K |
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Week1_jim.ipynb | Wed Feb 19 2025 10:31 pm | 23K |
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fourier.html | Wed Feb 19 2025 10:31 pm | 328K |
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fourier.ipynb | Wed Feb 19 2025 10:31 pm | 69K |
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fourier_128_tophat.html | Wed Feb 19 2025 10:31 pm | 294K |
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fourier_128_tophat.ipynb | Wed Feb 19 2025 10:31 pm | 35K |