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.
|Week1.ipynb||Tue Dec 05 2023 08:03 am||37K|
|Week1_jim.html||Tue Dec 05 2023 08:03 am||277K|
|Week1_jim.ipynb||Tue Dec 05 2023 08:03 am||23K|
|fourier.html||Tue Dec 05 2023 08:03 am||328K|
|fourier.ipynb||Tue Dec 05 2023 08:03 am||69K|
|fourier_128_tophat.html||Tue Dec 05 2023 08:03 am||294K|
|fourier_128_tophat.ipynb||Tue Dec 05 2023 08:03 am||35K|