I am familiar with the continuous Fourier transform yet the more I try to understand FFT, the more I'm confused. If we've got a discrete N sample signal, FFT is a faster way to calculate DFT. If calculating the DFT is independent of frequency bins why do they prop up? For example in the code below that I took from webpage, we're clearly filtering frequencies, in this case the daily temperature, but again I do not understand how can you partition an already discrete sequence in further frequencies called bins. Is there a practical purpose for bins and their interpretability?
from numpy.fft import rfft, irfft, rfftfreq def low_pass(s, threshold=2e4): fourier = rfft(s) frequencies = rfftfreq(s.size, d=2e-3 / s.size) display(1/frequencies) fourier[frequencies > threshold] = 0 return irfft(fourier)