# Understanding FFT bins interpretability

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)

• Welcome to SE.SP! I'm not sure what you mean by how can you partition an already discrete sequence in further frequencies called bins ? If the original time-domain signal is $x[n]$ then its DFT is $X[k]$. The value $X[k]$ is the frequency-domain value at the $k^{\rm th}$ bin. The term bin is just used to indicate the frequency domain index $k$.
– Peter K.
Jul 6, 2022 at 16:21
• This is a really bad way to do a lowpass filter. I suggest not using it or trying to draw any conclusions from it Jul 6, 2022 at 17:26
• @Hilmar Yes. This seems to be the trap that everyone falls into when they first come across the FFT and decide they need to filter using it.
– Peter K.
Jul 6, 2022 at 18:15