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In signal processing, I have heard of two terms:
Are these two terms similar or different?
How and when we use each of these methods?
Thanks in advance
Fast Fourier transform does not extract any frequency bands. It only shows the frequency content of a given signal. But while applying FFT, one should be careful about choosing the sampling frequency. As an example, if a signal contains a frequency range of $0-100\,\text{Hz}$ and $f_{max}=100\,\text{Hz}$ $$f_{max} = \dfrac{F_s}{2}$$ and the sampling frequency $F_s \geq 2\cdot f_{max}$ of the signal should be greater than $200\,\text{Hz}$ (according to Nyquist frequency rule). Then FFT will show all the frequencies present in the signal i.e. $0-100\,\text{Hz}$.
If the sampling frequency is less than $<200\,\text{Hz}$ then aliasing will occur and will provide an aliased frequency representation.
On the other hand, band-pass filters eliminate some frequency content of the signal. As an example say one signal has $0-100\,\text{Hz}$ frequency components but you are interested in exploring the frequencies of range $10-30\,\text{Hz}$, then one should use a bandpass filter.
As a system identification researcher, I can provide an example where FFT and bandpass filters are used. Say a signal has its main frequencies in the $10-30\,\text{Hz}$ range. But the signal is acquired with a sampling frequency of $200\,\text{Hz}$.
Performing FFT will show frequency components from $0-100\,\text{Hz}$. Say there are measurement noises all over the frequency ranges. I use a bandpass filter to get rid of that measurement noise.
An FFT extracts frequency bands, similar to a bank of (mediocre) bandpass filters.
An FFT is just a bank of bandpass FIR filters, all of equal length, that because they are in default form rectangularly windowed, have very poor stop-band characteristics (except for deep notches at periodic orthogonal-in-window frequencies), but steep transitions. But they are computationally efficient when one wants a complete orthogonal set of filter outputs over a certain data window (or wants to use them for convolution, etc.)
Bandpass filters are typically not in the form of a rectangular windowed sinusoid (or complex exponential), and can be varied in length and envelope for the targeted frequency band, and thus can have much better filter characteristics for most parameters (stopband attenuation, etc.)
