Dear Researchers,
suppose I have an wideband is signal with F_low=200MHz and F_high 400MHz. I want to decompose this wideband signals into 26 narrowband signals using 256-points FFT.
What I understood is that each FFT point will represents a frequency bin. does it mean we will end up with 256 narrowband signals? if yes, why published works said that we apply 256-points FFT to decompose this wideband into 26 narrowband signals?
I am just confused with these terms (FFT points, Frequency bins and narrowband signals).
I appreciate your clarification
Thank you for your responses
Researcher
Bakhtiar
Here is a compact version with examples: https://docs.scipy.org/doc/scipy/reference/tutorial/fft.html Here is a detailed version with theory and examples: https://realpython.com/python-scipy-fft/
Dear Karim,
the first issue is periodicity: you can only deal this way if the original wideband signal is periodic. If not, forget your story!
the second point is the number of "bins" or points of the FFT: on periodic signals, FFT is legitimate (and reversible) irrespectively to the number of bins, as long as the integration time is properly set wrt your window type (Hanning is the most common): the B*T product must exceed 1. If you specifically requires 26 bins for the targeted octave, you probably have to encode yourself the FFT to match this (unusual) demand, its perfectly feasible but it requires a good understanding of the FFT maths... In physical terms, you have to create a serial of adjacent 1/26th octave filters "digesting" in the time domain your original wideband signal and collect their output at the right periodicity. It will not work with your standard 256 bins (or points) algorithm as 26 is not a divider of 256 nor a power of 2 - you might anyway approach it by aggregating successively 10 adjacent FFT points to drive each of your 26 sources as 26 is almost 256/10 but it will not be an "exact" substitute of your broadband signal.
Effectively you need to follow good tutorials, but it is even better if you properly understand Hilbert, Laplace and Fourier mathematics for understanding what you will encode!
good work!
Bernard
Dear Dr. Bernard Garnier
Thank you so much for you answers. Actually my narrowband number resulted from the decomposition of the wideband is NOT limited to 26. Just I want to know why most of the published work make this claim.
For my general case (say 256 FFT points is applied). what is the most straight forward way to understand the number of narrowband signals, please?
Each FFT point materializes precisely the corresponding narrowband contribution. The corresponding bandwidth depends precisely of the number of points of the FFT. The more points the longer signal sample required, which means that if your signal is not stationary over a long time you have to renounce to a high resolution in the frequency domain...
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