I have trouble finding the bandwidth of a signal. Say I have an info bearing signal m(t)=sinc(2t/pi). I found the fourier transform of the sinc function and found that the angular frequency was 1/pi. I am confused whether the the bandwidth is w or 2w. Since it is band-limited, does that mean only the positive w is counted and the bandwidth is just 1/pi?
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$\begingroup$ Could you, please, review my answer? If it answers your question, could you mark it? $\endgroup$– RoyiCommented Sep 24, 2022 at 17:23
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$\begingroup$ What is the definition of the bandwidth of a signal? $\endgroup$– Cris LuengoCommented Aug 4, 2023 at 14:10
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$\begingroup$ The bandwidth is w, you don’t count the “negative” frequencies. $\endgroup$– Cris LuengoCommented Aug 4, 2023 at 14:12
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When you look on a signal's DFT transform what you see is given in normalized units in the range $ [ -\pi, \pi ] $ where $ \pi $ equals half the sampling rate.
Since the DFT is periodic and the way FFT work when one calculate the DFT in modern software (MATLAB / Python, etc...) the DFT is given in the $ [0, 2 \pi ] $ range.
In order to view it in the more intuitive way one could use fftshift() (MATLAB).
When you display it then, probably you won't see it gets to zero anywhere.
What you'll probably see (If the signal is band limited with bandwidth lower than the sampling rate) is a big drop in the magnitude.
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1$\begingroup$ In your first sentence shouldn't it be "where π equals half the sampling rate"? $\endgroup$ Commented Oct 16, 2021 at 15:19
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$\begingroup$ @RichardLyons, indeed. Thank you. By the way, feel free to offer an edit to any of my answers you see. I'd be glad. $\endgroup$– RoyiCommented Oct 16, 2021 at 16:45
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$\begingroup$ @ Royi As far as I recall your answers have been trustworthy. $\endgroup$ Commented Oct 16, 2021 at 22:46