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As defined in the CCSDS (section 3.1.2), the impulse response of the Gaussian filter is given by

$$ h(t) = \frac{1}{\sigma T \sqrt{2\pi}}e^{-\frac{t^2}{2\sigma^2T^2}} $$ where $$ \sigma = \frac{\sqrt{\ln{2}}}{2 \pi B T} $$ $B$ is defined as

one-sided 3-dB bandwidth of the filter with impulse response $h(t)$.

What is exactly the meaning of "one-sided" in this context? What would be $B$ if it were the two-sided version instead?

A good reference can be found in Gaussian Pulse – FFT & PSD in Matlab & Python.

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    $\begingroup$ Please edit your question to tell us where you found this. Either a link, or a book or article citation. If you can pull out a short excerpt, please quote it. This probably means the bandwidth from 0Hz to the 3dB point, but without more context, I cannot say. $\endgroup$
    – TimWescott
    Nov 4, 2022 at 13:50
  • $\begingroup$ @TimWescott done. $\endgroup$ Nov 4, 2022 at 13:54
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    $\begingroup$ Typically that's just a convention: one-sided means "distance from the center frequency (0dB) to the -3 dB frequency". Two-sided would be the difference between the two -3dB points (below and above the center), so twice the one-sided bandwidth for a symmetrical filter (which the Gaussian is) $\endgroup$
    – Hilmar
    Nov 4, 2022 at 16:10

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Because that's a document that pertains to communications, where it makes sense to talk about signals that have negative frequencies, they're drawing a distinction between the one-sided bandwidth (from 0Hz to the positive-frequency $-3\mathrm{dB}$ point) vs. the two-sided bandwidth (from one $-3\mathrm{dB}$ point to the other).

If you haven't encountered doing signal processing with complex-valued signals (or, strictly, inphase/quadrature signal pairs), then the one-sided bandwidth, for a lowpass filter, is what you would call the "perfectly ordinary bandwidth". If you are building a radio system that translates some chunk of spectrum down to baseband with an I/Q demodulator, then -- because you have both inphase and quadrature parts -- it suddenly not only makes sense to have different signal components at positive vs. negative frequencies, but it also makes sense to have filters whose response is asymmetric around $0 \mathrm{Hz}$. For such filters, you care about the two-sided bandwidth.

In this particular case, the modulation signal is purely real, so the lowpass Gaussian filter is, of necessity, symmetrical around $0 \mathrm{Hz}$, so the one-sided bandwidth is the most sensible specification for it.

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  • $\begingroup$ This signal converted to bandpass and centered at the frequency $f_c$, would have a bandwidth equals to $2B$, which is $[f_c-B, f_c+B]$, right? Can I conclude that the bandpass signal have twice the bandwidth of its lowpass equivalent? $\endgroup$ Nov 5, 2022 at 16:49

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