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.

  • 2
    $\begingroup$ 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
  • 2
    $\begingroup$ 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

1 Answer 1


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.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.