0
$\begingroup$
  • How does upsampling factor relate to pulse duration?

  • If I want to do pulse shaping and I have rcosdesign(beta,span=8,sps=4) should I upsample by 8, 4 or 33(8*4+1) and why?

  • I've seen you'd normally upsample by 4 and I can't see why.

  • Like, that way you're not using the whole pulse to shape a symbol, shouldn't it be 33?

I'd appreciate very much someone explained this to me. Thanks!

$\endgroup$
1
$\begingroup$

If the number of samples per symbol (sps) is 4, then you should upsample by 4. The input to the pulse shaping filter is 1 sample/symbol, and the output is 4 samples per symbol, so the upsampling rate is 4.

The span is the number of symbol periods in the filter's impulse response. Intuitively, this means that a particular symbol influences the pulse-shaped output for 8 symbol periods, or that the pulse-shaped signal at any moment in time contains a linear combination of 8 different symbols. The number of taps in the filter is span*sps+1, which is 33 in this case. The delay of the filter is span/2. For a fixed filter span in symbol periods, the number of taps in the filter goes up with the number of samples per symbol because the output sample rate increases. However, the span of the filter in symbol periods and the upsampling factor are two independent variables. Changing the span does not change the upsampling rate. Changing the number of samples per symbol in the pulse shaping filter is equivalent to changing the upsampling rate.

| improve this answer | |
$\endgroup$
  • $\begingroup$ Exactly, this is what's bugging me "Intuitively, this means that a particular symbol influences the pulse-shaped output for 8 symbol periods, or that the pulse-shaped signal at any moment in time contains a linear combination of 8 different symbols." I was thinking the exact same thing and how is that desirable? $\endgroup$ – researcher9 Jul 27 '19 at 9:21
  • 1
    $\begingroup$ It is desirable because it allows the pulse shape to have a frequency response that is more bandlimited, and therefore the pulse-shaped signal to occupy less spectrum. A rectangular pulse shape that had no overlap between symbols in the time domain would have a broad spectrum, which would cause interference to adjacent channels. Signals that are limited in the frequency domain are spread out in the time domain, so the RRC pulse shape must span multiple symbol periods to be effective. $\endgroup$ – Ill-Conditioned Matrix Jul 28 '19 at 15:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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