Learn SDR 14: Pulse Shaping

Lesson 14 Pulse shaping and Nyquist criteria (Nyquist ISI criterion)

Each symbol must have zeros at the peaks of all other symbols.

Raised-cosine filter is a popular choice, but we want a low-pass-like filter at the TX and a matched filter at the RX.

Root-raised-cosine filter (RRC) on both TX and RX. There's a block.

roll-off factor, beta (alpha in GNUradio), is a measure of the excess bandwidth of the filter, i.e. the bandwidth occupied beyond the Nyquist bandwidth of 1/T.

Look at different alphas and their effect in time and frequency on random binary data.

Talk about how the tails help you do clock recovery.

Plot of a pulse passed through the filter along with delayed versions of those pulses. Then random binary data,, which looks like a mess, but when sampled right gives back the data. Eye diagrams.

HW: set up a flow graph that outputs a pattern of data that goes both positive and negative followed by zeros. Add so much Gaussian noise that you can barely see it. Send it through a matched filter, whose taps are the time-reverse and complex conjugate of the pattern you care about (the filtering process is a convolution, which is the time-reverse of correlation). Our pulses were all symmetric in time and real, so the filter taps were identical to the pulse we wanted to match.

HW: Modulate data with 4 different levels (2 bits per symbol); look at waveform and eye diagram

HW: Change the samples per symbol from 10 to 20. Why does the bandwidth change the way it does? What about changing it to 4 or 2? Why is 2 the absolute minimum?


https://gallicchio.github.io/learnSDR...

All GNURadio flowgraphs are at:
https://github.com/gallicchio/learnSDR

--- Learn SDR with Professor Jason Gallicchio