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My professor said that: in order to avoid interferences/harmonics caused by the nature of the square wave g(t) (sinc will have these secondary lobes), it's better to change the basic pulse g(t) to something like a arc of sine or something like that instead of having a square wave. I couldn't find anything on web. So I wanted to ask: is it really used? Or square wave is still the most used? For example I guess PAM, QAM, PSK all use square wave as basic pulse, right? So when and which other basic pulse is used? enter image description here

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The most common pulse used is the “Root Raised Cosine Pulse” (formed with an RRC filter) This is the pulse commonly used in a transmitter and a subsequent RRC filter used in the receiver. The cascade of the two forms the Raised Cosine Pulse which has the benefit of restricting the spectral occupancy combined with zero inter-symbol interference: the time domain response of prior symbols cross zero at all the subsequent symbols where we would make decision on what was transmitted. For more details on the RRC Pulse Shaping implementation see DSP.SE #40094.

The graphic I have copied below shows the significance of using pulse shaping, in this case for a 16-QAM waveform (where the real component which is shown in the top as a time domain signal with and without pulse shaping would have 4 levels, and the imaginary component would be similar). Note the blue spectrum which is associated with the rectangular transitions in the time domain, compared to the red spectrum after pulse shaping is applied. Given our concern with efficient use of spectrum, this is very important!

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    $\begingroup$ Correct; and just to emphasize: the square pulse is never used, except in very simple systems, where extreme cost reduction is worth the waste in bandwidth. Note that many undergrad-level books on communications only mention the square pulse; the reason is that they don't want to deal with the additional math required by pulse shaping. Those books are doing students a disservice! $\endgroup$
    – MBaz
    Mar 13 at 0:06
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    $\begingroup$ @MBaz agreed and without diminishing your statement, I want to add that GPS is one example where the square pulse is used (or nearly square: over 24 MHz BW for a 1 MHz chipping rate BPSK). In this case it is because the signal is so weak that there is no interference concerns and any such pulse shaping would diminish navigation and timing accuracy. $\endgroup$ Mar 13 at 0:54
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    $\begingroup$ @DanBoschen And in radar. We want maximum energy for the precious time we have when transmitting a pulse. Pulses are almost exclusively only phase (or frequency) modulated per the desired pulse compression response. $\endgroup$
    – Envidia
    Mar 13 at 20:39

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