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I previously asked at which stage pulse shaping is applied in a WiFI transmitter and my question was closed due to duplication. The answers I was directed to have only served to confuse the issue for me. I have therefore reworded my question as suggested. I understand the need for pulse shaping of an RF signal (to reduce bandwidth) and the purpose of a matched filter in the receiver (to deal with the ISI that results) but it is not clear at which stage pulse shaping is applied in the transmitter; before or after modulation. This post was deemed to be an answer to my original question (which I read before I first posed).

The first graphic in the post implies that pulse shaping, at least for 16QAM, is done after line coding but before modulation, because it shows a shaped square wave. I understood that a 16QAM signal in the time domain, after modulation, is a sequence of sinusoidal waveforms of various phases and amplitudes, and that this modulated signal includes sudden changes in amplitude that would benefit from smoothing, just before the signal is converted to radio waves. Because the diagram shows the result of shaping a square wave, it implies either that pulse shaping is done immediately after line coding but before the symbols are created by modulation, or that it is the shaped square wave that gets modulated.

I would like to known which? Alex’s response to my previous question seemed to confirm what I originally thought. He said that “Pulse shaping (for the purpose of waveform smoothing and bandwidth limiting) is always applied at the far end of the TX chain, ie before DAC and therefore after the BPSK modulation.” I am not familiar with Alex’s terminology but by “the far end of the TX chain” I presume Alex means just before the antenna converts the signal to radio waves, and that “DAC” (digital to analogue conversion) is what is going on in the antenna. This seems to contradict the diagram which shows a shaped square wave.

My new question is therefore exactly when is pulse shaping applied in the radio transmitter, before or after modulation, and is it applied differently in BPSK, QPSK and 16QAM?

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  • $\begingroup$ Pulse shaping (for the purpose of waveform smoothing and bandwidth limiting) is always applied at the far end of the TX chain, ie before DAC and therefore after the BPSK modulation. Check this answer. I would also consider this question as a duplicate of this. $\endgroup$
    – AlexTP
    Commented Oct 29, 2023 at 10:58
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    $\begingroup$ Pulse shaping is not typically used in WiFI OFDM modulations. See this other post that details this further. dsp.stackexchange.com/questions/74087/… $\endgroup$ Commented Oct 29, 2023 at 12:34
  • $\begingroup$ Thanks for the reply. Forgive my unfamiliarity with the terminology but by “the far end of the TX chain” do you mean at the antenna end? and by “DAC” do you mean the generation of an RF wave in the antenna? Before I posted, I read the one you linked to but the graphic threw me. I thought that a 16QAM signal, after modulation, was a sequence of waveforms of various phases and amplitudes. The diagram shows the result of shaping a square wave, implying that shaping is done before the symbols are created by modulation. Is pulse shaping in the transmitter applied at a different stage with BPSK? $\endgroup$
    – Drummy
    Commented Oct 30, 2023 at 10:04
  • $\begingroup$ If the question is re-opened I'll post a more complete answer; in the meantime: in modern digital narrowband radios, pulse-shaping should be thought of as part of line coding. The digital back-end generates a sequence of pulses of varying amplitude $\sum_k a_k p(t-kT)$ that convey information. Here, $a_k$ are the BPSK, QPSK, 16-QAM or whatever amplitudes. This signal is then fed to a DAC and then to the analog front-end for upconversion, amplifications and transmission. $\endgroup$
    – MBaz
    Commented Oct 31, 2023 at 16:57

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