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Sep 19, 2021 at 16:18 comment added MBaz @user13764383 You're very welcome; I'm glad the answer was helpful.
Sep 19, 2021 at 11:12 comment added user13764383 Hi Mbaz, thank you for your detailed, formally defined response, it will take some work to decode, but now I have a useful future reference on hand! Also your lexical definition is helpful: “a symbol is a real number that belongs to a set called a constellation, selected as a pulse amplitude in order to convey a specific group of 𝑘 bits to the receiver.”
Sep 14, 2021 at 17:40 history edited MBaz CC BY-SA 4.0
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Sep 14, 2021 at 17:29 comment added MBaz @user253751 That is correct, but I thought that was too much detail to add to an already long answer.
Sep 14, 2021 at 15:00 comment added MBaz @TimWescott Thanks for the comments. The symbols are in fact real numbers. In note six I mentions FSK. I will add a note on OFDM, where each subcarrier is still linearly-modulated.
Sep 14, 2021 at 14:50 comment added TimWescott "Assign each of the M bit combinations to a real number $c_i$" -- better wording would be "integer" rather than "real number" -- a real number implies continuity. Not all signals are impressed on Nyquist pulses (i.e., GMSK), or on the same Nyquist pulse (i.e. OFDM, with each frame viewed as a collection of a whole lot of signals).
Sep 14, 2021 at 12:54 history answered MBaz CC BY-SA 4.0