The reason it's hard to pin down an exact definition of "symbol" is because it's a really handy concept that can be stretched to aid us in doing a lot of useful math, but an all-inclusive definition gets tediously vague, while the nice concise definition that I might use for my problem over here may not fit with the nice concise definition that you need to use for your problem over there. In the words of that great communications theorist, William Shakespear, "There are more things in heaven and earth, Horatio, than are dream'd of in your philosophy". I'm not certain if this is the appropriate StackExchange to post the question if it's not should I try one of the following? : Out of interest, is there a mathematical/formal definition of a symbol? Perhaps that would help me.
Wikipedia Definition 2 (under Symbol (disambiguation): “Symbol (data), the smallest amount of data transmitted at a time in digital communications” A symbol is a waveform, a state or a significant condition of the communication channel that persists, for a fixed period of time” Wikipedia Definition 1 (under Symbol Rate): “A symbol may be described as either a pulse in digital baseband transmission or a tone in passband transmission using modems. Signal Processing StackExchange Definition: "A symbol is a symbolic representation of a baseband signal in digital communication."Įlectrical Engineering StackExchange Definition 1: "A symbol is any distinct state of the communication channel."Įlectrical Engineering StackExchange Definition 2: "A symbol is an information entity" Khan Academy definition: “A symbol can be broadly defined as the current state of some observable signal, which persists for a fixed period of time.” 4m 15s on this video which persists for a fixed unit of time in a communication channel" My definition 2: "A distinct state of a quantity of a waveform. My definition 1: "A distinct, observable state of a property of a physical medium. Here are various definitions I have found: The fellow defines the term symbol informally as "different states" and I do grasp the concept intuitively, however I am seeking a more formal definition. I’m looking for the simplest, precise definition of a Symbol
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