Thursday, August 1, 2019

Very basic question about how we define frequency in signal processing


When talking about general periodic continuous-time signals for which x(t+T0)=x(t)

where T0 is the fundamental period we define the fundamental frequency ω0 as ω0=2π/T0.


The way I interpret this is that 1/T0 is the frequency of the signal in cycles per second and there are 2π radians in one cycle, therefore the angular frequency is 2π/T0 radians per second. But are there really 2π radians in one cycle in general?



Take x(t)=tan(t) for example. Its fundamental period is π and using the definition of fundamental frequency above, its fundamental frequency is 2 radians per second. But in the case of the tangent function, aren't there π radians in one cycle, as opposed to 2π radians? This would give us a definition of frequency as ω0=π/T0. Or do we refer to the unit circle by convention when talking about "cycles"?


Apologies if this question sounds very basic.




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