Mathematics of Periodicity 1
Functions
Function: procedure which, for any set of inputs
in some range, assigns a corresponding output
Some Non-Periodic Functions (of 1 Variable)
- f(x) = 5
- f(x) = x
- f(x) = x^2 ("x squared")
Some Periodic Functions
- Continuous periodic functions
- sin (x)
- cox (x)
- Discontinuous periodic functions
- Functions with varying periods or amplitudes
- cos (x^2)
- (cos (x)) / x
Phase
- Phase: in a periodic process, the point to which the
repeating process has advanced considered in relation to
an assumed starting point
- Phase vs. time: phase ignores absolute time because it
cares only about position within the cycle, independent of
which cycle it is and how long the period is
- Phase angle: a measure of phase, usually in
radians (0 to 2
) or a proportion of a cycle
(0 to 1)
- In phase: describing two or more periodic processes
whose phases match; that is, the phases of maximum or minimum
amplitude are simultaneous
- Functions in phase with each other
- sin(x), .5 sin(x)
- cos(x), cos(2x)
- Functions out of phase with each other
- sin(x), cos(x)
- sin(x), sin(x+)
