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FUNDER - Theoretical Background |
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SIGNALS - DEFINITIONS Real time The clock time, as opposed to any other time at which a significant event occurs. Perturbation time The shortest time at which a function of real time is not zero. Deterministic signal
Any observable, non-random function of real time,
Causal signal A signal that is zero before a given time. In other words, a signal for which a perturbation time is well defined. Periodic signal A signal which satisfies
where Heaviside's unit step function A signal defined as
Note that the value at initial time has been arbitrarily defined to be zero. The unit step is a causal signal. Furthermore, any causal signal satisfies the identity
for some time
Impulse An instantaneous signal of the form of a Dirac's delta. Final value of a signal The limit of the signal at long times,
Periodic signals do not have a final value.
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is the period.
Causal signals may be considered periodic if
eq. (1) holds at least after the perturbation time.
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