Aperiodic Function (Non periodic Function) Definition
The class of aperiodic (non periodic) functions includes the subtypes of almost periodic and quasiperiodic functions.
Although an aperiodic function isn’t not periodic in nature, there is a very close relationship: mathematically, you can think of them as periodic functions with a period of infinity (Adams, 2020).
“The transition from a periodic function to an aperiodic function is accomplished by allowing the fundamental period T to increase without limit. In other words, if T becomes infinite, the function never repeats itself and, therefore, the function is aperiodic” ~ Caggiano (1996)
Aperiodic Function Subclasses
Two important subclasses of aperiodic functions are almost periodic and quasiperiodic functions.
At first, it might seem that subclasses of “non periodic functions” isn’t useful at all. But the opposite is true: many of these functions have very close relationships with periodic functions, mathematically speaking. What is considered “close” differs from author to author, but in general they are connected by their periodic nature:
- Almost-periodic function, although not periodic themselves, can be represented by a sum of two or more periodic functions.
- Quasiperiodic functions are a combination of periodic functions of different frequencies that never completely match up.
References
Adams, M. (2020). Continuous-Time Signals and Systems (Edition 2.0).
Caggiano, D. (1996). Comparison of Different Signal Processing Algorithms to Extract the Respiration Waveform from the ECG. Retrieved November 13, 2020 from: http://archives.njit.edu/vol01/etd/1990s/1996/njit-etd1996-014/njit-etd1996-014.pdf
Depner, J. & Rasmussen, T. (2017). Hydrodynamics of Time-Periodic Groundwater Flow: Diffusion Waves in Porous Media, Geophysical Monograph 224. American Geophysical Union.
Dua, R. (2014). Experimentation of Transforms. Retrieved November 13, 2020 from: http://web.mst.edu/~rdua/Digital%20Signal%20Processing_files/Sample%202.pdf
Stephanie Glen. "Aperiodic Function (Non Periodic)" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/aperiodic-function-non-periodic/
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