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Aperiodic Function (Non Periodic)

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Aperiodic Function (Non periodic Function) Definition

aperiodic functions

The class of aperiodic (non periodic) functions includes the subtypes of almost periodic and quasiperiodic functions.

An aperiodic function (or non periodic function) is any function that isn’t periodic (Depner & Rasmussen, 2017). As periodic functions repeat their values at set periods, you could also think of a non periodic function as one that doesn’t have repeating intervals.

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.


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:
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:

Stephanie Glen. "Aperiodic Function (Non Periodic)" From Calculus for the rest of us!

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