Perusjaksoja

Perusjaksoja is the plural form of perusjakso, a Finnish term meaning fundamental period or base period. In mathematics and physics, perusjakso refers to the smallest positive interval T over which a periodic function repeats, so that f(t + T) = f(t) for all t in its domain. If such a smallest T exists, it is the fundamental period; any other period of the function is a multiple of T. In discrete-time contexts, for a sequence x[n], the fundamental period N is the smallest positive integer with x[n + N] = x[n] for all n.

The concept is central to analyses that rely on repeating behavior, such as Fourier analysis, spectral decomposition, and signal reconstruction. Knowing the fundamental period enables the definition of the fundamental frequency f0 = 1/T (or, in discrete time, f0 = 1/N samples per sample interval) and clarifies how a signal can be efficiently represented in the frequency domain.

Examples: sin(t) has fundamental period 2π in continuous time. A square wave with period T has the fundamental period T (provided the waveform repeats every T without a smaller repeating unit). In discrete time, a sequence that repeats every N samples has fundamental period N.

Notes: The term is common in Finnish technical literature dealing with periodic phenomena, waves, and harmonic analysis. The plural form perusjaksoja is used when discussing multiple fundamental periods or several functions. The concept is related to, but distinct from, a function’s overall period, which may be a multiple of the fundamental period. See also Period, Fundamental frequency, Fourier series, Signal processing.