Basperiod

Basperiod refers to the fundamental period of a periodic function or signal—the smallest positive interval T with f(t+T) = f(t) for all t. The term is encountered mainly in translations from Germanic languages where the equivalent term basperioden or basperiod is used.

For a signal composed of multiple frequency components, the basperiod is the least common multiple of the component periods, i.e., the smallest T such that every component repeats. If component frequencies are integer multiples of a fundamental frequency f0, then basperiod T0 = 1/f0.

In continuous time, f0 = 1/T0; angular frequency ω0 = 2π/T0. For discrete-time signals, the basperiod is the smallest positive integer N such that x[n+N] = x[n] for all n. The corresponding fundamental frequency is ω0 = 2π/N radians.

Examples help clarify the concept. A pure sine wave with period 5 has basperiod 5. A signal composed of sin(2πt/5) + sin(2πt/10) has basperiod 10, since the second component imposes a longer repetition cycle that governs the overall periodicity.

Applications of basperiod include Fourier analysis, sampling, synchronization, and systems design. In many English-language contexts, the term is more commonly expressed as base period or fundamental period. See also fundamental frequency, period, and least common multiple.