pulsedtrain

A pulsedtrain, often called a pulse train, is a periodic sequence of pulses used in signal generation, measurement, and communications. It is produced by repeating a single pulse shape p(t) at a fixed interval T, yielding s(t) = sum_{n=-∞}^{∞} p(t - nT). The pulse width is τ, and the duty cycle is D = τ/T (for non-overlapping pulses, τ ≤ T).

The repetition frequency is f0 = 1/T. The time-domain periodicity leads to a discrete spectrum: the Fourier transform of s(t) consists of spectral lines at multiples of f0, with amplitudes proportional to the Fourier transform of the single pulse, P(f). In general, shorter pulses (smaller τ) broaden the spectral content, while a longer period T increases line spacing in frequency.

Applications include radar and lidar for range finding, fiber-optic and microwave communications for timing and signaling, and instrumentation such as sampling clocks, pulsed-laser systems, and time-domain reflectometry. Pulse trains are also used to drive switches and to implement timing references in digital systems.

Practical design must consider non-idealities: pulse shape distortion, jitter in timing, bandwidth limitations, and the finite observation window. In theory, a perfect infinite pulse train carries infinite energy; real implementations use finite duration and finite energy pulses.

Related concepts include impulse trains (Dirac combs) and pulse-width modulation, with the latter varying τ within each period to control average power.