Rectangular function

A function that has a constant value over a finite interval and is zero outside it. Its graph forms a rectangular pulse, with endpoint values depending on convention.

Indicator function: A function equal to one on a specified set and zero elsewhere. A rectangular pulse is a scaled indicator of an interval.
Pulse-amplitude modulation: A modulation method that encodes information in the amplitudes of regularly spaced pulses. Its signal pulses can be modeled as shifted rectangular functions.
Piecewise function: A function defined by different formulas or rules on different parts of its domain. A rectangular function is a simple piecewise function with constant and zero regions.
Triangular function: A piecewise-linear function that rises to a peak and falls to zero, forming a triangle when graphed. Unlike a rectangular pulse, its amplitude varies continuously across its support.
Gibbs phenomenon: Overshoot near a jump discontinuity that persists when a function is approximated by Fourier series. The pulse's abrupt edges produce ringing in truncated Fourier representations.
Heaviside step function: A function that is zero for negative inputs and one for positive inputs, with a convention at zero. Subtracting two shifted steps creates a finite rectangular pulse.
Zero-order hold: A reconstruction method that holds each sampled value constant until the next sample. Each held sample contributes a rectangular segment to the reconstructed signal.
Support (mathematics): The closure of the set where a function is nonzero, under the usual topological definition. Its support identifies the interval occupied by a rectangular pulse.
Gaussian function: A smooth bell-shaped function defined by an exponential of a negative quadratic. Its tails extend indefinitely instead of ending at sharp rectangular boundaries.
Spectral leakage: The spreading of signal energy across measured frequency bins when an observation does not contain an integer number of cycles. Finite rectangular observation windows convolve spectra with a sinc-shaped response.

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