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Plot of normalized function (i.e. ()) with its spectral frequency components.. The unitary Fourier transforms of the rectangular function are [2] = = (), using ordinary frequency f, where is the normalized form [10] of the sinc function and = (/) / = (/), using angular frequency , where is the unnormalized form of the sinc function.
Pulse wave. A pulse wave or pulse train or rectangular wave is a non-sinusoidal waveform that is the periodic version of the rectangular function. It is held high a percent each cycle (period) called the duty cycle and for the remainder of each cycle is low. A duty cycle of 50% produces a square wave, a specific case of a rectangular wave.
Microwave cavity. Two microwave cavities (left) from 1955, each attached by waveguide to a reflex klystron (right) a vacuum tube used to generate microwaves. The cavities serve as resonators (tank circuits) to determine the frequency of the oscillators. A microwave cavity or radio frequency cavity (RF cavity) is a special type of resonator ...
Spectral leakage. The Fourier transform of a function of time, s (t), is a complex-valued function of frequency, S (f), often referred to as a frequency spectrum. Any linear time-invariant operation on s (t) produces a new spectrum of the form H (f)•S (f), which changes the relative magnitudes and/or angles (phase) of the non-zero values of S ...
Sinc function. In mathematics, physics and engineering, the sinc function, denoted by sinc (x), has two forms, normalized and unnormalized. [1] In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa (x). [2]
Most popular window functions are similar bell-shaped curves. In signal processing and statistics, a window function (also known as an apodization function or tapering function[1]) is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are symmetric around the middle of the interval, approach ...
Bandwidth is a key concept in many telecommunications applications. In radio communications, for example, bandwidth is the frequency range occupied by a modulated carrier signal. An FM radio receiver's tuner spans a limited range of frequencies. A government agency (such as the Federal Communications Commission in the United States) may ...
Sinc-in-time. Sinc-in-time is an ideal filter that removes all frequency components above a given cutoff frequency, without attenuating lower frequencies, and has linear phase response. It may thus be considered a brick-wall filter or rectangular filter. Its impulse response is a sinc function in the time domain: