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The Rayleigh bandwidth of a simple radar pulse is defined as the inverse of its duration. For example, a one-microsecond pulse has a Rayleigh bandwidth of one megahertz. [1] The essential bandwidth is defined as the portion of a signal spectrum in the frequency domain which contains most of the energy of the signal. [2]
Another method of specifying spectral width is a special case of root-mean-square deviation where the independent variable is wavelength, λ, and f (λ) is a suitable radiometric quantity. The relative spectral width, Δλ/λ, is frequently used where Δλ is obtained according to note 1, and λ is the center wavelength.
It equals the spatial frequency. For example, a wavenumber in inverse centimeters can be converted to a frequency expressed in the unit gigahertz by multiplying by 29.979 2458 cm/ns (the speed of light, in centimeters per nanosecond); [5] conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space.
The power spectrum is always real and non-negative, and the spectrum of a real valued process is also an even function of frequency: () = (). For a continuous stochastic process x(t), the autocorrelation function R xx ( t ) can be reconstructed from its power spectrum S xx (f) by using the inverse Fourier transform
Free spectral range (FSR) is the spacing in optical frequency or wavelength between two successive reflected or transmitted optical intensity maxima or minima of an interferometer or diffractive optical element. [1]
In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum amplitude. Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric. The term full duration at half maximum (FDHM) is preferred when the independent variable is time.
Early uses of the term Nyquist frequency, such as those cited above, are all consistent with the definition presented in this article.Some later publications, including some respectable textbooks, call twice the signal bandwidth the Nyquist frequency; [6] [7] this is a distinctly minority usage, and the frequency at twice the signal bandwidth is otherwise commonly referred to as the Nyquist rate.
For the case of a carrier modulated by a single sine wave, the resulting frequency spectrum can be calculated using Bessel functions of the first kind, as a function of the sideband number and the modulation index. The carrier and sideband amplitudes are illustrated for different modulation indices of FM signals.