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・ Chiroteuthis imperator
・ Chiroteuthis veranyi
・ Chirothecia
・ Chirotherium
・ Chirothrix
・ Chiroti
・ Chiroubles
・ Chiroxiphia
・ Chirp
・ Chirp (disambiguation)
・ Chirp (magazine)
・ Chirp (Modern Family)
・ Chirp (scratch)
・ Chirp compression
・ Chirp mass
Chirp spectrum
・ Chirp spread spectrum
・ Chirp transmitter
・ Chirp Z-transform
・ ChiRP-Seq
・ Chirpan
・ Chirpan Peak
・ Chirped mirror
・ Chirped pulse amplification
・ Chirpin'
・ Chirping
・ Chirping cisticola
・ Chirplet transform
・ Chirpy
・ Chirpy Burpy Cheap Sheep


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Chirp spectrum : ウィキペディア英語版
Chirp spectrum
The spectrum of a chirp pulse describes its characteristics in terms of its frequency components. This frequency-domain representation is an alternative to the more familiar time-domain waveform, and the two versions are mathematically related by the Fourier transform.
The spectrum is of particular interest when pulses are subject to signal processing. For example, when a chirp pulse is compressed by its matched filter, the resulting waveform contains not only a main narrow pulse but, also, a variety of unwanted artifacts many of which are directly attributable to features in the chirp's spectral characteristics.
The simplest way to derive the spectrum of a chirp, now computers are widely available, is to sample the time-domain waveform at a frequency well above the Nyquist limit and call up an FFT algorithm to obtain the desired result. As this approach was not an option for the early designers, they resorted to analytic analysis, where possible, or to graphical or approximation methods, otherwise. These early methods still remain helpful, however, as they give additional insight into the behavior and properties of chirps.
== The Fourier transform of a chirp pulse ==
A general expression for an oscillatory waveform, centered on frequency
is
s(t)= a(t).exp(+ \theta(t)) )
where a(t) and (t) give the amplitude and phase variations of the waveform s, with time.
The frequency spectrum of this waveform is obtained by calculating the Fourier Transform of s(t), i.e.
S(\omega) =\int_^s(t).exp(-j\omega t).dt =
\int_^a(t).exp(t + \theta(t)) ).exp(-j\omega t).dt
so
S(\omega)=\int_^a(t).exp(\left \ ).dt
In a few special cases, the integral can be solved to give an analytical expression, but often the characteristics of a(t) and (t) are such that the integral can only be evaluated by an approximation algorithm or by numerical integration.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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