Chirp spectrum

<p>The spectrum of a <a href="/facts/Chirp/hCQrvcz8">chirp</a> 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 <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a>.  The spectrum is of particular interest when pulses are subject to <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>.    For example, when a chirp pulse is compressed by its <a href="/facts/Matched_filter/Tl8Bm687">matched filter</a>, 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.
</p><p>A simple way to derive the spectrum of a chirp using a computers, is to sample the time-domain waveform at a frequency well above the <a href="/facts/Nyquist_limit/zwFUKdVR">Nyquist limit</a> and use an <a href="/facts/Fast_Fourier_transform/caT7UUCh">FFT</a> algorithm to obtain the desired result.  As this approach was not an option for the early designers, they resorted to analytic analysis, or and to graphical or approximation methods. These early methods still remain helpful, however, as they give additional insight into the behavior and properties of chirps.
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Chirp spectrum open-in-new

Chirp spectrum