# Unity amplitude

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A sinusoidal waveform is said to have a unity amplitude when the amplitude of the wave is equal to 1.

$x(t)=a\sin(\theta (t))$ where $a=1$ . This terminology is most commonly used in digital signal processing and is usually associated with the Fourier series and Fourier Transform sinusoids that involve a duty cycle, $\alpha$ , and a defined fundamental period, $T_{o}$ .

Analytic signals with unit amplitude satisfy the Bedrosian Theorem. 

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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 that 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.