Exponentials

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Exponentials

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Exponentials

The canonical form of an exponential function, as typically used in signal processing, is

\

where $\ is called the time constant of the exponential. $A$ is the peak amplitude, as before. The time constant is the time it takes to decay by $1/e$, i.e.,
\

A normalized exponential decay is depicted in Fig. 5.5.
Figure 5.5:The decaying exponential$Ae^{-t/\.
\



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