The Fourier Integral Transform
The natural extension of the Fourier series to encompass time signals of infinite length, i.e., non-repetitive continuous signals, is the Fourier Integral Transform, or more simply the Fourier Transform. This integral will transform any continuous time signal of arbitrary shape into a continuous spectrum extending to infinite frequency. An interesting characteristic of the Fourier Transform is that an event encompassing a short time interval will be spread out over a wide frequency range and vice versa. This was seen in the Introduction to Vibration chapter where a spectrum of a short impulse is shown.
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