3.6.3 Fourier Transforms
Fourier series are useful for spectral analysis of a periodic function, with different
configurations of other functions that are not repeated regularly. For example,
thunder can occur once or repeatedly at irregular intervals, causing interference with
electronic or electrical equipment operating over a wide frequency range. This
suggests intuitively that a discrete signal produced by thunder has a spectrum of
diverse frequencies. When such discrete phenomena are analyzed, the Fourier
integral can be used instead of the Fourier series. The FðixÞ function denoted the f
(t) transform, the Fourier integral f(t), or spectral density function f(t) is defined by
Fig. 3.3 a 3D representation of a sinusoid in the time and frequency domain, b time domain,
c frequency amplitude, and d phase frequency (adapt. Chapra and Canale 1989)
66
3 Characterization of Turbulent Flow in the Surface Boundary Layer
Fourier series are useful for spectral analysis of a periodic function, with different
configurations of other functions that are not repeated regularly. For example,
thunder can occur once or repeatedly at irregular intervals, causing interference with
electronic or electrical equipment operating over a wide frequency range. This
suggests intuitively that a discrete signal produced by thunder has a spectrum of
diverse frequencies. When such discrete phenomena are analyzed, the Fourier
integral can be used instead of the Fourier series. The FðixÞ function denoted the f
(t) transform, the Fourier integral f(t), or spectral density function f(t) is defined by
Fig. 3.3 a 3D representation of a sinusoid in the time and frequency domain, b time domain,
c frequency amplitude, and d phase frequency (adapt. Chapra and Canale 1989)
66
3 Characterization of Turbulent Flow in the Surface Boundary Layer