Principles of Marine Bioacoustics pp 177-226 | Cite as

# Fourier Analysis

Chapter

First Online:

## The Time and Frequency Domains

Any signal can be represented either in the time domain with its amplitude displayed as a function of time or in the frequency domain with its amplitude displayed as a function of frequency. The time domain representation of a signal is usually referred to as the waveform, or waveshape of the signal. Oscilloscopes are often used to observe the waveforms of signals. The frequency representation of a signal is usually referred to as the frequency spectrum (or just spectrum) of the signal. Spectrum analyzers are often used to observe the spectral characteristics of continuous or long-duration (on the order of several seconds) signals. An example of a 1 v rms, 120 kHz sinusoidal signal observed with an oscilloscope and a sweep frequency spectrum analyzer is shown in Fig.
6.1 . The frequency resolution of the spectrum analyzer used to obtain the display was 1 kHz. The frequency analyzer display in Fig.
6.1is essentially the magnitude of the output of a...

## Keywords

Fast Fourier Transform Fourier Series Discrete Fourier Transform Inverse Fourier Transform Side Lobe
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

- Au, W. W. L. and Floyd, R. W. (1979). “Digital equalization of underwater transducers for the projection of broadband acoustic signals,” J. Acoust. Soc. Am.
**65**, 1585–1588.CrossRefGoogle Scholar - Bogert, B. P., Healy, M. J., and Tukey, J. W. (1963). “The quefrequency analysis of time series for echoes: cepstrum, pseudo autocovariance, cross spectrum and Saphe cracking,” in
*Time Series Symposium*, M. Rosenblatt, ed. (Wiley, New York), pp. 201–243.Google Scholar - Brigham, E. O. (1988).
*The Fast Fourier Transform and Its Applications*(Prentice Hall, Englewood Cliffs, New Jersey).Google Scholar - Bracewell, R. M. (1976).
*The Fourier Transform and Its Application*(McGraw-Hill, New York).Google Scholar - Bracewell, R. N. (1978).
*The Fourier Transform and its Applications (2nd Edition)*. McGraw-Hill, N.Y.Google Scholar - Cooley, J. W. and Tukey, J. W. (1965). “An algorithm for the machine calculation of complex Fourier series,” Math. Of Comput.,
**19**, 297–301.CrossRefGoogle Scholar - Cooley, J. W., Lewis, P. A. W., and Welch, P. D. (1967), “Historical notes on the fast Fourier transform,” Proc. IEEE,
**55**, 1676–1677.CrossRefGoogle Scholar - Harris, F. J. (1976). “On the use of windows for harmonic analysis with the discrete Fourier Transform,” Proc. IEEE,
**66**, 51–83.CrossRefGoogle Scholar - Kemerait, R. C., and Childers, D. G. (1972). “Signal detection and extraction by cepstrum techniques.” IEEE Trans. Info. Theory,
**IT-18**, 745–759.Google Scholar - Kraniauskas, P. (1992).
*Transforms in Signals and Systems*(Addison-Wesley,Wokingham, England).Google Scholar - Lyons, R. (1997).
*Understanding Digital Signal Processing*(Addison-Wesley, Workingham, England).Google Scholar - Papoulis, A. (1984).
*The Fourier Integral and Its Applications*, 2 nd ed. (McGraw-Hill, New York).Google Scholar - Ramirez, R. W. (1985).
*The FFT Fundamentals and Concepts*(Prentice Hall, Englewood Cliffs, New Jersey).Google Scholar

## Copyright information

© Springer Science+Business Media, LLC 2008