Conclusion

This chapter has covered just enough about complex numbers to enable us to talk about the discrete Fourier transform.

Manipulations of complex numbers in Matlab and Octave are illustrated in §I.1.

To explore further the mathematics of complex variables, see any textbook such as Churchill [13] or LePage [35]. Topics not covered here, but which are important elsewhere in signal processing, include analytic functions, contour integration, analytic continuation, residue calculus, and conformal mapping.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.