Fundamental Data Compression

Appendix C

Fourier series and harmonic analysis

An important advantage of the Fourier series representation of a function is that it can represent a periodic function containing a number of finite discontinuities with no requisite of the use of successive differential coefficients as in Taylor series.

C.1 Fourier series

In mathematical expression, we have

(C.1)

where f(t)= f(t + nT) and n is an integer.

Using Euler’s identity e^jx= cos x + j sin x, the formula in C.1 can be represented in exponential form.

DFT may be useful for data compression ...