TABLE OF CONTENTS We all use Fourier analysis every day without even knowing it. Cell phones, disc drives, DVDs, and JPEGs all involve fast finite Fourier transforms. This chapter discusses both the computation and the interpretation of FFTs.
The acronym FFT is ambiguous. The first F stands for both "fast" and "finite." A more accurate abbreviation would be FFFT, but nobody wants to use that. In MATLAB the expression fft(x) computes the finite Fourier transform of any vector x. The computation is fast if the integer n = length(x) is the product of powers of small primes. We discuss this algorithm in section 8.6.
Touch-tone telephone dialing is an example of everyday use of Fourier analysis. The basis for touch-tone dialing is the Dual Tone Multi-Frequency (DTMF) system. The program touchtone demonstrates how DTMF tones are generated and decoded. The telephone dialing pad acts as a 4-by-3 matrix (Figure 8.1). Associated with each row and column is a frequency. These basic frequencies are
fr = [697 770 852 941]; fc = [1209 1336 1477];
If s is a character that labels one of the buttons on the keypad, the corresponding row index k and column index j can be found with
switch s case '*', k = 4; j = 1; case...
