Fourier Analysis By Example

This book begins with examples of calculating the Fourier Transform of various functions and shows that calculating the Fourier Transform of a periodic function leads to the Fourier Series, calculating the Fourier Transform of a sampled function leads to the Discrete-Time Fourier Transform (DTFT), and calculating the Fourier Transform of a sampled, periodic function leads to the Discrete Fourier Transform (DFT). The book includes a detailed derivation of the Fast Fourier Transform (FFT) algorithm for computing the Discrete Fourier Transform. Numerous MATLAB examples of using the FFT include examples of amplitude and frequency modulation as well as binary and quadrature phase shift keying of digital signals. The book shows how the Discrete Cosine Transform (DCT) can be derived from the FFT, and the example of using the two-dimensional DCT as part of the JPEG image compression algorithm is described. Examples from Fourier optics are also included in the book.