MATHEMATICAL BACKGROUND AND ANALYSIS TECHNIQUES

• Published in: Digital Communications with Emphasis on Data Modems pp. 1 - 80
• Main Author: Middlestead, Richard W
• Format: Book Chapter
• Language: English
• Published: United States Wiley 2017; John Wiley & Sons, Incorporated; John Wiley & Sons, Inc
• Edition: 1
• Subjects: amplitude modulation; correlation function; cumulative distribution functions; digital communications; discrete Fourier transform; ELECTRONICS & COMMUNICATIONS ENGINEERING; fast Fourier transform; frequency modulation; phase modulation; probability density functions; window functions; Frequency modulation; Baseband; Phase modulation; Mathematical model; Transforms; Demodulation
• ISBN: 9780470408520; 0470408529
• DOI: 10.1002/9781119011866.ch1

This chapter provides the foundation for modeling and finding practical design solutions to communication system performance specifications. It describes the commonly used waveform modulations characterized as amplitude modulation (AM), phase modulation (PM), and frequency modulation (FM) waveforms. The chapter discusses the discrete Fourier transform (DFT), the fast Fourier transform (FFT), the pipeline implementation of the FFT, and applications involving waveform detection, interpolation, and power spectrum estimation. It introduces the concept of random variables and various probability density functions (pdf) and cumulative distribution functions (cdf) for continuous and discrete random variables. It focuses on characterization of several window functions that are used to improve the performance the FFT, decimation filtering, and signal parameter estimation. The chapter focuses on the subject of autocorrelation and crosscorrelation of real and complex deterministic functions and concludes with a list of frequently used mathematical formulas.