MATHEMATICAL BACKGROUND AND ANALYSIS TECHNIQUES - Middlestead, Richard W (Digital Communications with Emphasis on Data Modems, 2017)
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.