Digital Signals, Processors and Noise

Part 1 Introduction: background; sampling and analog-to-digital conversion; time-domain analysis - describing signals and processors, digital convolution; Fourier analysis - the discrete Fourier series, the Fourier transform; the z-transform - definition and properties, z-plane poles and zeros. Part 2 Digital filter design: non-recursive filters - introduction, the Fourier transform method, window functions, equiripple filters; recursive filters - introduction, the bilinear transformation, impulse-invariant filters. Part 3 The discrete and fast Fourier transforms: the discrete Fourier transform; the fast Fourier transform (FFT) - basis of the FFT, index mapping, twiddle factors and FFT butterflies, decimation-in-time algorithms, decimation-in-frequency algorithms, FFT processing, fast convolution. Part 4 Describing random sequences: introduction; basis measures of random sequences - amplitude distribution, mean, mean-square and variance, ensemble averages and time averages, autocorrelation, power spectrum, cross-correlation, cross-spectrum. Part 5 Processing random sequences: response of linear processors; white noise through a filter; system identification by cross-correlation; signals in noise - introduction, signal recovery, matched filter detection, signal averaging; appendix A - computer programs - list of programs and introductory notes; basic programs; PASCL programs; appendix B - tables of Fourier and z-transforms - the discrete Fourier series - properties; the Fourier transform of speriodic digital signals - properties and pairs; the unilateral z-transform - pairs; the unilateral z-transform - properties; the discrete Fourier transform - properties.