Introduction to Discrete-time Signals and Systems

Index: 1. Introduction 1.1 Continuous- and discrete-time signals 1.2 Delta and step functions 1.3 Sampling 1.4 Aliasing and the sampling theorem 1.5 Anti-aliasing 1.6 Interpolation 1.7 Power and energy of DT signals 1.8 Linear time-invariant systems 1.9 Fourier descriptions of CT signals 1.10 Interpolation 1.11 Summary 1.12 Exercises 2. Difference Equations 2.1 A moving-average filter 2.2 An infinite impulse response filter 2.3 General form of difference equation 2.4 Discrete differentiation and integration 2.5 Solution of difference equations 2.6 Summary 2.7 Exercises 3. The z-transform 3.1 Definition 3.2 Taylor and Laurent series 3.3 Relation to Fourier transform 3.4 Illustrative examples 3.5 Fundamental properties 3.6 The system function H(z) 3.7 The z-plane 3.8 Frequency response of a DT system 3.9 The inverse z-transform 3.10 Time response of a DT system 3.11 Summary 3.12 Exercises 4. Infinite impulse response (IIR) filters 4.1 The bilinear transform 4.2 Impulse invariance 4.3 Summary 4.4 Exercises 5. The discrete Fourier transform 5.1 Spectrum of a sampled signal 5.2 Definition of the DFT 5.3 Illustrative examples 5.4 The inverse DFT 5.5 Further properties of the DFT 5.6 Parseval's theorem and DT signals 5.7 Truncation and windowing 5.8 Interpolation by zero-padding 5.9 Ideal interpolation 5.10 Linear filtering using the DFT 5.11 Summary 5.12 Exercises 6. Finite impulse response (FIR) filters 6.1 Properties of FIR filters 6.2 Fourier series truncation 6.3 Windowing 6.4 Frequency sampling method 6.5 Computer-based design 6.6 Summary 6.7 Exercises 7. The fast Fourier transform 7.1 Direct evaluation of the DFT 7.2 Radix-2 algorithms 7.3 Algorithms for composite-N 7.4 The DFT of real data 7.5 Summary 7.6 Exercises 8. Random signals 8.1 Moments of a random signal 8.2 Stationarity and ergodicity 8.3 The probability density function 8.4 The autocorrelation function 8.5 The cross-correlation function 8.6 The power spectrum 8.7 Random signals and linear systems 8.8 Estimation from finite-length sequences 8.9 Summary 8.10 Exercises Contents