First Principles of Discrete Systems and Digital Signal Processing

1. Introduction. Preview. Processing of Speech Signals. Processing of Seismic Signals. Radar Signal Processing. Image Processing. Kalman Filtering and Estimators. Review. References and Other Sources of Information 2. Signals and Systems. Preview. Types of Signals. Sequences Some Basic Sequences. Shifted and Special Sequences. Exponential and Sinusoidal Sequences. General Periodic Sequences. Sampling Continuous-Time Sinusoids and the Sampling Theorem. Systems and Their Properties. Linearity. Time-Invariance. Linear-Time Invariant (LTI) Systems. Stability. Causality. Approximation of Continuous-Time Processes by Discrete Models. Discrete Approximation of Integration. Discrete Approximation of Differentiation. Review. Vocabulary and Important Relations. Problems. References and Other Sources of Information. 3. Linear Time-Invariant Systems. Preview. Linear Constant-Coefficient Difference Equations. The Geometric Series--An Important Relationship. Difference Equations for Nth-Order Systems. Computer Solution of Difference Equations. System Diagrams or Realizations. Unit Sample Response. Convolution. A General Way to Find System Response. Computer Evaluation of Convolution. Analytical Evaluation of Convolution. An Application: Stability and the Unit Sample Response. Interconnected Systems. Cascade Connection. Parallel Connection. Initial Condition Response and Stability of LTI Systems. Forced and Total Response of LTI Systems. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 4. Frequency Response and Filters. Preview. Sinusoidal Steady-State Response of LTI Systems. Frequency Response. Sinusoidal Steady--State Response--General Statement. The Nature of H(Ejq). Computer Evaluation of Frequency Response. Frequency Response from the System Difference Equations. Filters. A Typical Filtering Problem. Comparison of Two Filters. Ideal Filters. Interconnected Systems. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 5. Frequency Response--A Graphical Method. Preview. Graphical Concepts. Geometric Algorithms for Sketching the Frequency Response. Graphical Design of Filters. Stability. Effects of Poles and Zeros on the Frequency Response. Correspondence Between Analog and Digital Frequencies. Some Design Problems. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 6. Z-Transforms. Preview. Definitions. Right-Sided Sequences--Some Transform Pairs. Sample (Impulse) Sequence. Step Sequence. Real Exponential Sequence. Complex Exponential Sequence. General Oscillatory Sequence. Cosine Sequence. Properties and Relations. Linearity. Shifting Property. Multiplication by n and Derivatives In z. Convolution. Transfer Functions. Stability. Frequency Response Revisited. The Evaluation of Inverse Transforms. Inverse Transforms from the Definition. Inverse Transforms from Long Division. Inverse Transforms from Partial Fraction Expansions and Table Look-Up. Partial Fraction Expansion--General Statement. Checking Partial Fraction Expansions and Inverse Transforms. Solution of Difference Equations. Connections Between the Time Domain and the z-Domain. Poles and Zeros and Time Response. System Response to Some Special Inputs. General Results and Miscellany. Noncausal Systems. Convergence and Stability. The Inversion Formula. Review. Vocabulary and Important Relations. Problems. References and Other Sources of Information. 7. Discrete Fourier Transform. Preview. Periodic Sequences. Complex Exponentials. Discrete Fourier Series. Finite Duration Sequences and the Discrete Fourier Transform. Some Important Relationships. DFTs and the Fourier Transform. Relationships Among Record Length, Frequency Resolution, and Sampling Frequency. Properties of the DFT. Linearity. Circular Shift of a Sequence. Symmetry Properties. Alternative Inversion Formula. Duality and the DFT. Computer Evaluation of DFTs and Inverse DFTs. Another Look at Convolution. Periodic Convolution. Circular Convolution. Frequency Convolution. Correlation. Some Properties of Correlation Sequences. Circular Correlation. Computer Evaluation of Correlation. Block Filtering or Sectioned Convolution. Spectrum Analysis. Periodogram Methods for Spectrum Estimation. Use of Windows In Spectrum Analysis. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 8. The Fast Fourier Transform. Preview. Decomposition in Time. Development of the Basic Algorithm. Computer Evaluation of the Algorithm. Decomposition in Frequency.Variations of the Basic Algorithms. Fast Convolution. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 9. Nonrecursive Filter Design. Preview. Design by Fourier Series. Fourier Coefficients. Lowpass Design. Highpass, Bandpass and Bandstop Design. Gibbs' Phenomenon. Windows in the Fourier design. Design of a Differentiator. Linear Phase Characteristics. Comb Filters. Design by Frequency Sampling. Design Using the Inverse Discrete Fourier Transform. Frequency Sampling Filters. Computer-Aided Design (CAD) of Linear Phase Filter. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 10. Recursive Filter Design. Preview. Analog Filter Characteristics Sinusoidal Steady-State. Frequency Response, Graphical Method. Computer Evaluation of Frequency Response. Determination of Filter Transfer Function from Frequency Response. Analog Filter Design. Butterworth Lowpass Prototype Design. Chebyshev Lowpass Prototype Design. Elliptic Lowpass Prototype Design. Analog Frequency Transformations. Design of Lowpass, Highpass, Bandpass, and Bandstop Filters. Digital Filter Design. Matched z-Transform Design. Impulse and Step-Invariant Design. Bilinear Transform Design. Digital Frequency Transformations. Direct Design of Digital Lowpass, Highpass, Bandpass, and Bandstop Filters. Optimization. Some Comments on Recursive and Nonrecursive Filters. Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. 11. Structures, State Equations, and Applications. Preview. System Implementations. Direct Structure. Second-Order Substructures. Cascade Realization. Parallel Realization (Partial Fraction Expansion). Lattice Filters. Mason's Gain Rule. State Difference Equations. Writing State Equations. Solution of State Equations. Computer Solution of State Equations. Two Different Systems. Digital Control of a Continuous-Time System. Deconvolution Review. Vocabulary and Important Relations Problems. References and Other Sources of Information. Appendix A: Complex Numbers. Appendix B: Fourier Series. Appendix C: Laplace Transform. Appendix D: Frequency Response of Continuous-Time (Analog) Systems. Appendix E: .A Summary of Fourier Paris. Appendix F: Matrices and Determinants. Appendix G: Continuous-Time Systems with a Piecewise Constant Input. Answers to Selected Problems. Index.