Linear Systems and Signals

PART I: INTRODUCTION. B. Background. B.1: Complex Numbers. B.2: Sinusoids. B.3: Sketching Signals. B.4: Some Useful Signal Operations. B.5: Mathematical Description of a Signal from its Sketch. B.6: Even and Odd Functions. B.7: Cramer's Rule. B.8: Partial Fraction Expansion. B.9: Vectors and Matrices. B.10: Miscellaneous. 1. Introduction to Systems. 1.1: Signals and Systems. 1.2: Classification of Systems. 1.3: System Model: Input-output Description. 1.4: Simultaneous Differential Equations. 1.5: Internal and External Description of a System. 1.6: State-Space Description of a System. 1.7: Summary. PART II: TIME-DOMAIN ANALYSIS OF LTI SYSTEMS. 2. Time-Domain Analysis: Continuous-Time Systems. 2.1: Introduction. 2.2: System Response to Internal Conditions: Zero-Input Response. 2.3: Unit Impulse Function. 2.4: System Response to External Input: Zero-State Response. 2.5: Numerical Convolution. 2.6: System Stability. 2.7: Intuitive Insights in System Behavior. 2.8: Classical Solution of Differential Equations. 2.9: Appendix 2.1: Determining the Impulse Response. 2.10: Summary. 3. Time-Domain Analysis: Discrete-Time Systems. 3.1: Discrete-Time Systems. 3.2: Discrete-Time Systems Equations. 3.3: System Response to Internal Conditions: zero-Input Response. 3.4: Unit Impulse Response. 3.5: System Response to External Input: zero-State Response. 3.6: System Stability. 3.7: Intuitive Insights in System Behavior. 3.8: Classical Solution of Linear Difference Equations. 3.9: Appendix 3.1: Determining Impulse Response. 3.10: Summary. PART III: FREQUENCY-DOMAIN (TRANSFORM) ANALYSIS OF LTI SYSTEMS. 4. Continuous-Time Systems: Laplace Transform Analysis. 4.1: The Laplace Transform. 4.2: Some Properties of the Laplace Transform. 4.3: Transform Solution of Differential and Integro-Differential Equations. 4.4: Analysis of Electrical Networks: Transformed Network Method. 4.5: Block Diagrams. 4.6: System Realization. 4.7: Frequency-Response of an LTIC System. 4.8: Bilateral Laplace Transform. 4.9: Appendix 4.1: Second Canonical Realization. 4.10: Summary. 5. Discrete-Time Systems: Z-Transform Analysis. 5.1: The Z-Transform. 5.2: Some Properties of the Z-Transform. 5.3: Z-Transform Solution of Difference Equations. 5.4: System Realization. 5.5: Frequency Response of Discrete-Time Systems. 5.6: Connection between the Z-Transform and Laplace Transform. 5.7: Bilateral Z-Transform. 5.8: Summary. PART IV: SIGNAL ANALYSIS. 6. Continuous-Time Signal Analysis: The Fourier Series. 6.1: Representation of Periodic Signals by Trigonometric Fourier Series. 6.2: Exponential. 6.3: Alternate View of Fourier Representation: Signal-Vector Analogy. 6.4: Summary. 7. Continuous-Time Signal Analysis: The Fourier Transform. 7.1: Nonperiodic Signal Representation by Fourier Integral. 7.2: Physical Appreciation of the Fourier Transform. 7.3: Transform of Some Useful Functions. 7.4: Some Properties of the Fourier Transform. 7.5: LTI System Analysis by Fourier Transform. 7.6: Signal Distortion During Transmission. 7.7: Ideal and Practical Filters. 7.8: Thinking in Time-Domain and Frequency-Domain: Two-Dimensional View of Signals and Systems. 7.9: Signal Energy. 7.10: Data Truncation: Window Functions. 7.11: Summary. 8. Sampling. 8.1: The Sampling Theorem. 8.2: Dual of the Sampling Theorem: Spectral Sampling. 8.3: Numerical Computation of Fourier Transform: The Discrete Fourier Transform (DFT). 8.4: Summary. 9. Analysis of Discrete-Time Signals. 9.1: Discrete-Time Periodic Signals. 9.2: Nonperiodic Signals: The Discrete-Time Fourier Transform (DTFT). 9.3: Properties of DTFT. 9.4: LTID System Analysis by STFT. 9.5: Relationships Among Various Transforms. 9.6: Derivation of the Z-Transform Pair. 9.7: Summary. PART V: STATE-SPACE ANALYSIS. 10. State-Space Analysis. 10.1: Introduction. 10.2: Systematic Procedure for Determining State Equations. 10.3: Solution of State Equations. 10.4: Linear Transformation of State Vector. 10.5: Controllability and Observability. 10.6: State-Space Analysis of Discrete-Time Systems. 10.7: Summary. Supplementary Reading. Index