Continuous and discrete signals and systems

1. Representing Signals. Continuous-Time vs. Discrete-Time Signals. Periodic vs. Aperiodic Signals. Energy and Power Signals. Transformations of the Independent Variable. Elementary Signals. Other Types of Signals. 2. Continuous - Time Systems. Classification of Continuous-Time Systems. Linear Time- Invariant Systems. Properties of Linear Time-Invariant Systems. Systems Described by Differential Equations. State Variable Representations. 3. Fourier Series. Orthogonal Representations of Signals. The Exponential Fourier Series. Dirichlet conditions. Properties of the Fourier Series. Systems with Periodic Inputs. The Gibbs Phenomenon. 4. The Fourier Transform. The Continuous-Time Fourier Transform. Properties of the Fourier Transform. Applications of the Fourier Transform. Duration-Bandwidth Relationships. 5. The Laplace Transform. The Bilateral Laplace Transform. The Unilateral Laplace Transform. Bilateral Transforms Using Unilateral Transforms. Properties of the Unilateral Laplace Transform. The Inverse Laplace Transform. Simulation Diagrams for Continuous-Time Systems. Applications of the Laplace Transform. State Equations and the Laplace Transform. Stability in the s Domain. 6. Discrete-Time Systems. Elementary Discrete-Time Signals. Discrete-Time Systems. Periodic Convolution. Difference-Equation Representation of Discrete-Time Systems. Stability of Discrete Time Systems. 7. Fourier Analysis of Discrete-Time Systems. Fourier-Series Representation of Discrete-Time Periodic Signals. The Discrete-Time Fourier Transform. Properties of the Discrete-Time Fourier Transform. Fourier Transform of Sampled Continuous-Time Signals. 8. The Z-Transform. The Z-Transform. Convergence of the Z-Transform. Properties of the Z-Transform. The Inverse Z-Transform. Z-Transfer Functions of Casual Discrete-Time Systems. Z-Transform Analysis of State-Variable Systems. Relation Between the Z-Transform and the Laplace Transform. 9. The Discrete Fourier Transform. The Discrete Fourier Transform and Its Inverse. Properties of the DFT. Linear Convolution Using the DFT. Fast Fourier Transforms. Spectral Estimation of Analog Signals Using the DFT. 10. Design of Analog and Digital Filters. Frequency Transformations. Design of Analog Filters. Digital Filters. Appendices.