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Signal Representation. Why Do We Discretize Continuous Systems? Periodic and Nonperiodic Discrete Signals. Unit Step Discrete Signal. Impulse Discrete Signal. Ramp Discrete Signal. Real Exponential Discrete Signal. Sinusoidal Discrete Signal. Exponentially Modulated Sinusoidal Signal. Complex Periodic Discrete Signal. Shifting Operation. Representing a Discrete Signal Using Impulses. Reflection Operation. Time Scaling. Amplitude Scaling. Even and Odd Discrete Signal. Does a Discrete Signal Have a Time Constant? Basic Operations on Discrete Signals. Energy and Power Discrete Signals. Bounded and Unbounded Discrete Signals. Some Insights: Signals in the Real World. Discrete System. Definition of a System. Input and Output. Linear Discrete Systems. Time Invariance and Discrete Signals. Systems with Memory. Causal Systems. Inverse of a System. Stable System. Convolution. Difference Equations of Physical Systems. Homogeneous Difference Equation and its Solution. Nonhomogeneous Difference Equations and Their Solutions. Stability of Linear Discrete Systems: The Characteristic Equation. Block Diagram Representation of Linear Discrete Systems. From the Block Diagram to the Difference Equation. From the Difference Equation to the Block Diagram: A Formal Procedure. Impulse Response. Correlation. Some Insights. Fourier Series and the Fourier Transform of Discrete Signals. Review of Complex Numbers. Fourier Series of Discrete Periodic Signals. Discrete System with Periodic Inputs: The Steady-State Response. Frequency Response of Discrete Systems. Fourier Transform of Discrete Signals. Convergence Conditions. Properties of the Fourier Transform of Discrete Signals. Parseval's Relation and Energy Calculations. Numerical Evaluation of the Fourier Transform of Discrete Signals. Some Insights: Why is this Fourier Transform? z-Transform and Discrete Systems. Introduction. Bilateral z-Transform. Unilateral z-Transform. Convergence Considerations. Inverse z-Transform. Properties of the z-Transform. Representation of Transfer Functions as Block Diagrams. x(n), h(n), y(n), and the z-Transform. Solving Difference Equation Using the z-Transform. Convergence Revisited. Final-Value Theorem. Initial-Value Theorem. Some Insights: Poles and Zeroes. State-Space and Discrete Systems. Review on Matrix Algebra. General Representation of Systems in State Space. Solution of the State-Space Equations in the z-Domain. General Solution of the State Equation in Real Time. Properties of an and its Evaluation. Transformations for State-Space Representations. Some Insights: Poles and Stability. Block Diagrams and Review of Discrete System Representations. Basic Block Diagram Components. Block Diagrams as Interconnected Subsystems. Controllable Canonical Form Block Diagrams with Basic Blocks. Observable Canonical Form Block Diagrams with Basic Blocks. Diagonal Form Block Diagrams with Basic Blocks. Parallel Block Diagrams with Subsystems. Series Block Diagrams with Subsystems. Block Diagram Reduction Rules. Discrete Fourier Transform and Discrete Systems. Discrete Fourier Transform and the Finite-Duration Discrete Signals. Properties of the DFT. Relation the DFT Has with the Fourier Transform of Discrete Signals, the z-Transform and the Continuous Fourier Transform. Numerical Computation of the DFT. Fast Fourier Transform: A Faster Way of Computing the DFT. Applications of the DFT. Some Insights. Sampling and Transformations. Need for Converting a Continuous Signal to a Discrete Signal. From the Continuous Signal to its Binary Code Representation. From the Binary Code to the Continuous Signal. Sampling Operation. How do we Discretize the Derivative Operation? Discretization of the State-Space Representation. Bilinear Transformation and the Relationship between the Laplace-Domain and the z-Domain Representations. Other Transformation Methods. Some Insights. Infinite Impulse Response Filter Design. Design Process. IIR Filter Design Using MATLAB®. Some Insights. Finite Implse Response Digital Filters. FIR Filter Design. Design Based on the Fourier Series: The Window