Digital Signal Processing (DSP)

  1. Discrete-Time Signals and Systems
    1. Discrete-Time Signal Representation
      1. Sequence Notation and Indexing
        1. Graphical Representation of Sequences
          1. Mathematical Description of Sequences
          2. Elementary Discrete-Time Signals
            1. Unit Impulse Sequence
              1. Definition and Properties
                1. Mathematical Representation
                2. Unit Step Sequence
                  1. Definition and Properties
                    1. Relationship to Unit Impulse
                    2. Sinusoidal Sequences
                      1. Frequency Parameters
                        1. Amplitude and Phase
                          1. Aliasing in Discrete Sinusoids
                          2. Exponential Sequences
                            1. Real Exponential Sequences
                              1. Complex Exponential Sequences
                                1. Relationship to Sinusoidal Sequences
                                2. Ramp Sequence
                                  1. Rectangular Pulse Sequence
                                  2. Operations on Discrete-Time Signals
                                    1. Time Shifting
                                      1. Forward Shift (Advance)
                                        1. Backward Shift (Delay)
                                        2. Time Reversal
                                          1. Amplitude Operations
                                            1. Scaling
                                              1. Addition
                                                1. Multiplication
                                                2. Signal Folding
                                                  1. Sampling Rate Alteration
                                                    1. Decimation
                                                      1. Interpolation
                                                    2. Discrete-Time Systems
                                                      1. System Representation Methods
                                                        1. Block Diagram Representation
                                                          1. Difference Equation Representation
                                                            1. Input-Output Description
                                                            2. System Properties
                                                              1. Linearity
                                                                1. Superposition Principle
                                                                  1. Additivity and Homogeneity
                                                                  2. Time-Invariance
                                                                    1. Shift-Invariance Property
                                                                      1. Time-Shift Test
                                                                      2. Causality
                                                                        1. Causal System Definition
                                                                          1. Non-causal System Examples
                                                                          2. Stability
                                                                            1. BIBO Stability Definition
                                                                              1. Stability Testing Methods
                                                                              2. Memory
                                                                                1. Memoryless Systems
                                                                                  1. Systems with Memory
                                                                                2. Linear Time-Invariant Systems
                                                                                  1. LTI System Properties
                                                                                    1. Impulse Response Characterization
                                                                                      1. Convolution Sum
                                                                                        1. Definition and Derivation
                                                                                          1. Convolution Properties
                                                                                            1. Commutativity
                                                                                              1. Associativity
                                                                                                1. Distributivity
                                                                                                  1. Identity Property
                                                                                                  2. Graphical Convolution Method
                                                                                                    1. Analytical Convolution Computation
                                                                                                    2. System Response to Arbitrary Input
                                                                                                    3. Difference Equations
                                                                                                      1. Linear Constant-Coefficient Difference Equations
                                                                                                        1. Recursive Systems
                                                                                                          1. Non-recursive Systems
                                                                                                            1. Initial Conditions and Complete Response
                                                                                                              1. Homogeneous and Particular Solutions

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                                                                                                          1. Introduction to Digital Signal Processing

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                                                                                                          3. The Z-Transform