Digital Signal Processing (DSP)

  1. Frequency Analysis of Discrete-Time Signals
    1. Discrete-Time Fourier Transform
      1. DTFT Definition and Formulation
        1. Existence Conditions
          1. Convergence Criteria
            1. Relationship to Z-Transform
              1. DTFT Properties
                1. Linearity
                  1. Time Shifting
                    1. Frequency Shifting
                      1. Time Reversal
                        1. Conjugation and Symmetry
                          1. Convolution Theorem
                            1. Multiplication Theorem
                              1. Parseval's Theorem
                              2. DTFT of Common Sequences
                                1. Frequency Response of LTI Systems
                                  1. Magnitude Response
                                    1. Phase Response
                                      1. Group Delay
                                    2. Discrete Fourier Transform
                                      1. DFT Definition and Motivation
                                        1. Mathematical Formulation
                                          1. DFT as Sampled DTFT
                                            1. Relationship to Other Transforms
                                              1. DFT Properties
                                                1. Linearity
                                                  1. Periodicity
                                                    1. Symmetry Properties
                                                      1. Circular Time Shift
                                                        1. Circular Frequency Shift
                                                          1. Circular Convolution
                                                            1. Parseval's Relation for DFT
                                                            2. Matrix Representation of DFT
                                                              1. Computational Complexity
                                                                1. Zero-Padding Effects
                                                                  1. Windowing in DFT Analysis
                                                                  2. Fast Fourier Transform
                                                                    1. FFT Algorithm Development
                                                                      1. Computational Complexity Reduction
                                                                        1. Decimation-in-Time FFT
                                                                          1. Radix-2 DIT Algorithm
                                                                            1. Butterfly Computation
                                                                              1. Signal Flow Graph
                                                                                1. Bit-Reversal
                                                                                2. Decimation-in-Frequency FFT
                                                                                  1. Radix-2 DIF Algorithm
                                                                                    1. Butterfly Computation
                                                                                      1. Signal Flow Graph
                                                                                      2. Other FFT Algorithms
                                                                                        1. Radix-4 FFT
                                                                                          1. Mixed-Radix FFT
                                                                                            1. Prime Factor Algorithm
                                                                                            2. Inverse FFT Implementation
                                                                                              1. Practical FFT Considerations
                                                                                                1. Windowing Functions
                                                                                                  1. Rectangular Window
                                                                                                    1. Triangular Window
                                                                                                      1. Hanning Window
                                                                                                        1. Hamming Window
                                                                                                          1. Blackman Window
                                                                                                            1. Kaiser Window
                                                                                                            2. Spectral Leakage
                                                                                                              1. Picket-Fence Effect
                                                                                                                1. Zero-Padding vs Interpolation

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                                                                                                            3. The Z-Transform

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                                                                                                            5. Digital Filter Design and Implementation