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Introduction | |

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Discrete-Time Signals and Systems | |

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Introduction | |

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Discrete-time Signals: Sequences | |

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Discrete-time Systems | |

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Linear Time-Invariant Systems | |

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Properties of Linear Time-Invariant Systems | |

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Linear Constant-Coefficient Difference Equations | |

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Frequency-Domain Representation of Discrete-Time Signals and Systems | |

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Representation of Sequence by Fourier Transforms | |

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Symmetry Properties of the Fourier Transform | |

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Fourier Transform Theorems | |

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Discrete-Time Random Signals | |

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Summary | |

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The z-Transform | |

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Introduction | |

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The z-Transform | |

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Properties of the Region of Convergence for the z-Transform | |

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The Inverse z-Transform | |

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Z-Transform Properties | |

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Summary | |

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Sampling of Continuous-Time Signals | |

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Introduction | |

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Periodic Sampling | |

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Frequency-Domain Representation of Sampling | |

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Reconstruction of a Bandlimited Signal from its Samples | |

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Discrete-Time Processing of Continuous-Time Signals | |

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Continuous-Time Processing of Discrete-Time Signals | |

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Changing the Sampling Rate Using Discrete-Time Processing | |

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Practical Considerations | |

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Oversampling and Noise Shaping | |

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Summary | |

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Transform Analysis of Linear Time-Invariant Systems | |

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Introduction | |

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The Frequency Response of LTI Systems | |

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System Functions for Systems Characterized by Linea | |

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Frequency Response for Rational System Functions | |

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Relationship Between Magnitude and Phase | |

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All-Pass Systems | |

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Minimum-Phase Systems | |

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Linear Systems with Generalized Linear Phase | |

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Summary | |

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Structures for Discrete-Time Systems | |

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Introduction | |

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Block Diagram Representation of Linear Constant-Coefficient Difference Equations | |

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Signal Flow Graph Representation of Linear Constant-Coefficient Difference Equations | |

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Basic Structures for IIR Systems | |

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Transposed Forms | |

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Basic Network Structures for FIR Systems | |

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Overview of Finite-Precision Numerical Effects | |

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The Effects of Coefficient Quantization | |

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Effects of Roundoff Noise in Digital Filters | |

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Zero-Input Limit Cycles in Fixed-Point Realizations of IIR Digital Filters | |

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Summary | |

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Filter Design Techniques | |

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Introduction | |

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Design of Discrete-Time IIR Filters from Continuous-Time Filters | |

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Design of FIR Filters by Windowing | |

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Examples of FIR Filter Design by the Kaiser Window Method | |

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Optimum Approximations of FIR Filters | |

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Examples of FIR Equiripple Approximation | |

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Comments on IIR and FIR Digital Filters | |

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Summary | |

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The Discrete Fourier Transform | |

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Introduction | |

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Representation of Periodic Sequences: the Discrete Fourier Series | |

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Summary of Properties of the DFS Representation of Periodic Sequences | |

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The Fourier Transform of Periodic Signals | |

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Sampling the Fourier Transform | |

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Fourier Representation of Finite-Duration Sequences: The Discrete-Fourier Transform | |

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Properties of the Discrete Fourier Transform | |

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Summary of Properties of the Discrete Fourier Transform | |

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Linear Convolution Using the Discrete Fourier Transform | |

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The Discrete Cosine Transform (DCT) | |

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Summary | |

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Computation of the Discrete Fourier Transform | |

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Introduction | |

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Efficient Computation of the Discrete Fourier Transform | |

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The Goertzel Algorithm Decimation-in-Time FFT Algorithms | |

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Decimation-in-Frequency FFT Algorithms | |

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Practical Considerations Implementation of the DFT Using Convolution | |

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Summary | |

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Fourier Analysis of Signals Using the Discrete Fourier Transform | |

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Introduction | |

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Fourier Analysis of Signals Using the DFT | |

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DFT Analysis of Sinusoidal Signals | |

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The Time-Dependent Fourier Transform | |

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Block Convolution Using the Time-Dependent Fourier Transform | |

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Fourier Analysis of Nonstationary Signals | |

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Fourier Analysis of Stationary Random Signals: the Periodogram | |

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Spectrum Analysis of Random Signals Using Estimates of the Autocorrelation Sequence | |

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Summary | |

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Discrete Hilbert Transforms | |

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Introduction | |

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Real and Imaginary Part Sufficiency of the Fourier Transform for Causal Sequences | |

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Sufficiency Theorems for Finite-Length Sequences | |

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Relationships Between Magnitude and Phase | |

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Hilbert Transform Relations for Complex Sequences | |

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Summary | |

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Random Signals | |

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Discrete-Time Random Process | |

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Averages | |

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Properties of Correlation and Covariance Sequences | |

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Transform Representation of Random Signals | |

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Continuous-Time Filters | |

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Butterworth Lowpass Filters | |

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Chebyshev Filters | |

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Elliptic Filters | |