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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 | |