Table of Contents
Sampling and Reconstruction
1.1 Introduction
1.2 Review of Analog Signals
1.3 Sampling Theorem
1.3.1 Sampling Theorem
1.3.2 Antialiasing Prefilters
1.3.3 Hardware Limits
1.4 Sampling of Sinusoids
1.4.1 Analog Reconstruction and Aliasing
1.4.2 Rotational Motion
1.4.3 DSP Frequency Units
1.5 Spectra of Sampled Signals*
1.5.1 Discrete-Time Fourier Transform
1.5.2 Spectrum Replication
1.5.3 Practical Antialiasing Prefilters
1.6 Analog Reconstructors*
1.6.1 Ideal Reconstructors
1.6.2 Staircase Reconstructors
1.6.3 Anti-Image Postfilters
1.7 Basic Components of DSP Systems
1.8 Problems
Quantization
2.1 Quantization Process
2.2 Oversampling and Noise Shaping*
2.3 D/A Converters
2.4 A/D Converters
2.5 Analog and Digital Dither*
2.6 Problems
Discrete-Time Systems
3.1 Input/Output Rules
3.2 Linearity and Time Invariance
3.3 Impulse Response
3.4 FIR and IIR Filters
3.5 Causality and Stability
3.6 Problems
FIR Filtering and Convolution
4.1 Block Processing Methods
4.1.1 Convolution
4.1.2 Direct Form
4.1.3 Convolution Table
4.1.4 LTI Form
4.1.5 Matrix Form
4.1.6 Flip-and-Slide Form
4.1.7 Transient and Steady-State Behavior
4.1.8 Convolution of Infinite Sequences
4.1.9 Programming Considerations
4.1.10 Overlap-Add Block Convolution Method
4.2 Sample Processing Methods
4.2.1 Pure Delays
4.2.2 FIR Filtering in Direct Form
4.2.3 Programming Considerations
4.2.4 Hardware Realizations and Circular Buffers
4.3 Problems
z-Transforms
5.1 Basic Properties
5.2 Region of Convergence
5.3 Causality and Stability
5.4 Frequency Spectrum
5.5 Inverse z-Transforms
5.6 Problems
Transfer Functions
6.1 Equivalent Descriptions of Digital Filters
6.2 Transfer Functions
6.3 Sinusoidal Response
6.3.1 Steady-State Response
6.3.2 Transient Response
6.4 Pole/Zero Designs
6.4.1 First-Order Filters
6.4.2 Parametric Resonators and Equalizers
6.4.3 Notch and Comb Filters
6.5 Deconvolution, Inverse Filters, and Stability
6.6 Problems
Digital Filter Realizations
7.1 Direct Form
7.2 Canonical Form
7.3 Cascade Form
7.4 Cascade to Canonical
7.5 Hardware Realizations and Circular Buffers
7.6 Quantization Effects in Digital Filters
7.7 Problems
Signal Processing Applications
8.1 Digital Waveform Generators
8.1.1 Sinusoidal Generators
8.1.2 Periodic Waveform Generators
8.1.3 Wavetable Generators
8.2 Digital Audio Effects
8.2.1 Delays, Echoes, and Comb Filters
8.2.2 Flanging, Chorusing, and Phasing
8.2.3 Digital Reverberation
8.2.4 Multitap Delays
8.2.5 Compressors, Limiters, Expanders, and Gates
8.3 Noise Reduction and Signal Enhancement
8.3.1 Noise Reduction Filters
8.3.2 Notch and Comb Filters
8.3.4 Line and Frame Combs for Digital TV
8.3.5 Signal Averaging
8.3.6 Savitzky-Golay Smoothing Filters*
8.4 Problems
DFT/FFT Algorithms
9.1 Frequency Resolution and Windowing
9.2 DTFT Computation
9.2.1 DTFT at a Single Frequency
9.2.2 DTFT over a Frequency Range
9.2.3 DFT
9.2.4 Zero Padding
9.3 Physical versus Computational Resolution
9.4 Matrix Form of DFT
9.5 Modulo-N Reduction
9.6 Inverse DFT
9.7 Sampling of Periodic Signals and the DFT
9.8 FFT
9.9 Fast Convolution
9.9.1 Circular Convolution
9.9.2 Overlap-Add and Overlap-Save Methods
9.10 Problems
FIR Digital Filter Design
10.1 Window Method
10.1.1 Ideal Filters
10.1.2 Rectangular Window
10.1.3 Hamming Window
10.2 Kaiser Window
10.2.1 Kaiser Window for Filter Design
10.2.2 Kaiser Window for Spectral Analysis
10.3 Frequency Sampling Method
10.4 Other FIR Design Methods
10.5 Problems
IIR Digital Filter Design
11.1 Bilinear Transformation
11.2 First Order Lowpass and Highpass Filters
11.3 Second Order Peaking and Notching Filters
11.4 Parametric Equalizer Filters
11.5 Comb Filters
11.6 Higher Order Filters
11.6.1 Analog Lowpass Butterworth Filters
11.6.2 Digital Lowpass Filters
11.6.3 Digital Highpass Filters
11.6.4 Digital Bandpass Filters
11.6.5 Digital Bandstop Filters
11.6.6 Chebyshev Filter Design*
11.7 Problems
Interpolation, Decimation, and Oversampling
12.1 Interpolation and Oversampling
12.2 Interpolation Filter Design*
12.2.1 Direct Form
12.2.2 Polyphase Form
12.2.3 Frequency-Domain Characteristics
12.2.4 Kaiser Window Designs
12.2.5 Multistage Designs
12.3 Design Examples*
12.3.1 4-fold Interpolators
12.3.2 Multistage 4-fold Interpolators
12.3.3 DAC Equalization
12.3.4 Postfilter Design and Equalization
12.3.5 Multistage Equalization
12.4 Decimation and Oversampling*
12.5 Sampling Rate Converters*
12.6 Noise Shaping Quantizers*
12.8 Problems
Appendix
A Random Signals*
A.1 Autocorrelation Functions and Power Spectra
A.2 Filtering of Random Signals
B Random Number Generators
B.1 Uniform and Gaussian Generators
B.2 Low-Frequency Noise Generators*
B.3 1/f Noise Generators*
B.4 Problems
C Complex Arithmetic in C
D MATLAB Functions |