Digital Signal Processing presents the basic principles of digital signal processing, and explains how the coefficients of the discrete time system equation are selected in order to implement the desired “digital filter.”.
Contents
Linear, Shift-Invariant Continuous Time Systems
- Time Domain Description
- The Laplace Transform and System Transfer Functions
- Impulse Response
- Convolution
- BIBO Stability of LSI Systems
Frequency Domain Analysis For LSI Continuous Time Systems
- Complex Numbers and Complex Functions of a Real Variable
- Introduction to the Frequency Response Function
- Complex Exponential Signals and Negative Frequency
- Frequency Response Function: Relationship to System Impulse Response
- Steady-State Response to Periodic Signals
Fourier Transform Analysis of Continuous Time LSI Systems
- The Fourier Transform, Signal Spectrum, and Frequency Response
- Relationship of Fourier and Laplace Transforms
- Relationship Between Frequency Response Function and System Poles and Zeros
- Fourier Transform Concolution Theorems
- Fourier Transform Time and Frequency Shifting Theorems
- Fourier Transform Symmetry Properties
- Fourier Transform Examples
Butterworth and Chebyshev Lowpass and Highpass Filters
- Frequency Response Function: Butterworth Lowpass Filter
- Frequency Response Function: Chebyshev Lowpass Filter
- Transfer Functions for Normalized Lowpass Filters
- Lowpass-to-Lowpass Transformation
- Active Lowpass Filter Circuits
- Highpass Filters
- Required Filter Order
Linear, Shift-Invariant Discrete Time Systems
- Time Domain Description
- Impulse Response and Convolution
- The Z Transform
- Transfer Function of a Discrete Time System
- BIBO Stability of LSI Discrete Time System
- The Z Transform and System Analysis
Frequency Domain Analysis of Discrete Time Systems
- Frequency Response Function
- Steady-State Response to Periodic Signals
- The Discrete Time Fourier Transform
- DTFT Symmetry and Periodicity
- DTFT of a Sinusoidal Sequence
- Relationship Between the Fourier Transform and the DTFT
- Discrete Time Processing of Continuous Time Signals
- Relationship Between Frequency Response Function and System Poles and Zeros
- DTFT Shifting and Modulation Theorems
- DTFT Convolution Theorems
- The Rectangular Window and Its Spectrum
- DTFT of a Truncated Sinusoid
- Ideal Lowpass Filter
- A Simple FIR Lowpass Filter
- Systems Having Generalized Linear Phase
- Phase Functions: Principal Value Versus Unwrapped Phase
Sampling Theorem and Real-World D/A Conversion
- Relationship Between the Fourier-Transform and the DTFT
- The Sampling Theorem and Ideal D/A Conversion
- Real-World D/A Conversion
Discrete Fourier Transform (DFT) and Fast Fourier Transform
- The DFT and Its Relationship to the DTFT
- The Fast Fourier Transform (FFT)
- Zero Padding
- The DFT and Convolution
Design of FIR Filters
- FIR Filter Design Using the Window Method
- The Kaiser Window
- Empirical Formulas for FIR Lowpass Filter Design Using the Kaiser Window Method
- FIR Bandpass, Highpass, and Bandstop Filters Designed Using the Kaiser Window Method
- Design of FIR Filters Using the Parks-McClellan Algorithm
- Effects of Coefficient Quantization in FIR Filters
- Scaling to Prevent Overflow
Design of IIR Filters Using the Bilinear Transformation
- The Bilinear Transformation
- The Design Problem
- Examples
- Required Filter Order
- Alternate Second-Order Structures
Adaptive FIR Filters Using the LMS Algorithm
- General Problem
- LMS Algorithm Derivation
- An Application: Suppression of Narrowband Interference
Random Signals and Power Spectra, A/D Conversion Noise, and Oversampling
- Discrete Time Random Signals
- Random Signals and LSI Systems
- Zero Mean White Noise Random Signal
- A/D Conversion, Quantization Noise, and Oversampling
- Decimation and Interpolation
Appendices
- Convolution
- Programming FIR Filter Algorithms in Higher-Level Languages
- Derivation of Equation (10-8)
- Parseval's Theorem
Index
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