Chapter 1 Discrete Sequences and Systems
1.1 DISCRETE SEQUENCES AND THEIR NOTATION
1.2 SIGNAL AMPLITUDE, MAGNITUDE, POWER
1.3 SIGNAL PROCESSING OPERATIONAL SYMBOLS
1.4 INTRODUCTION TO DISCRETE LINEAR TIME-INVARIANT SYSTEMS
1.5 DISCRETE LINEAR SYSTEMS
1.5.1 Example of a Linear System
1.5.2 Example of a Nonlinear System
1.6 TIME-INVARIANT SYSTEMS
1.6.1 Example of a Time-Invariant System
1.7 THE COMMUTATIVE PROPERTY OF LINEAR TIME-INVARIANT SYSTEMS
1.8 ANALYZING LINEAR TIME-INVARIANT SYSTEMS
REFERENCES
CHAPTER 1 PROBLEMS
Chapter 2 Periodic Sampling
2.1 ALIASING: SIGNALAMBIGUITY IN THE FREQUENCY DOMAIN
2.2 SAMPLING LOWPASS SIGNALS
2.3 SAMPLING BANDPASS SIGNALS
2.4 PRACTICAL ASPECTS OF BANDPASS SAMPLING
2.4.1 Spectral Inversion in Bandpass Sampling
2.4.2 Positioning Sampled Spectra at fs4
2.4.3 Noise in Bandpass-Sampled Signals
REFERENCES
CHAPTER 2 PROBLEMS
CHAPTER 3 The Discrete Fourier Transform
3.1 UNDERSTANDING THE DFT EQUATION
3.1.1 DFT Example
3.2 DFT SYMMETRY
3.3 DFT LINEARITY
3.4 DFT MAGNITUDES
3.5 DFT FREQUENCY AXIS
3.6 DFT SHIFTING THEOREM
3.6.1 DFT Example 2
3.7 INVERSE DFT
3.8 DFT LEAKAGE
3.9 WINDOWS
3.10 DFT SCALLOPING LOSS
3.11 DFT RESOLUTION, ZERO PADDING, AND FREQUENCY-DOMAIN
SAMPLING
3.12 DFT PROCESSING GAIN
3.12.1 Processing Gain of a Single DFT
3.12.2 Integration Gain Due to Averaging Multiple DFTs
3.13 THE DFT OF RECTANGULAR FUNCTIONS
3.13.1 DFT of a General Rectangular Function
3.13.2 DFT of a Symmetrical Rectangular Function
3.13.3 DFT of an All-Ones Rectangular Function
3.13.4 Time and Frequency Axes Associated with the DFT
3.13.5 Alternate Form of the DFT of an All-Ones Rectangular
Function
3.14 INTERPRETING THE DFT USING THE DISCRETE-TIME FOURIER
TRANSFORM
REFERENCES
CHAPTER 3 PROBLEMS
Chapter 4 The Fast Fourier Transform
4.1 RELATIONSHIP OF THE FFT TO THE DFT
4.2 HINTS ON USING FFTS IN PRACTICE
4.2.1 Sample Fast Enough and Long Enough
4.2.2 Manipulating the Time Data Prior to Transformation
4.2.3 Enhancing FFT Results
4.2.4 Interpreting FFT Results
4.3 DERIVATION OF THE RADIX-2 FFT ALGORITHM
4.4 FFT INPUTOUTPUT DATA INDEX BIT REVERSAL
4.5 RADIX-2 FFT BUTTERFLY STRUCTURES
4.6 ALTERNATE SINGLE-BUTTERFLY STRUCTURES
REFERENCES
CHAPTER 4 PROBLEMS
Chapter 5 Finite Impulse Response Filters
5.1 AN INTRODUCTION TO FINITE IMPULSE RESPONSE FIR FILTERS
5.2 CONVOLUTION IN FIR FILTERS
5.3 LOWPASS FIR FILTER DESIGN
5.3.1 Window Design Method
5.3.2 Windows Used in FIR Filter Design
5.4 BANDPASS FIR FILTER DESIGN
5.5 HIGHPASS FIR FILTER DESIGN
5.6 PARKS-MCCLELLAN EXCHANGE FIR FILTER DESIGN METHOD
5.7 HALF-BAND FIR FILTERS
5.8 PHASE RESPONSE OF FIR FILTERS
5.9 A GENERIC DESCRIPTION OF DISCRETE CONVOLUTION
5.9.1 Discrete Convolution in the Time Domain
5.9.2 The Convolution Theorem
5.9.3 Applying the Convolution Theorem
5.10 ANALYZING FIR FILTERS
5.10.1 Algebraic Analysis of FIR Filters
5.10.2 DFT Analysis of FIR Filters
5.10.3 FIR Filter Group Delay Revisited
5.10.4 FIR Filter Passband Gain
5.10.5 Estimating the Number of FIR Filter Taps
REFERENCES
CHAPTER 5 PROBLEMS
Chapter 6 Infinite Impulse Response Filters
6.1 AN INTRODUCTION TO INFINITE IMPULSE RESPONSE FILTERS
6.2 THE LAPLACE TRANSFORM
6.2.1 Poles and Zeros on the s-Plane and Stability
6.3 THE z -TRANSFORM
6.3.1 Poles, Zeros, and Digital Filter Stability
6.4 USING THE z -TRANSFORM TO ANALYZE IIR FILTERS
6.4.1 z -Domain IIR Filter Analysis
6.4.2 IIR Filter Analysis Example
6.5 USING POLES AND ZEROS TO ANALYZE IIR FILTERS
6.5.1 IIR Filter Transfer Function Algebra
6.5.2 Using PolesZeros to Obtain Transfer Functions
6.6 ALTERNATE IIR FILTER STRUCTURES
6.6.1 Direct Form I, Direct Form II, and Transposed
Structures
6.6.2 The Transposition Theorem
6.7 PITFALLS IN BUILDING IIR FILTERS
6.8 IMPROVING IIR FILTERS WITH CASCADED STRUCTURES
6.8.1 Cascade and Parallel Filter Properties
6.8.2 Cascading IIR Filters
6.9 SCALING THE GAIN OF IIR FILTERS
6.10 IMPULSE INVARIANCE IIR FILTER DESIGN METHOD
6.10.1 Impulse Invariance Design Method 1 Example
6.10.2 Impulse Invariance Design Method 2 Example
6.11 BILINEAR TRANSFORM IIR FILTER DESIGN METHOD
6.11.1 Bilinear Trans
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