Preface | p. xi |
Discrete Sequences and Systems | p. 1 |
Discrete Sequences and Their Notation | p. 2 |
Signal Amplitude, Magnitude, Power | p. 8 |
Signal Processing Operational Symbols | p. 9 |
Introduction to Discrete Linear Time-Invariant Systems | p. 12 |
Discrete Linear Systems | p. 12 |
Time-Invariant Systems | p. 17 |
The Commutative Property of Linear Time-Invariant Systems | p. 18 |
Analyzing Linear Time-Invariant Systems | p. 19 |
Periodic Sampling | p. 21 |
Aliasing: Signal Ambiquity in the Frequency Domain | p. 21 |
Sampling Low-Pass Signals | p. 26 |
Sampling Bandpass Signals | p. 30 |
Spectral Inversion in Bandpass Sampling | p. 39 |
The Discrete Fourier Transform | p. 45 |
Understanding the DFT Equation | p. 46 |
DFT Symmetry | p. 58 |
DFT Linearity | p. 60 |
DFT Magnitudes | p. 61 |
DFT Frequency Axis | p. 62 |
DFT Shifting Theorem | p. 63 |
Inverse DFT | p. 65 |
DFT Leakage | p. 66 |
Windows | p. 74 |
DFT Scalloping Loss | p. 82 |
DFT Resolution, Zero Padding, and Frequency-Domain Sampling | p. 83 |
DFT Processing Gain | p. 88 |
The DFT of Rectangular Functions | p. 91 |
The DFT Frequency Response to a Complex Input | p. 112 |
The DFT Frequency Response to a Real Cosine Input | p. 116 |
The DFT Single-Bin Frequency Response to a Real Cosine Input | p. 117 |
Interpreting the DFT | p. 120 |
The Fast Fourier Transform | p. 125 |
Relationship of the FFT to the DFT | p. 126 |
Hints on Using FFTs in Practice | p. 127 |
FFT Software Programs | p. 131 |
Derivation of the Radix-2 FFT Algorithm | p. 132 |
FFT Input/Output Data Index Bit Reversal | p. 139 |
Radix-2 FFT Butterfly Structures | p. 141 |
Finite Impulse Response Filters | p. 151 |
An Introduction to Finite Impulse Response FIR Filters | p. 152 |
Convolution in FIR Filters | p. 157 |
Low-Pass FIR Filter Design | p. 167 |
Bandpass FIR Filter Design | p. 183 |
Highpass FIR Filter Design | p. 184 |
Remez Exchange FIR Filter Design Method | p. 186 |
Half-Band FIR Filters | p. 188 |
Phase Response of FIR Filters | p. 190 |
A Generic Description of Discrete Convolution | p. 195 |
Infinite Impulse Response Filters | p. 211 |
An Introduction to Infinite Impulse Response Filters | p. 212 |
The Laplace Transform | p. 215 |
The z-Transform | p. 228 |
Impulse Invariance IIR Filter Design Method | p. 243 |
Bilinear Transform IIR Filter Design Method | p. 259 |
Optimized IIR Filter Design Method | p. 270 |
Pitfalls in Building IIR Digital Filters | p. 272 |
Improving IIR Filters with Cascaded Structures | p. 274 |
A Brief Comparison of IIR and FIR Filters | p. 279 |
Specialized Lowpass Fir Filters | p. 283 |
Frequency Sampling Filters: The Lost Art | p. 284 |
Interpolated Lowpass FIR Filters | p. 319 |
Quadrature Signals | p. 335 |
Why Care About Quadrature Signals | p. 336 |
The Notation of Complex Numbers | p. 336 |
Representing Real Signals Using Complex Phasors | p. 342 |
A Few Thoughts on Negative Frequency | p. 346 |
Quadrature Signals in the Frequency Domain | p. 347 |
Bandpass Quadrature Signals in the Frequency Domain | p. 350 |
Complex Down-Conversion | p. 352 |
A Complex Down-Conversion Example | p. 354 |
An Alternate Down-Conversion Method | p. 358 |
The Discrete Hilbert Transform | p. 361 |
Hilbert Transform Definition | p. 362 |
Why Care About the Hilbert Transform? | p. 364 |
Impulse Response of a Hilbert Transformer | p. 369 |
Designing a Discrete Hilbert Transformer | p. 371 |
Time-Domain Analytic Signal Generation | p. 377 |
Comparing Analytical Signal Generation Methods | p. 379 |
Sample Rate Conversion | p. 381 |
Decimation | p. 382 |
Interpolation | p. 387 |
Combining Decimation and Interpolation | p. 389 |
Polyphase Filters | p. 391 |
Cascaded Integrator-Comb Filters | p. 397 |
Signal Averaging | p. 411 |
Coherent Averaging | p. 412 |
Incoherent Averaging | p. 419 |
Averaging Multiple Fast Fourier Transforms | p. 422 |
Filtering Aspects of Time-Domain Averaging | p. 430 |
Exponential Averaging | p. 432 |
Digital Data Formats and Their Effects | p. 439 |
Fixed-Point Binary Formats | p. 439 |
Binary Number Precision and Dynamic Range | p. 445 |
Effects of Finite Fixed-Point Binary Word Length | p. 446 |
Floating-Point Binary Formats | p. 462 |
Block Floating-Point Binary Format | p. 468 |
Digital Signal Processing Tricks | p. 471 |
Frequency Translation without Multiplication | p. 471 |
High-Speed Vector-Magnitude Approximation | p. 479 |
Frequency-Domain Windowing | p. 484 |
Fast Multiplication of Complex Numbers | p. 487 |
Efficiently Performing the FFT of Real Sequences | p. 488 |
Computing the Inverse FFT Using the Forward FFT | p. 500 |
Simplified FIR Filter Structure | p. 503 |
Reducing A/D Converter Quantization Noise | p. 503 |
A/D Converter Testing Techniques | p. 510 |
Fast FIR Filtering Using the FFT | p. 515 |
Generating Normally Distributed Random Data | p. 516 |
Zero-Phase Filtering | p. 518 |
Sharpened FIR Filters | p. 519 |
Interpolating a Bandpass Signal | p. 521 |
Spectral Peak Location Algorithm | p. 523 |
Computing FFT Twiddle Factors | p. 525 |
Single Tone Detection | p. 528 |
The Sliding DFT | p. 532 |
The Zoom FFT | p. 541 |
A Practical Spectrum Analyzer | p. 544 |
An Efficient Arctangent Approximation | p. 547 |
Frequency Demodulation Algorithms | p. 549 |
DC Removal | p. 552 |
Improving Traditional CIC Filters | p. 556 |
Smoothing Impulsive Noise | p. 561 |
Efficient Polynomial Evaluation | p. 563 |
Designing Very High-Order FIR Filters | p. 564 |
Time-Domain Interpolation Using the FFT | p. 568 |
Frequency Translation Using Decimation | p. 571 |
Automatic Gain Control (AGC) | p. 571 |
Approximate Envelope Detection | p. 574 |
A Quadrature Oscillator | p. 576 |
Dual-Mode Averaging | p. 578 |
The Arithmetic of Complex Numbers | p. 585 |
Graphical Representation of Real and Complex Numbers | p. 585 |
Arithmetic Representation of Complex Numbers | p. 586 |
Arithmetic Operations of Complex Numbers | p. 588 |
Some Practical Implications of Using Complex Numbers | p. 593 |
Closed Form of a Geometric Series | p. 595 |
Time Reversal and the DFT | p. 599 |
Mean, Variance, and Standard Deviation | p. 603 |
Statistical Measures | p. 603 |
Standard Deviation, or RMS, of a Continuous Sinewave | p. 606 |
The Mean and Variance of Random Functions | p. 607 |
The Normal Probability Density Function | p. 610 |
Decibels (DB and DBM) | p. 613 |
Using Logarithms to Determine Relative Signal Power | p. 613 |
Some Useful Decibel Numbers | p. 617 |
Absolute Power Using Decibels | p. 619 |
Digital Filter Terminology | p. 621 |
Frequency Sampling Filter Derivations | p. 633 |
Frequency Response of a Comb Filter | p. 633 |
Single Complex FSF Frequency Response | p. 634 |
Multisection Complex FSF Phase | p. 635 |
Multisection Complex FSF Frequency Response | p. 636 |
Real FSF Transfer Function | p. 638 |
Type-IV FSF Frequency Response | p. 640 |
Frequency Sampling Filter Design Tables | p. 643 |
Index | p. 657 |
About the Author | p. 667 |
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