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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