## Active Noise Control PrimerActive noise control - the reduction of noise by generating an acoustic signal that actively interferes with the noise - has become an active area of basic research and engineering applications. The aim of this book is to present all of the basic knowledge one needs for assessing how useful active noise control will be for a given problem and then to provide some guidance for designing, setting up, and tuning an active noise-control system. Written for students who have no prior knowledge of acoustics, signal processing, or noise control but who do have a reasonable grasp of basic physics and mathematics, the book is short and descriptive. It leaves for more advanced texts or research monographs all mathematical details and proofs concerning vibrations, signal processing and the like. The book can thus be used in independent study, in a classroom with laboratories, or in conjunction with a kit for experiment or demonstration. Topics covered include: basic acoustics; human perception and sound; sound intensity and related concepts; fundamentals of passive noise-control strategies; basics of digital systems; basics of adaptive controllers; and active noise control systems. |

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### Contents

Introduction | 1 |

Chapter Summary | 2 |

Do I Have to Read the Whole Book? | 3 |

Adaptive Feedforward Active Noise Control | 4 |

Advanced Reading | 5 |

Background Fundamentals of Sound | 7 |

What Is Noise? | 8 |

Sound Waves | 10 |

Passive Noise Control Approaches | 84 |

Sidebranch Resonator | 85 |

Expansion Chamber | 86 |

Helmholtz Filter | 87 |

Dissipative Passive Control Techniques | 88 |

Active Noise Control Approaches | 89 |

Reference and Error Signal Quality | 90 |

Reference SensorControl Source Separation Distance | 91 |

Frequency Analysis | 14 |

Sine Waves | 15 |

Fourier Analysis | 19 |

Harmonics | 21 |

1 Anything that Rotates | 22 |

2 Many Devices Which Use Mains Electricity | 24 |

3 Devices Which Are Driven Beyond Their Capabilities | 25 |

Human Perception of Sound | 27 |

Acceptable Sound Levels | 30 |

Fundamentals of Noise Control | 36 |

The Magnitude of Acoustic Power | 40 |

Power Pressure and Hearing Loss | 41 |

Real and Imaginary Impedance | 42 |

What Is Noise Control? | 43 |

What Is Active Noise Control? | 44 |

Free Space Noise Control | 46 |

Active Control Approaches | 51 |

Enclosed Space Noise Control | 67 |

How Does the Sound Get Out Again? | 68 |

How Does the Sound Field Arrange Itself? | 69 |

Passive Noise Control Approaches | 74 |

Active Noise Control Approaches | 76 |

Control of Sound Propagation in Ducts | 81 |

Modes in Ducts | 82 |

Impedance in Ducts | 83 |

Control Source Position in the Duct | 92 |

Active Noise Controller Overview | 95 |

Some Important Facts | 96 |

Controller Output Digital Control Filter Requirements | 104 |

Adaptive Algorithm Requirements | 107 |

Controller Fundamentals | 113 |

General Control System Outlines and Definitions | 114 |

Physical System Limitations | 119 |

Interfacing a Digital System | 121 |

Required Additions for Digital Control | 124 |

Overview of the Controller | 127 |

The Digital Filter What Is a Digital Filter? | 128 |

Specifying the Appropriate Digital Filter | 132 |

Specifying the Digital Filter Length | 134 |

The Adaptive Algorithm Background Making Use of Adaptive Signal Processing | 135 |

Gradient Descent Algorithms | 136 |

Evaluating the Gradient | 139 |

The Convergence Coefficient | 140 |

Quantization Errors and Leakage | 143 |

Slowing Down the Algorithm to Improve Performance | 145 |

Cancellation Path Modeler | 146 |

Selecting the Sample Rate | 150 |

So What Is the Optimum Sample Rate? | 154 |

157 | |

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### Common terms and phrases

acoustic energy acoustic power acoustic pressure acoustic wave active noise control adaptive algorithm adaptive feedforward active amplitude analog cancellation path transfer chapter control source cut,on dB(A decibel digital filter digital system discrete discussion disturbance duct electronic enclosed space enclosure energy flow environment error criterion error microphone error sensor error signal error surface example feedforward active noise FIR filter free space frequency components gradient descent harmonic Hertz impedance implementation increase input loudspeaker low,frequency mathematical measurement meters microprocessor milliseconds mode Noise Control Approaches noise control system noise source optimum output passive noise control path transfer function peak phase physical pressure fluctuations quantity quantization error radiation reduced reference signal resonance frequency response result sample rate shown in Figure sine wave sound attenuation sound field sound levels sound pressure sound pressure levels sound propagation sound source sound wave tion unwanted noise vibration voltage wall waveform wavelength weight values