九十年代经典回顾：自适应 ANC 算法教程

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本文档《Active Noise Control: A Tutorial Review》由沈吴(KUO)和丹尼尔·Morgan（Dennis R. Morgan）撰写，他们是IEEE资深会员，专注于主动降噪(Active Noise Control, ANC)技术的实用应用。该论文在20世纪90年代提供了对主动降噪技术的一次经典概述，着重于信号处理和数字信号处理(DSP)在实际应用中的自适应算法。文章的核心内容包括了主动降噪的基本原理，即通过一系列次级声源引入相消的反噪声波，这些次级声源通过特定的电子系统连接，并利用专门的信号处理算法来实现特定的消声效果。主动降噪技术广泛应用于制造业、工业操作以及消费电子产品中，如降低背景噪音、改善音频设备性能等。论文首先介绍了基于单一通道宽频前馈控制的基本自适应算法。这种算法通过实时分析环境噪声，调整次级声源产生的反噪声波，以达到最佳的降噪效果。作者深入剖析了这一过程，展示了如何通过数学模型和优化方法来提高系统的稳定性和效率。接着，作者针对窄带前馈控制和自适应反馈控制进行了算法的改进。窄带前馈控制关注特定频率范围内的噪声，提高了降噪的精度，而自适应反馈控制则能够根据环境变化动态调整策略，增加了系统的灵活性。为了进一步增强降噪效果，文章探讨了多通道的应用，这涉及到次级声源布局、信号同步以及空间滤波等复杂问题。论文详细介绍了几种在线次级路径建模技术，例如格网法(lattice modeling)、频率域方法(frequency-domain techniques)、子带方法(subband processing)以及递归算法(recursive algorithms)，这些技术旨在优化信号处理流程，提升降噪性能。这篇论文不仅为读者提供了一个关于主动降噪技术的基础框架，还涵盖了从理论到实践的关键步骤和技术细节，对于从事音响工程、电子设备设计或噪音控制领域的专业人士具有重要的参考价值。通过阅读这篇综述，读者将能深入了解如何利用先进的信号处理技术来实现高效的主动降噪系统。

Fig. 6. Block diagram of ANC system with feedback.

Fig. 7. ANC with acoustic feedback neutralization.

1) Feedback Neutralization: The simplest approach to

solving the feedback problem is to use a separate feedback

cancellation, or “neutralization,” ﬁlter within the controller,

which is exactly the same technique as used in acoustic echo

cancellation [43]. This electrical model of the feedback

path is driven by the secondary signal, and its output

is subtracted from the reference sensor signal [44]. A

duct-acoustic ANC system using the FXLMS algorithm

with feedback neutralization is illustrated in Fig. 7. The

feedback component of the reference microphone signal

is canceled electronically using a feedback neutralization

ﬁlter

which models the feedback path

Since the primary noise is highly correlated with the

antinoise, the adaptation of the feedback neutralization ﬁlter

must be inhibited when the ANC system is in operation,

similar to adaptive echo cancellation during periods of

double talk. Thus, feedback neutralization is achieved, in

effect, by using an ofﬂine adaptive method for determining

the transfer function of the feedback path. The models

and can be estimated simultaneously by using the

ofﬂine modeling technique [4].

2) Adaptive IIR Filter: Equation (14) shows that when

feedback is present, the optimal solution of the adaptive

ﬁlter is generally an IIR function with poles and zeros. This

rational function can be approximated by an FIR function

of sufﬁcient order, but a smaller step size

then has to

be used for stability reasons. The poles of an IIR ﬁlter

make it possible to obtain well-matched characteristics with

a lower order structure, thus requiring fewer arithmetic

Fig. 8. ANC system using the ﬁltered-U recursive LMS algo-

rithm.

operations [41]. However, the disadvantages of adaptive

IIR ﬁlters are: 1) IIR ﬁlters are not unconditionally stable

because of the possibility that some pole(s) of the ﬁlter

will move outside of the unit circle during the adaptive

process, causing instability; 2) the adaptation may converge

to a local minimum because the MSE function of adaptive

IIR ﬁlters is generally nonquadratic; and 3) IIR adaptive

algorithms can have a relatively slow convergence rate

in comparison with that of FIR ﬁlters. A comprehensive

discussion of adaptive IIR ﬁlters can be found in the

literature [45], [46].

A block diagram of an adaptive IIR ANC system [47]

is illustrated in Fig. 8. The output signal of the IIR ﬁlter

is computed as

(16)

where

is the weight

vector of

is the reference signal vector,

is the weight vector of and

is the output signal vector delayed by one sample.

Many algorithms can be employed to ﬁnd the optimal set

of coefﬁcients

and to minimize the error signal

In 1976, Feintuch [48] suggested that the recursion based

on the old output gradients is negligible. Based on this

suggestion, the “ﬁltered-U recursive LMS algorithm” [49]

for ANC is derived as [4]

(17)

(18)

where

is the ﬁltered version

of the canceling signal vector at time

In practice, it

is reasonable to use a higher order for

than for

[50]. Real-time experiments have been conducted to test

the system performance for various reference microphone

locations, error microphone locations, and different time-

varying sources, such as a centrifugal fan and diesel engine

[51].

Given the complexities associated with the pole-zero

structure of

and one cannot predict the

values to which

and will converge. Also, global

convergence and stability of the ﬁltered-U recursive LMS

948 PROCEEDINGS OF THE IEEE, VOL. 87, NO. 6, JUNE 1999

Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on August 6, 2009 at 09:24 from IEEE Xplore. Restrictions apply.

Fig. 9. Basic conﬁguration of narrow-band ANC system.

algorithm have never been proven formally. A modiﬁed

leaky version of the simpliﬁed hyperstable adaptive re-

cursive ﬁlter (SHARF) algorithm [52] has been developed

for ANC applications to improve the stability of the IIR

adaptive ﬁlter [53]. In that algorithm, a lowpass ﬁlter is

used to smooth the error signal for the ﬁltered-U recursive

LMS algorithm, thereby providing a higher stability margin.

III. N

ARROWBAND FEEDFORWARD ANC

Many noises are periodic, such as those generated by

engines, compressors, motors, fans, and propellers. Direct

observation of the mechanical motion of such sources

generally is possible by using an appropriate sensor, which

provides an electrical reference signal that contains the

fundamental frequency and all the harmonics of the primary

noise. However, this technique is only effective for periodic

noise because the fundamental driving frequency is the only

reference information available.

A. Introduction

A basic block diagram of narrow-band ANC for reducing

periodic acoustic noise in a duct is illustrated in Fig. 9. This

system controls harmonic sources by adaptively ﬁltering a

synthesized reference signal

internally generated by

the ANC system. This technique has the following advan-

tages: 1) undesired acoustic feedback from the canceling

loudspeaker back to the reference microphone is avoided;

2) nonlinearities and aging problems associated with the

reference microphone are avoided; 3) the periodicity of the

noise removes the causality constraint; 4) the use of an

internally generated reference signal results in the ability

to control each harmonic independently; and 5) it is only

necessary to model the acoustic plant transfer function over

frequencies in the vicinity of the harmonic tones; thus, an

FIR ﬁlter with substantially lower order may be used.

The reference signal generator is triggered by a syn-

chronization pulse from a nonacoustic sensor, such as a

tachometer signal from an automotive engine. In general,

two types of reference signals are commonly used in

narrow-band ANC systems: 1) an impulse train with a

period equal to the inverse of the fundamental frequency

of the periodic noise [54] and 2) sinewaves that have the

same frequencies as the corresponding harmonic tones to

be canceled. The ﬁrst technique is called the waveform

synthesis method, which was proposed by Chaplin [55].

The second technique embodies the adaptive notch ﬁlter,

which was originally developed for the cancellation of tonal

interference [56] and applied to periodic ANC [57].

The waveform synthesis method discussed next in

Section III-B employs synchronous sampling. However,

for some applications, the actual period will vary from

the nominal value as a function of loading conditions.

Therefore, it is sometimes desirable to operate asynchro-

nously with a ﬁxed sampling rate so that the secondary-path

estimate ﬁlter coefﬁcients do not have to be changed as

a function of actual machine rotation rate. Also, some

digital signal processors cannot be efﬁciently utilized on

a synchronous signal-driven basis. Asynchronous ANC

systems using the FXLMS algorithm eliminate the problem

of having to change

as the sampling rate varies and

are implicit in the later formulations of Sections III-C and

III-D.

B. Waveform Synthesis Method

1) Structures and Algorithms: The waveform synthesizer

[55] stores canceling noise waveform samples

in unique contiguous memory addresses,

where

is the number of samples over one cycle of the

waveform and

is the current time index. These samples

represent the required waveform to be generated and are

sequentially sent to a D/A converter to produce the actual

canceling noise waveform for the secondary loudspeaker.

Thus

(19)

represents the

th element of waveform samples, where

mod and can be implemented as a pointer

incremented in a circular fashion between zero and

for each sampling period, controlled by interrupts generated

from the synchronization signal.

The residual noise picked up by the error microphone

is synchronously sampled with the reference signal timing

pulses. In a practical system, there is a delay between the

time the signal

is fed to the loudspeaker

and the time it is received at the error microphone. This

delay can be accommodated by subtracting a time offset

from the circular pointer

Thus, the adaptation unit

adjusts the values of the waveform samples using a variant

of the LMS algorithm

otherwise

(20)

where

and is the time delay, which is

constant for a given loudspeaker-microphone arrangement,

is the sampling period, and greatest integer less

than or equal to

This offset number must be updated

as the sampling rate varies, since it is synchronized with

the noise source.

KUO AND MORGAN: ACTIVE NOISE CONTROL 949

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