主题：关于非线性科学

哈哈，这个命题有点严肃啊，既然这么多大师博导在，就给大家出个数学提吧！

男人三妻四妾，按现行法律，该判多少次重婚罪呢？

用激光测扬声器振动部件的位移和速度，在国外已经是业界公认的做法。丹麦B&K公司的B&K3544激光传感器就是干这事的，配合B&K3550就可以得到多个通道的信息。在此基础上可以在PC机上获得振动图像。
NXT就制作过大量这一类的东西。
DUMAX 和Klippel 也都是用激光测试的。

扬声器的非线性失真一直是扬声器研究者最关注的焦点之一。国际音频工程协会把JAES从1953年到2000年之间发表的9317篇文章做成了带有查询系统的光盘。我们可以通过查询发现，约有一半的文章谈到失真（4589篇），约有四分之一的文章谈到非线性（2261篇）；2000年以后，这两个比例都还在不断提高。
在扬声器非线性研究中，使用最广泛的数学手段是Volterra级数，其他数学方法有NARMAX模型，Legendre多项式，Hilbert-Huang变换等等。

扬声器的非线性研究应用前景，看上去还是很土．

能否具体介绍一下可能产生的影响．

俺不懂这些！！郁闷ing.................

目前，主要还是根据所建立的非线性数学模型，通过电子方式进行补偿。据说效果还是很不错的。请参见：
http://isp.imm.dtu.dk/nonlincomp/

Klippel发明他的仪器，决非仅仅为了测试。他老早就在做对非线性进行线性化补偿的工作了。
我的一个朋友，很早就跟Klippel有过通信，后来在杂志上介绍过Klippel的仪器。又过了一两年，有人问我的朋友：“我是看了你的介绍才知道Klippel仪器的，现在我都买了，你们公司怎么反而不买？”
我朋友的回答是：“我们公司没有搞信号处理的实力，做不了补偿，光知道失真情况没有多少意义。”
听说Klippel的仪器现在在中国卖得很好。

不禁想引用杨老师在一个帖子中讲的一个故事：
“还是写一段往事.在1975年,在清华大学住了十多天,就是为那个激光测振的那个项目.有一天,正在工程力学系的一个实验室,一个女老师走过来,问问我们课题的情况,我作了简单的介绍.她说:好,你们肯定能测出来的,我信.但是你们想过没有,测出来又怎么样?我老实说:想的不多,外国人拍出来了,我们也想拍出来啊.她笑笑:啊,其实是应该想想的啊.
后来,我在再接任务和项目时就会想到这个女老师的话.
为她的评论,我感到清华就是清华啊.可贵的多问一个怎么样的思路啊.”

并请注意文章发表的年份（这才知道作为扬声器大国的生力军的我们，竟落后了多少年）。

Compensation for Nonlinear Distortion of Horn Loudspeakers by Digital Signal Processing
Author(s): Klippel, Wolfgang
Publication: JASE Volume 44 Number 11 pp. 964-972; November 1996
Abstract: Nonlinear distortion of horn loudspeakers can be compensated by prefiltering the electrical input signal inversely. A new filter architecture is derived from the results of nonlinear loudspeaker modeling using static nonlinear and dynamic linear subsystems. This special structure requires less computational effort and less memory than other generic architectures and allows complete compensation for the modeled nonlinear mechanisms. In practice, simplified versions of this filter can be implemented to compensate for dominant nonlinearities only. System identification performed on a particular horn loudspeaker provides valuable information about the dominant nonlinearity and allows adjustment of the free filter parameters. The implementation of an adequate filter structure for a professional loudspeaker in a DSP56000 is discussed, and results of the distortion reduction are presented.

Direct Feedback Linearization of Nonlinear Loudspeaker Systems
Author(s): Klippel, W.
Publication: Preprint 4439; AES Convention 102; March 1997
Abstract: The control law used in regular static-state feedback is expressed in a novel direct form which is advantageous for the linearization of loudspeaker systems. Compared with the straightforward integrator-decoupled form, the direct form increases the computational efficiency, requires less loudspeaker parameter, and can be easily implemented on signal processors working with a fixed-point format. The control law in the direct form can be applied to loudspeaker systems with different acoustic radiation aids (closed-box system, vented-box system) and dispenses with measurement of the internal states and full identification of the acoustic parameters. The relationship between feedback linearization and feedforward filter techniques (Volterra filter, mirror filter) is discussed.

Adaptive Adjustment of Nonlinear Filters Used for Loudspeaker Linearization
Author(s): Klippel, Wolfgang J.
Publication: Preprint 4646; AES Convention 104; May 1998
Abstract: Signal distortions caused by loudspeaker nonlinearities can be compensated by inverse nonlinear processing of the electric driving signal. This concept is based on an adequate control architecture having free control parameters adjusted to the particular loudspeaker. Optimal performance requires a self-tuning (adaptive) system to compensate for variations of loudspeaker parameters due to the effect of heating and aging while reproducing the audio signal. Straightforward adaptive controllers use an additional nonlinear filter for modeling the loudspeaker and for transforming the identified parameters into control parameters. This approach is susceptible to systematic errors and cannot be implemented in available DSP-systems at low costs. This paper presents a novel technique for direct updating of the control parameters which makes separate system identification superfluous.

好深奥啊,不过我还是坚持 看完了 谢谢

学习一下！