ACTIVE NOISE CONTROL By Leonardo Andrés Zheng Xuezhi Active noise control implemented by adaptive filtering

Part 1 Introduction to active noise control (on Nov 13rd) Why is “active” noise control?Why is “active” noise control? How can I achieve active noise control? Part 2 Simulation of active noise control (still waited for being studied) (on Dec 18 th ) What is the LMS algorithm? Do I need some update versions? How does this algorithm (or updated one) work? How can I realize them? (Matlab simulation)

Why is “active” noise control? Passive noise controlActive noise control Physical PrinciplesAbsorption and dampingDestructive Interference MaterialsBarriers and Sound Absorbing materials Acoustic-electro components, electro- acoustic components and electrical components, etc… FrequencyHigh frequencyLow frequency Definition of Active noise control: active noise control works on the principle of destructive interference between the sound fields generated by the original “primary” sound source and that due to other secondary sources, whose acoustic outputs can be controlled. Physical principle Signal Processing Task (Might DSP be used here?)

Historical Review Paul Leug: feed-forward control strategy and noise elimination (patent, in 1936) Harry Olson and Everet May: feedback control strategy and noise elimination (article, in 1956) An important thing to know here is that both of these two orginal ideas are analog apporches.

How can I achieve active noise control? Firstly, I need to find some appropriate acoustic principles to suppress the noise. So, what are these acoustic principles? Secondly, closely related to the first question, to what extent do I want to attenuate the noise: just eliminating or making it small? Please see the slides on acoustic principles and objectives.Please see the slides on acoustic principles and objectives. Finally, how can I achieve this attenuation? In other words, what kind of control strategies will I use in active noise control? (Feedback and Feedforward)control strategies

Acoustic Principles All strategies of active noise control rely on the principle of linear superpositon. Two kinds of things can screw up the linearity: first, very loud noise (just like in the amplifier);second, loudspeaker (but this problem can be minimized). Interference: if we do not control the phase difference between two sound waves (like Thomas Young’s two slits interference experiment in optics), in the sound field: at some points, the presure of the sound wave is destructive; however, at other points, the presure of the sound wave is constructive. (Why?) And this way only makes sure some local quiet zone and this acoustic control mechanism is called “vicinity control”. Also, this way will eliminate the noise in the local area.Why?vicinity control If we do control the phase difference between two sound waves, for example, making the troughs of the one wave exactly match with the peaks of another wave, the wide area control or global control can be achieved. Ideally, in this way, all noise is eliminated but actuallly in such a large area the well-match between the peaks and troughs can not be achieved. So, we will pay a lot of attention to the minimization of output power.global control Please first recall the design of Olson and May…

Destructive Interference (vicinity control) Destructive Interference: Olson and May’s arrangement is: Loudspeaker (secondary source) Microphone (monitor) Loudspeaker and microphone are closely arranged. 1 2 Microphone Loudspeakers Remarks: 1.Microphone is well-coupled to the secondary source and able to detect the error accurately. 2.Loudspeaker requires a modest voltage, which means the sound wave will not affect other points in the sound field significantly; and also the loudspeaker doesn’t suffer from the nonlinear problem

Global Control Remarks: 1.An important prerequisite of global control is the distance between two sources is small enough to compare with the wavelength. (Notice the highlighted condition in the appendix!) 2.But, in reality, we do not know the distance of the amplitude and the phase of the primary source beforehand. So, an optimal design here is employed.

FEEDBACK CONTROL According to Olson and May’s arrangement (1956) : TF from the feedback loop TF from the loudspeaker Primary source Signal from the mic Active noise system (block diagram) using feedback control Equivalent electrical configuration Compensating filter can be used here, but it has a big drawback. Because the compensating filter can only deal with the noise in one frequencyband. However, in reality, the primary source always changes frequency. So, it is a great idea to use adaptive filter here to replace the compensating filter. Block diagram with the digital controller Equivalent block diagram if C’(z) = C(z) Indeed, it is a feedforward system. Feedforward has an ability to “predict”. C’(z) = Adaptative filter LMS. W(z) = Adaptative filter x LMS.

FEEDFORWARD CONTROL According to Paul Leug’s design: Reference signal (correlated with primary source) C: TF from the seconday source source). P: TF from the primary source. W: TF from the controller (adaptative filter). A reference signal (obtained from a mechanical source) is used to drive the controller via the electrical controller. An electrical model is used within controller to extract the influence of the secondary source in the reference signal. Ideal case: In the broadband case, the filter will be desinged to give the best approximate response.

Summary Acoustic ObjectivesControl Strategy Feed-forward Feedback Noise elimination Quiet zone Power absorption Noise minimization---power output minimization Not an efficient way! Remarks: indeed the feedback strategy ends up as a similar feed- forward strategy.

Further study and reference To study LMS algorithm or its updated algorithm in step 2. To design and simulate an adaptive filter in Matlab. To solve any possible problem that is to pop up later. Reference: 1. Active Noise Control, S.J. ELLIOTT AND P.A.NELSON Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Max Born and Emil Wolf, Cambridge University Press, 1999