Moulton  Lectures

 

On

Electro-Acoustics

 

 

 

Presented by:

Dave L Moulton

 

 

 

 

 

Location:  Thales Acoustics Harrow UK

Date:  28-January-2004

 

Content

In this lecture I want to take a break from wave acoustics and have another look at Digital Active Noise Reduction, or DANR as it is more commonly known. In lectures 10 and 11 we looked at the fundamentals of a feedback ANR system and derived a very simplistic feedback equation. In lectures 16 through to 19 we looked at a possible configuration for producing digital noise cancellation by means of an adaptive filter. In each case we needed to know the  acoustic transfer function of the transducers and earshell acoustics, known in these lectures as H(s) or H(z).  I now want to take things a little further and explore the difficulties in realizing a digital ANR system with a stable feedback function.  I intend to cover the following:

 

·        Reminder of the simplistic ANR system and transfer function.

·        Introduce compensation to convert a feedback system in to feed forward system.

·        Look at the factors which make the system stable.

·        Discuss the difficulties of a real life digital ANR system.

 

On With The Lecture

Let us first remind ourselves of the configuration for a feedback ANR system in module form (i.e not partitioned). This is shown in figure 24.1 below: 

 

Where P_n is the noise pressure incident at the face of the sensing microphone. P_t is the cancelling pressure (anti noise) generated from the earphone transducer. The resulting residue pressure P_e at the face of the microphone comes from the scalar addition of the P_n and P_t.

 

Thus:

 

 

 

 

 

 

Figure 24.1

 

The feedback system for the headset can be easily represented as a block function diagram shown in figure 24.2.

 

 

Figure 24.2

Where:

 

E(s) is the earphone transfer function.

M(s) is the microphone transfer function.

T(s) is the transfer function of the acoustic space between the earphone and the microphone.

kG(s) is the desired Gain and Filter circuit transfer function.

 

This leads to the now familiar feedback function for the system.

 

 

In reality equation 24.2 is very difficult to optimize for  high levels of ANR without the risk of instability. The equation neatly describes a catch 22 dilemma which should become obvious from studying the signal path in figure 24.2.  It goes a bit like this:

 

·        To achieve high levels of noise reduction the equation requires that the gain k be very high so that the error signal e is made very small.

·        The higher the gain k in the feedback loop, the greater the risk of instability.

·        In the limit we try and make the error signal e reduce to zero, which means that the gain k has to tend to infinity, this guarantees instability in a system like this.

 

Feedback Compensation

One possible way of improving the situation is to apply an element of feedback compensation into the control loop. The idea here is to reduce the dependency of the input of the multi-pole filter kG(s) on the error signal e. This can be made possible by adding a clone of the headset transfer function H(s) (which we shall identify as Ĥ(s)) as an element which controls the input to the filter kG(s) . A compensated system is shown below in figure 24.3.  What we have done is prevent the input to the multi-pole filter from being entirely dependant on the error signal e.

 

 

Figure 24.3

 

We can derive the new transfer function in the following way:

 

At summing junction ‘A’ we have:

Thus

 

At summing Junction ‘B’ we have:

 

Thus

 

factorizing

 

Substituting [24.7] into [24.4] we get:

 

 

Remembering that H(s) = E(s)T(s)M(s), we get:

 

Thus

 

 

A little more rearranging:

 

 

And finally:

 

 

If we are able to create an accurate clone of H(s) then the system simply reduces to a feedforward arrangement, where it is relatively easy to make kG(s) and Ĥ(s) inherently stable.

 

Thus if  H(s) = Ĥ(s)

 

We have:

 

 

A block diagram representation of this system is shown in figure 24.4.

 

 

Figure 24.4

 

The Big Problem

The compensation method is an ideal, the difficulty comes in creating an accurate clone of H(s) in order for the  feedforward condition to exist. Variations in human head profiles, headset fitting and environmental conditions such as body vibration can all make H(s) very unpredictable and variable .

 

Using Adaptive Digital Filters to system identify H(s)

Adaptive signal processing can be used to system identify H(s) in terms of a discrete FIR or IIR filter, thus transforming Ĥ(s) to Ĥ(z). The difficulty here is the fact that Ĥ(z) will need to be system identified before any digital filter convolution can take place. Thus for a situation where H(Z) changes it will need to be continually updated through periodic system identification. In the case of a headset this could involve injecting a periodic burst of white noise into the earshell to establish the latest H(z).

 

The acoustic variations inside a headset earshell can be compounded by a lot of factors including the types of foam used and even how well and consistently they are fitted into the earshell.  Figure 24.5 below shows a typical ANR headset with foams. A lot of modern headsets contain significant amounts of circuitry, wires and other transducers, all packed into the earshell. The consistency in the build standard can also affect the variations in H(s). How critical and how sensitive H(s) is to these variations depends a lot on the physical and acoustic nature of the headset. Baffled earshells are a lot less prone to large variations in H(s). However, this is usually a trade off with the level of low frequency passive attenuation achievable by the headset.

 

 

Figure 24.5

 

Variations in H(Z) can result in a delta value ΔH(z),  Where,

 

 

Analysis of ΔH(z) can reveal the level of matching accuracy required for optimum ANR and stability.

 

Other Considerations  for achieving Digital Active Noise Reduction

When opting for the digital route to ANR it is important to include any reconstruction filters and anti-aliasing filters in the calculation of H(Z). Usually these types of filter are analogue and have their own gain and phase characteristics which could affect the system impulse  response.

 

 

Figure 24.6

 

Other methods for achieving Digital ANR include the following:

 

·        Doing all the processing in the frequency domain .

·        Sub-band processing  which involves breaking the frequency domain into discrete blocks and processing the blocks individually.

·        A mixture of digital and Analogue, also known as DIGILOG ANR.

 

 

End of Lecture