Active Noise Control

Environmental noise has a large influence on the human health and is an increasing problem in modern society. In everyday life, it appears mostly as traffic noise, especially in densely populated areas. There are also various professions where humans are exposed to unhealthy levels of noise, e.g. in factories or at airports. Convenient methods for avoidance or cancellation of this noise are required.

Passive approaches, such as earmuffs, offer a good protection against noise which includes high frequency components. However, they lose feasibility for lower frequencies, since large masses are required to achieve sufficient damping.

Active methods on the other hand allow for good reduction of lower frequency noise. This is due to the fact, that the phase velocity is proportional to the frequency. For a given latency, the change in phase is therefore lower. This qualifies active approaches, where latency is highly critical, to obtain good attenuation. Therefore, active approaches, typically named Active Noise Cancellation (ANC), are an efficient supplement for passive approaches.

An example for the combined cancellation performance of passive and active attenuation of a headphone is shown in Fig. 1.

The principle of ANC is visualized in Fig. 2. One microphone is capturing the external noise signal x(n) and another microphone is measuring the internal error signal e(n). The acoustic transmission from the external reference signal to the inner error signal is described by the primary path P(z). An ANC algorithm determines a cancellation signal y(n), which is played via the internal loudspeaker. The transmission from the loudspeaker to the inner microphone is given by the secondary path S(z).

The challenge is to create a suitable cancellation signal, as slight deviations in amplitude and phase already result in a severe degradation of the system performance. The signal processing needs to have as little latency as possible. All latency gathered between acquisition of the reference signal and emission of the cancellation signal, leads to a worse performance. Thus, the requirements for the real-time hardware are very challenging. To allow for real-time validation of new algorithms, we are working with hardware from dSPACE, which provides a round trip delay of one sample at a sampling rate of 48 kHz. That corresponds to a system latency of roughly 21 us. Furthermore, the creation of a suitable signal requires good knowledge of the underlying acoustic system. The positioning of microphones and loudspeakers within the acoustic front-end is crucial.

In general, the topic of ANC is a combination of various different fields and the construction of a complete system requires knowledge in signal processing, control engineering, acoustical measurements, acoustic front-end design and real-time systems including hardware.

An adaptive approach, as well as the connected acoustic front-end is illustrated in Fig. 3.

The cancellation signal y(n) is created by filter W_hat(z), which is adapted by the use of an adaptation algorithm. The illustrated topology is a feedforward structure, because it uses the external reference signal x(n) to create the cancellation signal y(n). One further topology, which may be used, is the feedback structure. It only uses an error signal e(n), and creates the cancellation y(n) by feeding the measured signal back to the loudspeaker. Both systems have their advantages and specific applications.

The adaption may be performed by different algorithms, e.g. the Least Mean Squares (LMS), the Recursive Least Squares (RLS) or the Kalman Filter.

In order to allow for convergence of the adaptation algorithm, the reference signal needs to be filtered by an estimation S_hat(z) of the secondary path. The resulting structure is called Filtered-X (FX) structure. One further improvement would be the Modified Filtered-X (MFX) structure, which corrects internal errors occurring for fast converging algorithms.

The secondary path estimation needs to be accurate to ensure the convergence of the cancellation filter W_hat(z). Under time-varying conditions, the secondary path needs to be estimated online, which is addressed by online secondary path estimation algorithms. They typically also include an adaptation algorithm. We further investigated different additionally induced noise signals for the adaptation, within so-called added noise approaches in [Liebich16].

So far the cancellation filter W_hat(z), was time-variant due to the underlying adaptation process. It may, however, also be optimized in advance, given a set of use-cases, and used as a time-invariant filter. This is possible for the feedforward, as well as the feedback topology. The time-invariant approaches are mostly based on control theory. Within this research field, various approaches for the optimization, especially for feedback systems, exist.

One sophisticated approach is the so-called H-infinity Optimization. It considers the nominal path, which represents the normal use-case, its variation captured in the path uncertainty as well as a desired performance within the optimization process. The optimization results in a time-invariant filter, which is guaranteed to be stable in all considered cases within the uncertainty bounds. Guaranteed stability is a crucial property for many control problems, and also a desired characteristic for hearing protection. We have applied the H-infinity Optimization for a noise cancelling headphone and validated the applicability within a real-time system in [Liebich16a].