Analysis and optimal design of delayless subband active noise control systems for broadband noise
Introduction
Active noise control (ANC) is a technique of canceling acoustic noise by generating an appropriate anti-noise using loud-speakers and directing it towards the region where noise cancelation is required. Anti-noise generation in its simplest form can be thought of as the negation of the input noise along with a compensating filter. The compensating filter equalizes the transfer function that models the transmission of anti-noise from the generating point to the canceling point. These operations can be performed using analog filters or in a better way using adaptive digital filters. In spite of their inferior performance, analog methods are widely adopted even in state-of-the-art consumer electronics ANC headsets. The main difficulty towards widespread adoption of adaptive digital filters is the high cost owing to the computational complexity of the filter update operation. For broadband ANC systems, the difficulty becomes more pronounced since traditional full-band FXLMS based approaches have prohibitively high computational cost, low convergence rate, and low attenuation. Multirate based subband adaptive filtering, on the other hand, greatly reduces the computational complexity, accelerates convergence and can achieve the best possible performance for a given ANC set-up.
However, multirate subband adaptive filtering systems are complex with a number of parameters influencing the overall performance, thus impeding their widespread use in consumer electronic ANC systems. A detailed understanding of their performance characteristics and a systematic method of designing subband based active noise control algorithms is needed for their effective deployment. This paper identifies and addresses this need by analyzing a practical ANC system and developing an optimal design strategy.
Active noise control is a real time adaptive signal processing application with the following requirements:
- 1.
Minimum computational complexity.
- 2.
Maximum noise attenuation.
- 3.
Fast convergence.
- 4.
Good tracking ability.
- 5.
Stability, which directly depends on the eigenvalue spread of the noise.
- 6.
Robustness to input noise's dynamics.
- 7.
Conservation of the above requirements when expanded to the multi-channel case.
Subband adaptive filtering can be exploited to meet the above requirements associated with a broadband ANC system design. This technique decomposes the signal spectrum into several subbands and handles each band separately. Therefore, the dynamic spectral range, and eventually the eigenvalue spread in each subband decreases. This reduction results in improved stability and robustness of the adaptive filters. The number of computations drastically reduces due to the downsampling operations. Among the different techniques in subband filtering [1], [2], [3], [4], delayless subband filtering, first introduced by Morgan and Thi [5], provides an ideal ANC implementation platform. This method involves: (a) a full-band filter that filters the input signal, (b) decomposition of input and error signals into subbands, (c) decimation in subbands, (d) adaptive filters working in subbands, and (e) a weight stacking method to combine all subbands weights into a full-band filter.
Our simulations and observations on using DSANC's as the ANC method of choice reveal that their performance has two distinct dependencies:
- 1.
Environmental/physical (input spectrum, and ) which represent the nature of the noise to be canceled, and the acoustic paths that have to be modeled.
- 2.
Parameters that can be controlled: The type of adaptive filter like RLS (recursive least squares), NLMS (normalized least mean square), APA (affine projection algorithm), learning rate, number of taps, number of subbands, the type of weight stacking, etc.
The contributions of this paper are:
- •
Recognition of the non-minimum phase nature of the secondary path as a main performance limiting factor and derivation of an upper bound for the obtainable noise attenuation level based on causal Wiener filtering.
- •
Investigation of the dependency of the DSANC systems on eigenvalue spread, the weight stacking distortion and number of subbands. Weight stacking procedure and delayless filter banks are thoroughly discussed and formulated. A model for the weight stacking distortion is derived. The weight stacking distortion is shown to increase with the number of subbands.
- •
Development of a step by step and systematic method for designing an efficient DSANC structure for canceling the broadband acoustic noise. The optimization objectives are: selecting the appropriate adaptive filtering algorithm, weight stacking method and number of subbands in order to maximize noise attenuation level while minimizing the computational complexity.
Section snippets
Notation
In this paper, vectors and matrices are denoted by bold lower case and bold upper case characters, respectively. The following notations are used in the paper: DSANC delayless subband ANC SAF subband adaptive filter EVS eigenvalue spread AEVS average eigenvalue spread EVSD eigenvalue spread standard deviation NAL noise attenuation level n time index N length of M number of subbands k subband index D the decimation factor in filter banks L length of each subband adaptive filter the canceling adaptive filter weight
Causal Wiener solution and upper bound
Design of a practical high performance ANC system involves a simulation based study in order to select an appropriate linear adaptive filtering scheme and its corresponding parameters. Simulations are typically carried out using recorded and measured , for comparing the performances of the various adaptive filtering algorithms. Since the filtering operation is linear, assuming the stationarity of , it can be shown that the performances of adaptive filtering schemes are bounded
Eigenvalue spread and subband filtering
Convergence rate and stability of the least square adaptive filter deteriorate when the eigenvalue spread (EVS) of input's covariance matrix increases. Eigenvalue spread of a signal is related to its spectrum by [12] and are the maximum and minimum eigenvalues of input's autocovariance matrix, respectively, which has the order of (i.e., the length of subband adaptive filters). According to (23) eigenvalue spread can be decreased
Weight stacking and distortion modeling
The weight stacking operation introduces distortion, which influences the performance of subband adaptive filters. The effect of weight stacking distortion was explored in a previous study [14] in the context of fMRI acoustic noise and is presented in a more generalized manner in this section. Section 5.1 gives a brief sketch of the weight stacking procedure [5], [15] using two different schemes. In Section 5.2 we define and quantify the effects of weight stacking by formulating it as a
Simulations and results
The two key factors governing the DSANC performance are EVS and stacking distortion. In the previous sections the variation of weight stacking distortion and EVS with M were separately studied and were shown to have opposite effects on DSANC performance. In this section we examine their combined effects through simulations.
In this paper the primary path and secondary path from [8] are used. The acoustic paths are shown in Fig. 7(a) and (b), respectively. They are impulse responses
Optimal design of DSANC
Optimal design is achieved by adjusting the following parameters:
- 1.
Number of taps, initial value of taps.
- 2.
The type of adaptive filter, i.e., NLMS, APA, and RLS.
- 3.
Number of subbands.
- 4.
The type of weight stacking.
Conclusion
The focus of this paper is a performance study of subband adaptive filtering based broadband ANC systems and development of a systematic design approach. DSANC is shown to be a good candidate for implementing broadband ANC systems owing to its reduced spectral dynamic range and computational complexity. Noise canceling performance and computational complexity of DSANC are influenced by the number of subbands, weight update, and stacking schemes, , , and the spectral characteristics of
Acknowledgments
This study was supported by the VA IDIQ contract number VA549-P-0027 awarded and administered by the VA Medical Center, Dallas, TX. The content of this paper does not necessarily reflect the position or the policy of the US government, and no official endorsement should be inferred.
References (15)
- et al.
A delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control
Signal Process.
(2006) A delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control
Signal Process.
(2002)- et al.
Analysis of the adaptive filter algorithm for feedback-type active noise control
Signal Process.
(2003) - et al.
An embedding approach to frequency-domain and subband adaptive filtering
IEEE Trans. Signal Process.
(2000) Frequency-domain and multirate adaptive filtering
IEEE Signal Process. Mag.
(1992)- et al.
A delayless subband adaptive filter architecture
IEEE Trans. Signal Process.
(1995) - A.A. Milani, I.M. Panahi, R. Briggs, LMS-based active noise cancellation methods for fMRI using sub-band filtering, in:...
Cited by (23)
Wavelet packet transform applied to active noise control system for mixed noise in nonlinear environment
2023, Digital Signal Processing: A Review JournalCitation Excerpt :With the development of high performance digital signal processing chip, the ANC technique becomes more feasible [4–6]. In the past few decades, the broadband active noise control (BANC) system has been proposed, this structure has no ability to attenuate the noise generated from rotating machine because they do not consist of narrowband subsystem [7–9]. In the industrial environment, acoustic transmission path is usually nonlinear, and many nonlinear ANC systems have been proposed [10–12].
A hybrid multi-reference subband control strategy for active noise control headphones
2022, Applied AcousticsCitation Excerpt :However, the practical challenge associated with both HANC and the proposed HMRANC controller is the increase in computational burden. The computational complexity of adaptive filters can be reduced by using frequency-domain filtering techniques based on decomposing, processing, and reconstructing the signals using filter banks such as subband adaptive filtering (SAF) and block adaptive filtering (BAF) techniques [20–22]. The major drawback of conventional SAF is that a delay is introduced into the signal path by virtue of the bandpass filters used to derive the subband signals [23].
A survey on active noise control in the past decade—Part I: Linear systems
2021, Signal ProcessingActive headrests with selective delayless subband adaptive filters in an aircraft cabin
2021, Mechanical Systems and Signal ProcessingCitation Excerpt :In case of a perfect weight stacking process the synthesis filter bank should be a set of ideal bandpass filters, which is practically unfeasible. As such the weight stacking process introduces distortion, which increases with the number of subbands, limiting the attenuation performance [27,28]. The computational load of the DSAF is summarised in Table 1.