A New Delayless Subband Adaptive Filtering Algorithm for Active Noise Control Systems
Abstract
Subband adaptive filtering (SAF) techniques play aprominent role in designing active noise control (ANC) systems.They reduce the computational complexity of ANC algorithms,particularly, when the acoustic noise is a broadband signal and thesystem models have long impulse responses. In the commonly useduniform-discrete Fourier transform (DFT) -modulated (UDFTM)filter banks, increasing the number of subbands decreases thecomputational burden but can introduce excessive distortion,degrading performance of the ANC system. In this paper, we proposea new UDFTM-based adaptive subband filtering method thatalleviates the degrading effects of the delay and side-lobe distortionintroduced by the prototype filter on the system performance.The delay in filter bank is reduced by prototype filter design andthe side-lobe distortion is compensated for by oversampling andappropriate stacking of subband weights. Experimental resultsshow the improvement of performance and computational complexityof the proposed method in comparison to two commonlyused subband and block adaptive filtering algorithms.Index Terms—Active noise control (ANC), discrete Fouriertransform (DFT), filter bank, subband adaptive filter.
I. INTRODUCTION
ACTIVE noise control (ANC) is a method of cancellinga noise signal in an acoustic cavity by generating anappropriate anti-noise signal via canceling loudspeakers. Dueto recent advances in wireless technology, new applications ofANC have emerged, e.g., incorporating ANC in cell phones,Bluetooth headphones, and MP3 players, to mitigate the environmentalacoustic noise and therefore improve the speechand music quality. For practical purposes, ANC as a real-timeadaptive signal processing method should meet the followingrequirements: 1) minimum computational complexity (lowercomputational delay and power consumption), 2) stability androbustness to input noise dynamics, and 3) maximum noiseattenuation. Acoustical and electrical signal transmission path modelssuch as those encountered in realistic ANC applications, e.g.,the primary path and the secondary path (see Fig. 1),usually have long impulse responses [1], [2]. Consequently,noise cancellation algorithms require long adaptive filters, resultingin significant computational burden. The computationalcomplexity can be reduced by using frequency-domain filteringtechniques based on decomposition, processing, and reconstructingthe signals using filter banks such as subband adaptivefiltering (SAF) and block adaptive filtering (BAF) techniques.SAF techniques have been used in other audio applicationssuch as speech enhancement and hearing aids [3]–[5]. Amongthe SAF methods [1], [6], [7], the delayless SAF introduced byMorgan and Thi (MT) in [1] provides a better approach to meetthe aforementioned requirements for ANC system. Merchedand Sayed [2] introduced a BAF algorithm named discreteFourier transform multidelay adaptive filter (DFT-MDF). Thisalgorithm exploits the properties of circulant matrices to implementa high-performance block adaptive processing algorithm.DFT-MDF (as it will be shown later) performs well with asmall block lengths (or small number of subbands).Zhou et al. [8] proposed an ANC system that requires nosecondary path identification, whereby to cancel a single toneat frequency , the adaptive filter, denoted by (seeFig. 1), needs to estimate the ratio of notand individually, and the phase is set to either 0 or 180by trial and error. Expanding on this concept, [8] shows that anon-tonal noise signal can be canceled by decomposing it intovery narrow subbands and treating each subband like a tonalcomponent. According to [8], the narrower the subbands are,i.e., the higher the number of subbands, the better should be theperformance of the system. Hence, an appropriate SAF techniquewith a large number of subbands may be used to avoid secondarypath identification.

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