Delay-free subband algorithm with variable bandwidth for a broadband active noise cancellation system, vehicle and process

Abstract

Vehicle (10) comprising the following: an active noise cancellation system (12) comprising a processor (14) to implement a delayless subband x-filtered least squares control algorithm, wherein the control algorithm comprises a variable bandwidth discrete Fourier transform filter bank (36) with a number of subbands (38), such that the noise cancellation system (12), in response to a broadband white noise reference signal of road noise in the vehicle (10), determines a uniform gain spectrum defined by the subbands (38) over a frequency range that partially cancels out the road noise.

Description

TECHNICAL FIELD

[0001] This application relates to active noise cancellation (ANC) systems for a vehicle. BACKGROUND

[0002] In recent years, lightweight construction has helped achieve more energy-efficient vehicles. It has also been estimated that fuel economy would increase by 6 to 8% if vehicle weight is reduced by 10%. However, lightweight construction can increase structural vibrations and consequently interior noise, especially at low frequencies. Passive noise control may not be ideal, as it tends to add to vehicle weight and cost. Thus, active noise cancellation (ANC) technology has been developed that uses the audio system as a secondary speaker to cancel out engine noise, drivetrain noise, and road noise.

[0003] DUAN, J. [et al.]: Combined feedforward-feedback active control of road noise inside a vehicle cabin. In: Journal of Vibration and Acoustics. Vol. 136, August 2014, p. 041020-1-041020-8 discloses a vehicle with an active noise cancellation system including a processor for implementing a delay-free subband x-filtered least-squares control algorithm, wherein the control algorithm includes a discrete Fourier transform filter bank with a number of subbands.

[0004] US 2009 / 0 046 868 A1 discloses a method for controlling a headset with a microphone for receiving noise and user signals, wherein the received noise is used to reduce the noise at a headset output. A signal is detected by the microphone, and if the signal has a predefined characteristic, the signal is mapped to a control command.

[0005] EP 1 638 079 A2 discloses a method and system for active noise cancellation. The system uses subband processing and preferably implements an oversampled filter bank. The system is applicable to adaptive noise cancellation and adaptive echo cancellation for wearable hearing aids, such as headphones and other similar hearing aids. SUMMARY

[0006] In many noise cancellation (ANC) applications, computational overhead and slow convergence speed caused by large signal eigenvalue spread are significant. A delay-free subband algorithm, which decomposes signals from a full band into a set of subbands, was previously introduced to reduce computational complexity and improve the convergence properties of the control system. Here, a detailed derivation of a uniform, delay-free subband algorithm is presented. Furthermore, the inherent limitation of uniform discrete Fourier transform (DFT) filter banks is discussed. (An aliasing problem between adjacent subbands was found.) This inherent aliasing effect can degrade system performance.As a result, one example proposes a zero-delay subband algorithm with variable bandwidth as the basis for an active noise cancellation system for various types of road noise. This algorithm can overcome the aliasing effect of the standard zero-delay subband algorithm. This algorithm is effective in certain implementations and has low computational overhead. To validate the performance of the proposed algorithm, numerical simulations were conducted to suppress the measured road noise. The simulation results show that the zero-delay subband algorithm with variable bandwidth is an option for a broadband ANC system implementation.

[0007] In one example, a vehicle has an active noise cancellation system that includes a processor. The processor implements a delay-free subband x-filtered least-squares control algorithm, the control algorithm including a variable-bandwidth discrete Fourier transform filter bank with a number of subbands such that, in response to a broadband white noise reference signal of road noise in the vehicle, the noise cancellation system determines a uniform gain spectrum defined by the subbands over a frequency range that partially cancels the road noise. The delay-free subband x-filtered least-squares control algorithm may further include a uniform filter bank.Center frequencies of the variable-bandwidth discrete Fourier transform filter bank may be offset from center frequencies of the uniform filter bank by half the bandwidth of the uniform filter bank. A bandwidth of the variable-bandwidth discrete Fourier transform filter bank may be smaller than the bandwidth of the uniform filter bank. A bandwidth of the variable-bandwidth discrete Fourier transform filter bank may be at least half the bandwidth of the uniform filter bank. The active noise cancellation (ANC) system may further include a loudspeaker. The ANC system may partially cancel road noise via an output from the loudspeaker. BRIEF DESCRIPTION OF THE DRAWINGS Fig. Figure 1 is a diagram of a single-input, single-output (SISO) subband instantaneous algorithm in an active noise cancellation system for a vehicle. Fig. Figure 2 is a diagram of a uniform discrete Fourier transform (DFT) analysis filter bank. Fig. 3A and Fig. 3B are graphs of the response strengths of the DFT filter banks for different numbers of subbands. Fig. Figure 4 is a diagram of a variable bandwidth DFT analysis filter bank. Fig. 5A and Fig. 5B are graphs of the response strengths of the variable bandwidth DFT filter banks for different numbers of subbands. Fig. Figure 6 is a graph comparing computational complexity of different delay-free subband algorithms. Fig. 7A and Fig. 7B are graphs of strength and phase responses of a primary and a secondary path, respectively. Fig.Figures 8A to 8D are graphs comparing the steady-state performance of uniform and variable-bandwidth zero-delay subband algorithms using different numbers of subbands for synthesized data. Fig. 9A and Fig. 9B are graphs of steady-state performance comparisons of uniform and variable bandwidth zero-delay subband algorithms using different numbers of subbands for a concrete road. Fig. 10A and Fig. 10B are graphs of steady-state performance comparisons of uniform and variable bandwidth zero-delay subband algorithms using different numbers of subbands for a rough road. DETAILED DESCRIPTION

[0008] Embodiments of the present disclosure are described herein. It should be understood, however, that the disclosed embodiments are merely examples, and other embodiments may take various and alternative forms. The figures are not necessarily to scale; some features may be exaggerated or minimized to show details of particular components. The specific structural and functional details disclosed herein are therefore not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art how to variously practice the present invention.It will be apparent to one of ordinary skill in the art that various features illustrated and described with reference to one of the figures may be combined with other features illustrated in one or more other figures to create embodiments not explicitly illustrated or described. The combinations of illustrated features provide representative embodiments for typical applications. However, various combinations and modifications of the features consistent with the teachings of this disclosure may be desirable for particular applications or implementations. INTRODUCTION

[0009] Active Noise Cancellation (ANC) is based on the principle of superposition, whereby the unwanted primary noise is canceled out by a secondary noise of equal amplitude and opposite phase. Generally, road noise is a colored broadband noise whose energy lies in the frequency range of 60–400 Hz. Many attempts have been made over the past three decades to develop a feasible ANC system for vehicle applications. For example, a feasible approach to canceling road noise using an ANC system was demonstrated several years ago. Later, a multi-channel ANC system was developed using the conventional x-filtered least squares (FXLMS) algorithm to cancel road noise, along with reference accelerometers and a secondary loudspeaker. This was followed by an ANC system combined with a vehicle audio system and a real-time ANC system using the FXLMS algorithm.Most of these examples use the conventional FXLMS algorithm. However, this algorithm has inherent disadvantages when compensating for road noise. Broadband noise requires a higher-order adaptive filter, which increases the computational load. The step size of this algorithm is not suitable for all frequencies due to the very large eigenvalue spread of the colored reference signal, which leads to a slow convergence rate.

[0010] To overcome the above problems, a subband algorithm based on the FXLMS algorithm was previously developed. This reduced the computational burden because adaptive filtering is performed at a lower decimation rate. Furthermore, fast convergence is possible because the spectral dynamic range is reduced in each subband. Furthermore, subband algorithms have been used in acoustic echo cancellation. Unfortunately, such techniques cannot be directly applied to an ANC system due to unwanted delays introduced in the signal path. These delays limit the performance and stability of the algorithm. Therefore, a delay-free subband algorithm was proposed for ANC applications. The signal-path delays were avoided while maintaining the advantage of a subband algorithm.Recently, a combined feedforward and feedback ANC system based on the zero-delay subband algorithm was developed to control interior road noise. However, the traditional zero-delay subband algorithm has an inherent limitation associated with the uniform discrete Fourier transform (DFT) analysis filter bank, which will lead to aliasing effects due to spectral leakage between adjacent filter banks. Here, a design of a variable-bandwidth DFT analysis filter bank is presented to minimize the aliasing effect and reduce the computational burden. Delay-free subband algorithm with variable bandwidth

[0011] Fig.1 shows a diagram of a vehicle 10 including an active noise cancellation (ANC) system 12. The ANC system 12, in this example, includes at least one processor 14 implementing a zero-delay, single-input, single-output Morgan subband algorithm 16, where x(n) is the reference signal picked up by the accelerometers and / or microphones 17, d(n) is the primary noise picked up by the microphone 18, and e(n) is the error signal after superimposing the primary noise and the secondary cancellation noise. The secondary cancellation noise is output to a cabin of the vehicle 10 via the loudspeaker 19. The algorithm 16 includes analysis filter banks 20, 22, subband secondary path blocks 24, least squares (LMS) algorithm blocks 26, fast Fourier transform (FFT) blocks 28, a frequency stack block 30, an inverse FFT block 32, and an adaptive filter block 34.As shown, the analysis filter bank consists of M subbands (note that M is an even number). For real signals, only M / 2+1 subbands are required. These M / 2+1 subbands correspond to the positive frequency components of the broadband filter response; the others are formed by complex conjugate symmetry. The reference signal x(n) and the error signal e(n) are decomposed into sets of subband signals. This arrangement can, of course, be extended to a multi-channel configuration.

[0012] The reference subband signal vector x m (n) and the error signal e m (n) are expressed as xm(n)=[x(nD+m)x((n−1)D+m)…x((n−K−1)D+m)]T em(n)=[e(nD+m)e((n−1)D+m)…e((n−K−1)D+m)]T where m = 0, 1, ..., D, the decimation factor D = M / 2, N is the length of the adaptive full-band filter and K is the number of weights for each adaptive sub-band filter K = N / D.

[0013] As a result of the decimation factor D, all the adaptive subband filter weights are updated every D samples. And the full band Ŝ(z) is divided into a set of subband functions Ŝ0(z), Ŝ1(z), ..., Ŝ M-1 (z). These subband transfer functions can be estimated using an offline or online system identification approach, in which the broadband noise generator can be decomposed into corresponding subbands. Consequently, the filtered reference signal in each subband is x′m(k)=xm(k)∗s^m where * denotes the folding process.

[0014] The m-th adaptive subband filter can be updated using the complex normalized least squares algorithm as wm(n+D)=wm(n)+μx′∗ m(n)‖x′ m(n)‖2+αem(n) where w m (n) = [w m0 (n) w m1 (n)...w mK-1 (n)] Tis the adaptive subband weight vector for the mth subband, and α is a small constant value to avoid an infinite step size. These adaptive subband weights are then transformed to full-band using a weight transformation scheme. There are several well-known weight transformation techniques. Here, the FFT stacking method is used to obtain the adaptive full-band weight.

[0015] In the delay-free subband algorithm, a full-band signal is decomposed into subband signals, thereby deriving a set of adaptive subfilters. This process primarily depends on the characteristics of an analysis filter bank. Currently, the analysis filter bank is mainly based on multi-rate signal processing techniques, and various filter bank approaches have been developed over the past twenty years. Among those filter banks, the cosine-modulated filter bank is popular because of its ease of implementation and perfect reconstruction. The DFT polyphase filter bank is another popular filter bank, providing high computational efficiency and simple structure. The DFT filter bank is selected for the delay-free subband algorithm due to several key advantages in filter structure and computational efficiency. Design of a uniform DFT analysis filter bank

[0016] Fig. Figure 2 shows the structure of a uniform DFT filter bank 36 with a number of M subbands 38. The DFT filter bank 36 can be used in conjunction with the ANC system 12 of the Fig. 1, for example, instead of the analysis filter bank 20, and is derived via modulation from a prototype filter P(z). Specifically, the analysis filter bank 36 of the M subbands is obtained via complex modulation in the following equation: Hi(z)=P(zej2πiM),i=0, 1,…,M−1 where P(z) is the real-valued prototype low-pass filter with a cutoff frequency of π / M. Then, the complex-modulated filters H i (z) 40 is obtained by shifting the low-pass filter P(z) to the right by multiples of 2π / M. This allows the uniform DFT filter bank 36 to divide the normalized frequency range from 0 to 2π into M subbands with a spacing of 2π / M between adjacent filters 40.

[0017] The Fig. 3A and Fig. Figure 3B shows the uniform DFT analysis filter bank designed for different subband numbers M. As shown for different subband numbers M, spectral leakage to adjacent subbands is unavoidable and will lead to the aliasing effect. As the number of subbands increases, leakage among subbands continues to occur. Thus, the uniform DFT filter bank suffers from the fact that it is unable to cancel aliasing components caused by the inherent drawback of the uniform DFT filter bank. Consequently, one goal of DFT filter bank design may be to minimize or limit spectral leakage to eliminate the aliasing effect. A new DFT filter bank design, the non-uniform DFT filter bank, is introduced here to overcome this drawback via a structure with inherent alias cancellation. Design of a DFT analysis filter bank with variable bandwidth

[0018] The variable-bandwidth DFT analysis filter bank is based on the previously proposed non-uniform DFT analysis filter bank. Other non-uniform subband methods, such as non-uniform pseudo-quadrature mirror filter (QMF) banks and all-pass transformed DFT filter banks, have inherent limitations. For example, the non-uniform pseudo-QMF is only used in the traditional subband algorithm, which requires both analysis and synthesis filters, which is considered unsuitable for delay-free subband algorithms. Furthermore, the all-pass transformed DFT filter bank is implemented only by changing the bandwidths, which cannot eliminate the aliasing effect.

[0019] Fig.4 shows an example structure of a DFT analysis filter bank with variable bandwidth 42. The DFT filter bank with variable bandwidth 42 can be used in conjunction with the ANC system 12 of the Fig. 1 can be used, for example, instead of analysis filter bank 20, etc. Two different prototype filters, P1(z) and P2(z), are used for this filter bank. The prototype filters P1(z) and P2(z) implement the classic finite impulse response (FIR) digital filter design method with a linear-phase window. They can be designed using an embedded MATLAB function: P1(z)=fir1(K−1,α) P2(z)=fir1(K−1,β) where K is the order of the prototype filter, M is the number of uniform subband filter banks, α is the uniform coefficient, which is equal to 1 / M, and β is the variable bandwidth coefficient, which lies between 1 / 2M and 1 / M. Here, β is set equal to 1 / 2M.

[0020] The first prototype filter P1(z) is the real-valued low-pass filter with a cutoff frequency of πα to preserve all odd-numbered subbands, whereas the secondary prototype filter P2(z) is the real-valued low-pass filter with a cutoff frequency of πβ to preserve all even-numbered subbands. In particular, analysis filter banks of the M-band DFT filter banks with variable bandwidth [H0(z), H1(z), H2, ..., H 2M-1 (z)] in the following equation via complex modulation: Hi(z)={P1(zejπiM),i=0,2,…,2M−2P2(zejπiM),i=1,3,…,2M−1

[0021] Then the complex modulated filters H i (z) 44 is obtained by shifting two low-pass filters P1(z) and P2(z) to the right by multiples of 2π / M. This allows the variable-bandwidth DFT filter bank 42 to divide the normalized frequency range from 0 to 2π into 2M subbands 46.

[0022] The Fig. 5A and Fig.Figure 5B shows the design of a DFT analysis filter bank with variable bandwidth for different subband numbers. Here, β is equal to 1 / 2M and the even order H i (z) (i = 1, 3, ...,2M - 1) is inserted between the filters H i (z) (i = 0, 2, ..., 2M - 2) is inserted. It can cover the spectral leakage between adjacent odd-order filters. This allows the variable-bandwidth DFT analysis filter banks to avoid and limit the aliasing effect in the delay-free subband algorithm. Computational complexity

[0023] This section evaluates the computational complexity of uniform and non-uniform delay-free subband algorithms. The computational requirements of the algorithms can be separated into five parts: 1) filter bank operation, 2) subband weight adjustment, 3) full-band filtering, 4) weight transformation, and 5) reference signal filtering. For convenience, the computational complexity is based on the number of multiplications per input sample. The computational complexity is summarized in Table 1. Table 1 Computational complexities of delay-free Morgan subband algorithms Calculation request Uniform DFT filter bank DFT filter bank with variable bandwidth C1: Filter bank operation 4K / M + 4log2M 2K / M + 2log22M C2: Subband weight adjustment 8NM+16NM2 4NM+4NM2 C3: Full-band filtering N N C4: Weight transformation [2log2(2NM)+log2N+4Mlog2(2NM)]J [2log2(NM)+log2N+2Mlog2(NM)]J C5: Filter X signal generation 8LM+16LM2 4LM+4LM2

[0024] In this table, N is the length of the adaptive full-band filter, K is the number of weights for each adaptive subband filter, and L is the length of the secondary path estimation filter Ŝ(z). This results in the total required multiplications of the uniform delayless Morgan subband algorithm being known to be as follows: N+4(K+2N+2L)M+16(N+L)M2+log2N+[2log2(M)+3log2N+4Mlog2(2NM)]J where J is a variable that determines how often the weight transformation is performed. The delay-free subband algorithm shows no serious performance degradation for values ​​of J ranging from one to eight. Note that different calculations are required for the proposed delay-free Morgan subband algorithm with variable bandwidth.

[0025] The number of calculations for the subband filtering of the reference signal and the error signal is C1=2×(K+2Mlog22M)2M / 2=2KM+2log22M

[0026] Here, only the complex M +1 subbands need to be processed for the real signals. Therefore, the subband weight update requires C2=4×(2N2M)×(2M / 2+1)2M / 2=4NM+4NM2

[0027] To transform the subband weight into full-band weights, the weight transformation process requires C4=[(2M / 2+1)×(4N2M)+Nlog2N]2 / J=[2log2NM+2Mlog2NM+log2N]J

[0028] Here, the output of the adaptive filter will result in computational effort C3 = N. Assuming that the secondary path is modeled with an L-th order FIR filter, then the generation of the filtered reference signal requires C5=4×(2L2M)×(2M / 2+1)2M / 2=4LM+4LM2

[0029] This results in the required total multiplications and additions of the delay-free Morgan subband algorithm with variable bandwidth as N+2(K+2N+2L)M+4(N+L)M2+log2N+[2log2(2M)+3log2N+2Mlog2(NM)]J

[0030] Fig. Figure 6 shows the comparison of the normalized computational complexity of these subband-based algorithms compared to the traditional FXLMS algorithm. Here, the length of the adaptive full-band filter N is 512 taps, the length of the estimated secondary path L is 256 taps, and the number of subbands M is 8, 16, 32, 64, and 128, respectively. As shown in Fig. As shown in Figure 6, the computational complexity of these two algorithms decreases as the number of subbands increases. In addition, the zero-delay, variable-bandwidth subband algorithm has lower computational complexity than the uniform zero-delay Morgan subband algorithm. Therefore, the zero-delay, variable-bandwidth subband algorithm will reduce the computational complexity as the number of subbands increases. Numerical simulation

[0031] To evaluate the performance of the proposed algorithms, extensive numerical simulations were conducted. In the first set of simulations, broadband white noise disturbances were synthesized in MATLAB. The well-known primary path P(z) and secondary path S(z) are used because they are widely used in simulation-based studies of ANCs. The frequency responses and secondary responses of the primary path and the secondary path are shown in the Fig. 7A and Fig.7B. The primary and secondary paths were modeled using a 256-tap FIR filter. In the second simulation, experimental data from vehicle road noise were used to further verify the performance of the zero-delay, variable-bandwidth subband algorithm. For demonstration purposes, different numbers of subbands, M, were used. The simulations were performed with uniform and zero-delay, variable-bandwidth subband algorithms for different numbers of subbands.

[0032] The results of the simulations are in the Fig.8A to 8D. Different numbers of subbands were used (M = 8, 16, 32, 64). The uniform delay-free subband algorithm exhibits severe aliasing in the spectra of the residual error signal, which is caused by the design of the uniform DFT analysis filter bank. And when the number of subbands is increased, the aliasing effect cannot be avoided. When the variable-bandwidth delay-free subband algorithm was used, it limited the aliasing effect and maintained better spectral leakage performance while maintaining the performance of the uniform delay-free subband algorithm. These results demonstrate that the use of the proposed system provides a feasible algorithm to limit and avoid the aliasing effect.

[0033] The Fig. 9A and Fig.9B show the error spectrum (of a concrete road) before and after convergence for the uniform and the delay-free subband algorithm with variable bandwidth using different numbers of subbands. Similarly, the Fig. 10A and Fig.Figure 10B shows the error spectrum (of a rough road) before and after convergence for the uniform and zero-delay variable-bandwidth subband algorithms using different numbers of subbands (concrete road). It can be seen that the uniform and zero-delay variable-bandwidth subband algorithms exhibit similar performance at most frequencies. However, due to the shortcomings of the uniform DFT filter bank, the variable-bandwidth DFT analysis filter bank achieved a smaller reduction in the gaps between adjacent subbands than the uniform subband algorithm. Furthermore, simulations with different data showed that the zero-delay variable-bandwidth subband algorithm is effective in maintaining the performance of the uniform zero-delay variable-bandwidth subband algorithm and limiting the aliasing effect in spectral leakage.

[0034] The processes, methods, or algorithms disclosed herein may be deliverable to or implemented by a processing device, controller, or computer, which may include any existing programmable electronic control unit or dedicated electronic control unit. Likewise, the processes, methods, or algorithms may be stored as data and instructions executable by a controller or computer in many forms, including, but not limited to, information permanently stored on non-writable storage media, such as read-only devices, and information modifiably stored on writable storage media, such as floppy disks, magnetic tapes, compact discs, random access memory devices, and other magnetic and optical media. The processes, methods, or algorithms may also be implemented in an executable software object.Alternatively, the processes, methods or algorithms may be implemented in whole or in part using suitable hardware components, such as application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), state machines, controllers or other hardware components or devices, or a combination of hardware, software and firmware components.

[0035] The terms used in the specification are for the purpose of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the invention. As previously described, the features of various embodiments may be combined to form further embodiments of the invention that may not be explicitly described or illustrated.While various embodiments may have been described as offering advantages or being preferred over other embodiments or prior art implementations with respect to one or more desired characteristics, as will be apparent to one of ordinary skill in the art, trade-offs may be made between one or more features or characteristics to achieve the desired overall system characteristics, depending on the particular application and implementation. These features may include, but are not limited to, cost, strength, durability, life cycle cost, marketability, appearance, packaging, size, serviceability, weight, manufacturability, ease of assembly, etc.Thus, embodiments that are described as less desirable than other embodiments or prior art implementations with respect to one or more characteristics are not outside the scope of the disclosure and may be desirable for certain applications.

Claims

[1] Vehicle (10) comprising: an active noise cancellation system (12) including a processor (14) for implementing a delay-free subband x-filtered least squares control algorithm, the control algorithm including a variable bandwidth discrete Fourier transform filter bank (36) having a number of subbands (38) such that the noise cancellation system (12), in response to a broadband white noise reference signal of road noise in the vehicle (10), determines a uniform gain spectrum defined by the subbands (38) over a frequency range that partially cancels the road noise. [2] The vehicle (10) of claim 1, wherein the delay-free subband x-filtered least squares control algorithm further includes a uniform filter bank, and wherein center frequencies of the variable bandwidth discrete Fourier transform filter bank (36) are offset from center frequencies of the uniform filter bank by half a bandwidth of the uniform filter bank. [3] The vehicle (10) of claim 2, wherein a bandwidth of the variable bandwidth discrete Fourier transform filter bank (36) is smaller than the bandwidth of the uniform filter bank. [4] The vehicle (10) of claim 2, wherein a bandwidth of the variable bandwidth discrete Fourier transform filter bank (36) is at least half the bandwidth of the uniform filter bank. [5] The vehicle (10) of claim 1, wherein the active noise cancellation (ANC) system (12) further includes a loudspeaker (19), and wherein the ANC system (12) partially cancels road noise via outputs from the loudspeaker (19). [6] Active noise cancellation method comprising: one or more processors (14) implementing an active noise cancellation (ANC) system (12) having a delay-free subband x-filtered least squares control algorithm, the control algorithm including a variable bandwidth discrete Fourier transform filter bank (36) having a number of subbands (38) such that the ANC system (12) determines a uniform gain spectrum defined by the subbands (38) over a frequency range in response to a broadband white noise reference signal comprising an audible frequency range of 20 Hz to 20 kHz. [7] The method of claim 6, wherein the delay-free subband x-filtered least squares control algorithm further includes a uniform filter bank, and wherein center frequencies of the variable bandwidth discrete Fourier transform filter bank (36) are offset from center frequencies of the uniform filter bank by half a bandwidth of the uniform filter bank. [8] The method of claim 7, wherein a bandwidth of the variable bandwidth discrete Fourier transform filter bank (36) is smaller than the bandwidth of the uniform filter bank. [9] The method of claim 7, wherein a bandwidth of the variable bandwidth discrete Fourier transform filter bank (36) is at least half the bandwidth of the uniform filter bank. [10] The method of claim 6, wherein the broadband white noise reference signal is representative of road noise, further comprising partially canceling the road noise. [11] Active Noise Cancellation (ANC) system (12) comprising: a loudspeaker (19); and one or more processors (14) programmed to implement a delay-free subband x-filtered least squares control algorithm, the control algorithm including a variable bandwidth discrete Fourier transform filter bank (36) having a number of subbands (38) such that the system (12), in response to a broadband white noise reference signal of road noise in a vehicle (10), determines a uniform gain spectrum over a frequency range defined by the subbands (38), whereby the road noise is partially canceled by outputting the gain spectrum through the loudspeaker (19). [12] The system (12) of claim 11, wherein the delay-free subband x-filtered least squares control algorithm further includes a uniform filter bank, and wherein center frequencies of the variable bandwidth discrete Fourier transform filter bank (36) are offset from center frequencies of the uniform filter bank by half a bandwidth of the uniform filter bank. [13] The system (12) of claim 12, wherein a bandwidth of the variable bandwidth discrete Fourier transform filter bank (36) is smaller than the bandwidth of the uniform filter bank. [14] The system (12) of claim 12, wherein a bandwidth of the variable bandwidth discrete Fourier transform filter bank (36) is at least half the bandwidth of the uniform filter bank.

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