Active acoustic attenuation system with differential filtering
BACKGROUND AND SUMMARY 
     The present invention arose during continuing development efforts relating to the subject matter of U.S. application Ser. No. 07/168,932, filed Mar. 16, 1988, and U.S. Pat. Nos. 4,665,549, 4,677,676, 4,677,677, 4,736,431, incorporated herein by reference. 
     The present invention involves differential bandpass filtering of the error signal to a narrower range than the input signal to improve system performance by reducing the range of modeling away from the cut-off frequencies of the input signal where sharp bandpass filtering is otherwise required to minimize regions of instabilities due to rapid phase change near the cut-off frequencies of the bandpass filtering. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a filtered nonadaptive system known in the prior art. 
     FIG. 2 shows a filtered adaptive system known in the prior art. 
     FIG. 3 shows a system in accordance with the invention. 
     FIGS. 4-6 are graphs of filter response showing input and error spectrums, with acoustic wave frequency on a log scale on the horizontal axis and log acoustic wave amplitude on the vertical axis. 
     FIGS. 7-12 are graphs showing performance of the variously described systems, with acoustic wave frequency on a log scale on the horizontal axis and log acoustic wave amplitude on the vertical axis. 
     FIG. 13 shows another system in accordance with the invention. 
     FIG. 14 shows a further system in accordance with the invention. 
     FIG. 15 is a graph illustrating operation and filter response of the system of FIG. 14, with acoustic wave frequency on a log scale on the horizontal axis and log acoustic wave amplitude on the vertical axis. 
    
    
     DETAILED DESCRIPTION 
     PRIOR ART 
     Filters are often required in active noise control systems to restrict system performance to the operational range of the controller and transducers. FIG. 1 shows a nonadaptive noise control system as known in the prior art. Input noise from an industrial fan, etc., enters a duct 20. The section of duct 20 between input microphone 24 and loudspeaker 26 is known in control theory as the plant. A model 22 of the plant and inverse of the filter 28 is determined beforehand and is fixed. The model senses the input noise at microphone 24 and outputs a cancelling soundwave at loudspeaker 26 to cancel or minimize the undesired noise. A sharp bandpass filter 28 is provided to minimize the region of instability due to rapid phase changes near cut-off frequency, M. A. Swinbanks, &#34;The Active Control of Sound Propagation in Long Ducts&#34;, Journal of Sound and Vibration (1973) 27(3) 411-436, pages 432 and 435. Model 22 must include a representation of the inverse of the filter. The inverse of the filter at the cut-off frequency is difficult to be accurately represented by the model. 
     In adaptive active noise control systems, the model is not fixed, but rather changes and adapts to the sensed input noise, for example as shown and described in the above incorporated patents. FIG. 2 shows an acoustic system 30 including an axially extending duct 32 having an input 34 for receiving an input acoustic wave and an output 36 for radiating an output acoustic wave. The acoustic wave providing the noise propagates axially left to right through the duct. The acoustic system is modeled with an adaptive filter model 38 having a model input 40 from input microphone or transducer 42, and an error input 44 from error microphone or transducer 46, and outputting a correction signal at 48 to omnidirectional output speaker or transducer 50 to introduce a cancelling acoustic wave such that the error signal at 44 approaches a given value such as zero. The cancelling acoustic wave from output transducer 50 is introduced into duct 32 for attenuating the output acoustic wave. Error transducer 46 senses the combined output acoustic wave and cancelling acoustic wave and provides an error signal at 44. 
     It is known in the prior art to bandpass filter the input signal at 40 and the error signal at 44 with appropriate highpass and lowpass filters. The lowpass filters avoid &#34;aliasing&#34; and &#34;imaging&#34; problems, B. A. Bowen et al, VLSI Systems Design for Digital Signal Processing, Volume 1: Signal Processing and Signal Processors, Prentice-Hall, Inc., Englewood Cliffs, N.J., page 11. The highpass filters restrict the input and error signals to regions where loudspeaker 50 can create noise and model 38 can effectively model the plant and inverse of the filters. The problem with the system of FIG. 2, as with the system of FIG. 1, is that the model must represent the inverse of the filters, and this is difficult to do well at the cut-off frequency of the highpass filters due to complex changes in phase and amplitude of the signal. 
     Loudspeakers are usually ineffective sound generators at frequencies below about 20 Hertz. Thus, in FIG. 2, it would be desirable to set the cut-off frequency of the highpass filters at about 20 Hertz, to thus allow only frequencies greater than 20 Hertz into the system. However, signals for frequencies just slightly greater than 20 Hertz exhibit the noted complex and rapid changes in phase and amplitude and cause instability of system operation. This is because the model, even though it can be made very accurate with digital processing technology and through the use of a recursive least means square algorithm, still has a limited number of coefficients and limited resolution in time. Thus, since the model must include a representation of the inverse of the filters, the computational task of the adaptive model becomes more and more difficult as the changes in phase and amplitude of the input signal become more complex near the cut-off frequencies of the filters. 
     A solution known in the prior art has been to increase the cut-off frequency of the highpass filters so that the model is better able to model the inverse of the highpass filters. This solution is shown in FIG. 2 where the input signal is highpass filtered with a highpass filter 52 having a cut-off frequency of 45 Hertz and is lowpass filtered with a lowpass filter 54 having a cut-off frequency of 500 Hertz. The error signal is highpass filtered with a highpass filter 56 having a cut-off frequency of 45 Hertz and is lowpass filtered with a lowpass filter 58 having a cut-off frequency of 500 Hertz. The correction signal is lowpass filtered with a lowpass filter 60 having a cut-off frequency of 500 Hertz. 
     The problem with the noted solution is that it causes loss of low frequency performance. This trade-off is unacceptable in various applications including industrial sound control where many of the noises desired to be attenuated are in a low frequency range, for example industrial fans and the like. The present invention addresses and solves the noted problem without the trade-off of loss of low frequency performance. 
     PRESENT INVENTION 
     In the present invention, it has been found that if the error signal at 44 is bandpass filtered to a narrower range than the input signal at 40, then the system can attenuate the desired low frequency noise. It has particularly been found that the cut-off frequency of the highpass filter for the input signal can be significantly lowered, to thus accept lower frequencies, if the cut-off frequency of the highpass filter for the error signal is kept high enough to exclude from the adaptive process those frequencies which would otherwise cause instability of the model. 
     FIG. 3 shows the simplest form of the invention and uses like reference numerals from FIG. 2 where appropriate to facilitate clarity. The input signal is highpass filtered at highpass filter 62 to a cut-off frequency of 4.5 Hertz. The cut-off frequency of highpass filter 56 remains at 45 Hertz. For the frequency range 45 Hertz to 500 Hertz, the input filter and its inverse are well behaved with a relatively flat response and with relatively small changes in amplitude and phase, FIGS. 4 and 6. Thus, while input highpass filter 62 accepts frequencies lower than 45 Hertz, the adaptive modeling process which models the plant and the inverse of the input filter, is better behaved, with less chance of instability because the range of modeling is limited, FIG. 5, to the flat smooth portion 68, FIG. 6, of the input filter response away from the lower frequency region 70 where instability occurs. 
     Even though the range of modeling is limited to the region of flat error filter response, it has neverthless been found that significant attenuation of low frequency noise below the error path highpass filter cut-off frequency has resulted. It has been found that the lower limit of attenuated frequency has been reduced by at least an octave, i.e. a 2:1 reduction, which is dramatic. Instead of the lower limit of attenuation being about 45 Hertz, such lower limit has been reduced with the present invention to below about 20 Hertz. This significantly expands the scope of industrial application, where such low frequency noises are present. 
     As seen in FIG. 5, the bandpass filtered error signal spectrum is from 45 Hertz to 500 Hertz. As seen in FIG. 4, the bandpass filtered input signal spectrum is from 4.5 Hertz to 500 Hertz. FIG. 6 shows FIGS. 4 and 5 superimposed. Region 68 shows the relatively flat well behaved range of the modeling process for the input filter response away from the region 70 of instability of the otherwise modeled inverse input filter. 
     FIG. 7 shows noise before and after cancellation at 72 and 74, respectively, for the acoustic system of FIG. 2. FIG. 8 shows the difference in amplitude between the cancelled and uncancelled noise of FIG. 7, such that the greater the vertical height in FIG. 8, the more the attenuation. In FIG. 8, attenuation starts at about 45 Hertz. 
     FIG. 9 shows noise before and after cancellation at 78 and 80, respectively, for the system of FIG. 3. FIG. 10 shows the difference in amplitude of the cancelled and uncancelled noise of FIG. 9, and shows that attenuation begins at a value less than about 20 Hertz. This is a significant improvement over FIG. 8 because the minimum attenuation frequency has been lowered by at least an octave, which is a dramatic reduction. 
     When the cut-off frequency for both the input signal highpass filter 52 and the error signal highpass filter 56 is reduced to 20 Hz, the system was unstable, and hence data for same is not shown. When the cut-off frequency for each of filters 52 and 56 is reduced to 4.5 Hz, the system is unstable. 
     FIG. 13 shows a further embodiment of an acoustic system in accordance with the invention and uses like reference numerals from FIG. 3 where appropriate to facilitate clarity. A second highpass filter 84 highpass filters the error signal at a cut-off frequency of 22.5 Hertz. The input signal is highpass filtered by highpass filter 86 to a cut-off frequency of 2.25 Hertz. 
     FIG. 11 shows noise before and after cancellation at 88 and 90, respectively, for the system of FIG. 13. FIG. 12 shows the difference in amplitude of the cancelled and uncancelled noise of FIG. 11, and shows reduction of the minimum frequency at which attenuation begins. 
     In each of FIGS. 3 and 13, the acoustic system is modeled with an adaptive recursive filter model having a transfer function with both poles and zeros, as in the above incorporated patents. The system provides adaptive compensation for feedback to input transducer 42 from output transducer 50 for both broadband and narrow band acoustic waves on-line without off-line pre-training. The system provides adaptive compensation of the error path from output transducer 50 to error transducer 46 and also provides adaptive compensation of output transducer 50 on-line without off-line pre-training. The feedback path from output transducer 50 to input transducer 42 is modeled with the same model 38 by modeling the feedback path as part of the model such that the latter adaptively models both the acoustic system and the feedback path, without separate modeling of the acoustic system and the feedback path, and without a separate model pre-trained off-line solely to the feedback. Each of the systems in FIGS. 3 and 13 also includes an auxiliary noise source, shown in above incorporated U.S. Pat. No. 4,677,676, introducing auxiliary noise into the model, such that error transducer 46 also senses the auxiliary noise from the auxiliary noise source. The auxiliary noise is random and uncorrelated to the input acoustic wave. 
     FIG. 14 shows a further acoustic system in accordance with the invention and uses like reference numerals from FIGS. 3 and 13 where appropriate to facilitate clarity. The input signal is highpass filtered at highpass filter 101 having a cut-off frequency f1, and is lowpass filtered by lowpass filter 106 having a cut-off frequency f6. The error signal is highpass filtered by highpass filter 102 having a cut-off frequency f2, and is highpass filtered by highpass filter 103 having a cut-off frequency f3. The error signal is lowpass filtered by lowpass filter 104 having a cut-off frequency f4, and is lowpass filtered by lowpass filter 105 having a cut-off frequency f5. In the embodiment shown, and as illustrated in FIG. 15, f1&lt;f2≦f3≦f4≦f5≦f6. Highpass filters 102 and 103 provide multiple stage highpass filtering of the error signal. Lowpass filters 104 and 105 provide multiple state lowpass filtering of the error signal. This multi-stage filtering shapes the filter response at the roll-off frequency. The frequency band between the lowpass filtered input signal and the highpass filtered input signal is greater than the frequency band between the multi-stage lowpass filtered error signal and the multi-stage highpass filtered error signal. 
     The invention is not limited to plane wave propagation, and may be used with higher order modes, for example above noted copending application Ser. No. 07/168,932, filed Mar. 16, 1988 &#34;ACTIVE ACOUSTIC ATTENUATION SYSTEM FOR HIGHER ORDER MODE NON-UNIFORM SOUND FIELD IN A DUCT&#34;. The invention is not limited to acoustic waves in gases, e.g. air, but may also be used for elastic waves in solids, liquid filled systems, etc. 
     It is recognized that various equivalents, alternatives and modifications are possible within the scope of the appended claims.