Abstract:
In a filtering system, a first input receives a signal contaminated with noise. A second input receives a noise reference signal. Each notch filter in a set of M notch filters is responsive to a corresponding tuning coefficient so as to attenuate a corresponding noise frequency in the signal contaminated with noise. A tuning parameter generator responds to the noise reference signal by generating a tuning parameter corresponding to a fundamental frequency of the noise and tracks that fundamental frequency. A filter coefficient generator responds to the tuning parameter by providing each of the M notch filters with the corresponding tuning coefficient. A gain normalizer adjusts the overall gain of the M notch filters.

Description:
TECHNICAL FIELD OF THE INVENTION 
   The present invention relates in general to a series of filters to filter out a fundamental frequency and its harmonics. 
   BACKGROUND OF THE INVENTION 
   Closed loop control systems are used in a wide variety of applications and generally provide good control. However, when sources of noise contaminate the control signals in closed loop systems, such closed loop control systems may fail to operate properly. The noise in a noise contaminated closed loop control systems often may be characterized by a slowly time-varying fundamental frequency component f 0  plus its harmonics. Such noise, for example, may be introduced into the control system by a nearby motor drive line. 
   Where noise contaminates the control signals of a closed loop control system to the point where the control system fails to operate properly, it is necessary to prevent or eliminate the noise. Generally, noise can be prevented from being introduced into the control system such as through the use of shielding, or noise can be removed from the control signals of the control system such as by the use of filtering. Shielding is often impractical, and filtering often introduces signal impairments which can be as bad or worse than the noise. As an example of the latter problem, noise removal by lowpass filtering is often not acceptable because of the amplitude and phase distortion introduced by the lowpass filter and because of the destabilizing influence of the resulting increased phase lag on the closed-loop system. 
   A low phase shift, low distortion noise attenuation type of filter has the potential of providing a better solution to the noise problem. Very narrow band low distortion notch filtering for the removal of a single spectral noise component are also well known. Moreover, it is known to interconnect such notching filters in order to remove plural offending noise components. However, it has not been known how to tune the notch filter sections so that the time- varying noise components are effectively filtered. Moreover, known narrow band notch filters are complex and do not combine simplicity, low coefficient sensitivity, low roundoff noise generation and propagation, and/or simple scaling for a wide dynamic range. 
   The present invention, therefore, is directed to a harmonic series filter which overcomes one or more of the problems of the prior art. 
   SUMMARY OF THE INVENTION 
   In accordance with one aspect of the present invention, a filtering system comprises first and second inputs, a set of M notch filters, a tuning parameter generator, a filter coefficient generator, and a gain normalizer. The first input receives a signal contaminated with noise. The second input receives a noise reference signal. Each of the M notch filters responds to a corresponding tuning coefficient by attenuating a corresponding noise frequency in the signal contaminated with noise. Based on the noise reference signal, the tuning parameter generator generates a tuning parameter corresponding to a fundamental frequency of the noise. The filter coefficient generator responds to the tuning parameter so as to provide each of the M notch filters with the corresponding tuning coefficient. The gain normalizer adjusts an overall gain of the M notch filters. 
   In accordance with another aspect of the present invention, a method comprises the following: generating a tuning parameter corresponding to a fundamental frequency of noise in a signal contaminated with the noise; generating tuning coefficients β 1 , β 2 , β 3 , . . . , β N  in response to the tuning parameter, wherein the tuning coefficients β 1 , β 2 , β 3 , . . . , β N  correspond to the fundamental frequency and to harmonics of the fundamental frequency; and, filtering the signal with notches positioned at frequencies determined by the tuning coefficients β 1 , β 2 , β 3 , . . . , β N  so that the noise is attenuated. 
   In accordance with yet another aspect of the present invention, a notch filter comprises an input, an output, first, second, third, fourth, and fifth summers, first and second multipliers, and first and second delays. The input receives an input signal contaminated with noise, and the noise has a fundamental frequency. The output provides an output signal from the notch filter, and the output signal is substantially free of a harmonic of the fundamental frequency of the noise. The first summer sums the input signal with an output of the first delay, and the first summer has an output providing the output signal. The first multiplier multiplies the output signal by a gain coefficient. The second summer subtracts an output of the first multiplier from the input signal. The third summer subtracts an output of a second delay from an output of the second summer. The second multiplier multiplies an output of the third summer by a tuning coefficient related to the harmonic. The fourth summer subtracts an output of the second multiplier from the output of the second summer, and the fourth summer has an output coupled as an input to the second delay. The fifth summer subtracts the output of the second multiplier from the output of the second delay, and an output of the fifth summer is coupled as an input to the first delay. 
   In accordance with still another aspect of the present invention, a notch filter applies a transfer function F(z,n) to an input signal contaminated with noise in order to produce an output signal in which a harmonic of the noise is attenuated. The transfer function F(z,n) is defined by the following equation: 
         F   ⁡     (     z   ,   n     )       =       1   -     2   ⁢     β   n     ⁢     z     -   1         +     z     -   2           1   -         β   n     ⁡     (     1   +   α     )       ⁢     z     -   1         +     α   ⁢           ⁢     z     -   2                 
 
where n designates the harmonic, β n  is a tuning coefficient related to a center frequency of a bandwidth of the notch filter, α is a quantity related to the bandwidth of the notch filter, z −1  represents a first order delay, and z −2  represents a second order delay.
 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features and advantages will become more apparent from a detailed consideration of the invention when taken in conjunction with the drawings in which: 
       FIG. 1  shows an overview of a filtering system according to one embodiment of the present invention; 
       FIG. 2  shows in additional detail a representative one of the notch filters of the filtering system shown in  FIG. 1 ; and, 
       FIG. 3  shows in additional detail the filter coefficient computer of FIG.  2 . 
   

   DETAILED DESCRIPTION 
     FIG. 1  shows a filtering system  10  for filtering out the fundamental and harmonic frequency components of noise introduced into a signal by a source of noise, such as a nearby motor drive line. The filtering system  10 , for example, may be digital filtering system whose sampling period is T. The filtering system  10  includes a tuning parameter extractor  12  which receives a noise reference signal on an input  14 . This noise reference signal may be provided, for example, by a monitor positioned to pick up the noise emanating from the noise source of concern. One of the advantages of using a noise reference signal is that the filtering system  10  can then follow any changes in phase or frequency of the noise. Thus, the filtering system  10  adapts to the noise environment. 
   The tuning parameter extractor  12  may be a phase-locked loop or a frequency-locked loop that derives the fundamental frequency f 0  of the noise reference signal and then provides a tuning parameter β 1  on an output  16  based upon the fundamental frequency f 0  in accordance with the following equation:
 
β 1 =cos(20 πf   0   nT )  (1) 
 
where T is the sampling period.
 
   The output  16  of the tuning parameter extractor  12  is coupled to an input of a filter coefficient computer  18  which provides, on a tuning coefficient bus  20 , a set of filter tuning coefficient β n  for n=1, 2, 3, . . . , N in accordance with the following equation:
 
β n =cos(2 πf   0   nT )  (2) 
 
where N is the number of possible harmonics.
 
   Depending on the noise source, one or more of the N harmonics of the noise fundamental frequency may not be present in the noise signal. If such a source is the noise source of concern, it is necessary to use only the tuning coefficients corresponding to the M harmonics that are present, such that the tuning coefficients corresponding to the others of the N possible harmonics that are not present may be ignored. The fundamental frequency of the noise is f 0  and the frequencies of the N harmonics of the noise fundamental frequency are f n=nf   0  where n=1, 2, . . . , N. The notch-filter tuning coefficients for attenuating these interfering frequency components are defined in accordance with the following equation:
 
β n =cos(2 πf   n    T )  (3) 
 
If some harmonics are absent, only M&lt;N frequency components (f m  where m=1, 2, . . . , M) are present, and the required notch-filter tuning coefficients are given by the following equation:
 
β m =cos(2πf m   T )  (4) 
 
However, as will be understood from the above, although each f m is an integer multiple of f 0 , generally f m ≠mf 0 . Although the filter coefficient computer  18  generates all N values of β, only the M required values are output onto the tuning coefficient bus  20 . Therefore, the filter coefficient computer  18  contains instructions that determine which output samples β 1 , β 2 , β 3 , . . . , β N  are to be provided on the tuning coefficient bus  20 . These instructions are based on the frequencies known to be in the noise signal.
 
   The noise contaminated input signal is received on an input  22 . A gain normalizer  24  attenuates the noise contaminated input signal in accordance with the following equation: 
               [       (     1   +   α     )     2     ]     M           (   5   )             
 
The quantity α in equation (5) is given by the following equation: 
             α   =       1   -     tan   ⁡     (     π   ⁢           ⁢     f   BW     ⁢   T     )           1   +     tan   ⁡     (     π   ⁢           ⁢     f   BW     ⁢   T     )                   (   6   )             
 
where α is the common bandwidth parameter for each filter stage. The common −3 dB bandwidth (in Hz) of each notch filter is the desired bandwidth f BW . The gain normalizer  24  provides the attenuated noise contaminated input signal on an output  26  which is coupled to a filter bank  28  comprising the M required notch filters  30   1 ,  30   2 ,  30   3 , . . .  30   M  coupled in tandem. An output  32  from the last notch filter  30   M  is a substantially noise free version of the signal on the input  22  with little phase and amplitude distortion.
 
   A notch filter  50  is shown in FIG.  2  and may be used for each of the notch filters  30   1 ,  30   2 ,  30   3 , . . .  30   M  shown in FIG.  1 . Each of the notch filters  30   1 ,  30   2 ,  30   3 , . . .  30   M  is a second-order single-multiplier-per-order Gray-Markel lattice all-pass filter based upon the filters shown by A. H. Gray, Jr. and J. D. Markel in “Digital lattice and ladder filter synthesis,”  IEEE Trans. on Audio and Electroacoustics , vol. AU- 21 , December 1973; pp. 491-500, although the notch filter  50  could be based on any of the other n-multiplier per order filters described therein. P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, in “The digital allpass filter; a versatile building block,”  Proc. IEEE , vol. 76, January, 1988; pp. 19-37, have shown that all pass filters may be interconnected in interesting ways to produce standard filtering functions with reduced complexity and high precision. Furthermore, U.S. Pat. No. 5,587,910 has shown a sign-assignment protocol that gives maximum dynamic range to a Gray-Markel lattice filter section. 
   The transfer function of the notch filter  50  shown in  FIG. 2  is given by the following equation: 
               F   ⁡     (     z   ,   n     )       =       1   -     2   ⁢     β   n     ⁢     z     -   1         +     z     -   2           1   -         β   n     ⁡     (     1   +   α     )       ⁢     z     -   1         +     α   ⁢           ⁢     z     -   2                     (   7   )             
 
where β n  is the tuning coefficient supplied to the notch filter  50  and α is given by equation (6). The notch filter  50  implements this transfer function in a simple manner and with a large dynamic range. The zero frequency gain for the transfer function of equation (7) is given by the following: 
               2     1   +   α       ≥   1           (   8   )             
 
where the −3 dB notch-width parameter a is common to all of the filter sections and is given by equation (6) and where the −3 dB notch width in Hz is f BW .
 
   The input signal on an input  52  of the notch filter  50  is coupled to a first positive input of a first summer  54 . The output of the first summer  54  delivers the output of the notch filter  50  on an output  56  and is also coupled to a bandwidth scaling multiplier  58  that applies the quantity a to the output of the first summer  54 . The bandwidth scaling multiplier  58  sets a −3 dB notch bandwidth on the notch implemented by the notch filter  50  in accordance with a. The output of the bandwidth scaling multiplier  58  is coupled to a negative input of a second summer  60 . The input signal on the input  52  of the notch filter  50  is also coupled to a positive input of the second summer  60 . 
   The output of the second summer  60  is coupled to a positive input of a third summer  62  and to a positive input of a fourth summer  64 . The output of the third summer  62  is coupled to a tuning coefficient multiplier  66  which forms the product of the output of third summer  62  and the tuning coefficient β n  from the tuning coefficient bus  20 . The output of tuning coefficient multiplier  66  is coupled to a negative input of the fourth summer  64  and to a negative input of a fifth summer  68 . The output of fourth summer  64  is coupled as an input of a first single-sample-period-delay element  70  whose output is connected to a negative input of the third summer  62  and to a positive input of the fifth summer  68 . The output of the fifth summer  68  is coupled to a second single-sample-period-delay element  72  whose output is coupled to a second positive input of the first summer  54 . 
   The notch filter  50  shown in  FIG. 2  is a narrow band notch filter that is centered on the n th  harmonic of the fundamental noise frequency as determined by the tuning coefficient β n . Thus, each of the notch filters  30   1 ,  30   2 ,  30   3 , . . .  30   M  filters out a corresponding fundamental or harmonic frequency of the noise signal at the input  22  to produce a substantially noise free signal at the output  32 . 
   The filter coefficient computer  18  as shown in  FIG. 3  is implemented as a second order recursive loop. The fundamental frequency tuning parameter β 1  provided by the tuning parameter extractor  12  is supplied as the initial condition to a first single-sample-period delay element  82  and also to a first input of a multiplier  84 . An output Γ n , from the first single-sample-period delay element  82  is coupled to a negative input of a summer  86 . The output of the summer  86  is coupled as an input to a second single-sample-period delay element  88  whose initial condition is set to unity. The output of the second single-sample-period delay element  88  is coupled to a second input of the multiplier  84  and to the Γ n+1  input of the first single-sample-period delay element  82 . Also, the output of the second single-sample-period delay element  88  provides the tuning coefficients β 1 , β 2 , β 3 , . . . , β N  over the tuning coefficient bus  20 . The output of the multiplier  84  is coupled through a multiply-by-two device  90  to a positive output of the summer  86 . Accordingly, the filter coefficient computer  18  recursively generates the tuning parameters β 1 , β 2 , β 3 , . . . , β N  and provides these tuning parameters over the tuning coefficient bus  20 . 
   Certain modifications of the present invention will occur to those practicing in the art of the present invention. For example, the present invention has been described above in terms of eliminating noise from such noise sources as a motor drive line. However, it should be understood from the above description that the filter of the present invention may be used to filter out noise from other sources as well. 
   Moreover, the embodiment of the present invention described above includes certain hardware components as shown in  FIGS. 1-3 . The present invention can be implemented, however, using a computer, a digital signal processor, a neural network, one or logic arrays, etc. 
   As described above, the tuning parameter extractor  12  extracts a tuning parameter β 1 , and the filter coefficient computer  18  is a second order recursive loop which recursively generates the tuning coefficients β 1 , β 2 , β 3 , . . . , β N  using the tuning parameter  1  as an input. Instead, the tuning parameter extractor  12  may be arranged to simply extract the noise fundamental frequency f 0  as the tuning parameter, and the filter coefficient computer  18  may be arranged to implement equation (2) directly in order to generate the tuning coefficients β 1 , β 2 , β 3 , . . . , βN from upon the tuning parameter f 0 . 
   Furthermore, as described above, the filter bank  28  is shown as including the notch filters  30   1 ,  30   2 ,  30   3 , . . .  30   M . Thus, a determination is made beforehand as to which noise frequencies will be present and which ones will not be present in the noise generated by the noise source. The tuning coefficient bus  20  is then arranged to deliver only the tuning coefficients generated by the filter coefficient computer  18  that correspond to the noise frequencies which are predicted to be present. These noise frequencies may change as the noise fundamental frequency changes. However, any changes in the noise fundamental frequency are tracked and are used to suitably adjust the tuning coefficients. 
   On the other hand, if it cannot be predicted which noise frequencies will be in the noise generated by the noise source, a harmonic analyzer can be used to determine which harmonics are present in the noise reference signal on the input  14 . In this case, the filter bank  28  should contain the notch filters  30   1 ,  30   2 ,  30   3 , . . .  30   N  where N represents the maximum number of noise frequencies likely to be encountered in the noise reference signal received over the input  14 . The output of the harmonic analyzer can then be used to control the tuning coefficient bus  20  to deliver to the required number of notch filters the tuning coefficients corresponding to the actual noise frequencies and to by-pass the unneeded notch filters, if any. 
   Accordingly, the description of the present invention is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the best mode of carrying out the invention. The details may be varied substantially without departing from the spirit of the invention, and the exclusive use of all modifications which are within the scope of the appended claims is reserved.