Abstract:
An electrical signal is applied to a band pass filter, a first notch filter, and a second notch filter in any order. The center frequencies of the notch filters straddle the pass band of the band pass filter. The notch filters improve group delay and steepen the skirts of the response curve of the band pass filter.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application includes material disclosed in the following applications assigned to the assignee of this invention. The entire contents of each of these co-pending applications are incorporated herein by reference.  
         [0002]    (1) Application No. 09/466,313 filed Dec. 17, 1999, entitled “Band Pass Filter from Two Notch Filters”.  
         [0003]    (2) Application No. ______, filed concurrently herewith, and entitled “Band Pass Filter from Two Filters”. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0004]    This invention relates to a filter circuit and, in particular, to an analog band pass filter having a more uniform group delay than such filters in the prior art.  
           [0005]    Band pass filters have been used, alone or combined, in a host of applications virtually since the beginning of the electronic industry. The continuing problem in any application is providing a band pass filter having the desired frequency response. It is known in the art that a band pass filter can include a pair of series coupled resonant circuits that are “de-tuned”, i.e. have slightly different resonant frequencies. See for example, “ Radio Engineering”  by Terman, McGraw-Hill Book Company, New York, 1937, pages 76-85.  
           [0006]    Today, a band pass filter can be implemented in any one of several technologies. For example, passive analog filters utilize resistors, capacitors, and inductors to achieve the desired frequency response. Active filters add one or more operational amplifiers to prevent a signal from becoming too attenuated by the passive components and to exaggerate or to minimize a particular response by controlled feedback. Switched capacitor circuits are basically analog circuits but divide a signal into discrete samples and, therefore, have some attributes of digital circuits.  
           [0007]    Finite Impulse Response (FIR) filters are completely digital, using a shift register with a plurality of taps. An FIR filter generally has a linear phase versus frequency response and a constant group delay. As such, FIR filters find widespread use in digital communication systems, speech processing, image processing, spectral analysis, and other areas where non-linear phase response is unacceptable.  
           [0008]    A problem using FIR filters is the number of samples versus the delay in processing a signal. In order to obtain a high roll-off, i.e. a nearly vertical skirt on the response curve, a very large number of taps is necessary. Although the group delay is constant, it is relatively large, ten to fifteen times that of an analog filter, because of the large number of taps. Another problem with FIR filters is ripple, which typically exceeds 3 decibels (dB). There are other digital circuits that could be considered filters but these circuits either do not operate in “real time” or have such long processing times that the delays limit the utility of the techniques.  
           [0009]    It is known in the art to use delay equalizers to improve the uniformity of the delay of a band pass filter; e.g. see “ Electronic Filter Design Handbook”  by Williams and Taylor, Third Edition, McGraw-Hill, Inc., 1995, pages 7.21-7.27 and 7.30. The effect on frequency response of adding such equalizers is not described.  
           [0010]    Obtaining a sharp roll-off from an analog filter is often difficult, particularly for narrow band filters, e.g. one third octave or less. Even with active elements, good filters tend to be complex and, therefore, expensive. As noted above, FIR filters can provide a sharp roll-off but typically suffer from long group delay, making an FIR filter unsuitable in telephone systems, for example.  
           [0011]    Frequency response, phase shift linearity, group delay, ripple, and roll-off are characteristics of all filters, whether or not the characteristic is mentioned in a particular application. The Q, or sharpness, of a filter circuit is often specified as the ratio of the center frequency to the band width at −3 dB. A problem with this definition is that the roll-off on each side of the center frequency is assumed to be symmetrical (when amplitude is plotted against the logarithm of frequency). Another assumption is that the skirts of the response curves of two filters are similar. If the assumption is not valid, then comparing one filter to another becomes difficult.  
           [0012]    In view of the foregoing, it is therefore an object of the invention to provide an analog band pass filter having short, relatively constant, group delay  
           [0013]    Another object of the invention is to provide an analog band pass filter that is relatively inexpensive despite improved performance when compared with filters of the prior art.  
           [0014]    A further object of the invention is to provide an analog band pass filter having higher Q than such filters in the prior art.  
         SUMMARY OF THE INVENTION  
         [0015]    The foregoing objects are achieved in this invention in which an electrical signal is applied to a band pass filter, a first notch filter, and a second notch filter in any order. The center frequencies of the notch filters straddle the pass band of the band pass filter. The notch filters improve group delay and steepen the skirts of the response curve of the band pass filter. The invention can be implemented with analog filters, IIR (Infinite Impulse Response) filters, bi-quad filters, or switched-C filters. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]    A more complete understanding of the invention can be obtained by considering the following detailed description in conjunction with the accompanying drawings, in which:  
         [0017]    [0017]FIG. 1 is a schematic of a band pass filter of the prior art;  
         [0018]    [0018]FIG. 2 is a schematic of a notch filter of the prior art;  
         [0019]    [0019]FIG. 3 is a partial block diagram of a band pass filter constructed in accordance with one aspect of the invention;  
         [0020]    [0020]FIG. 4 is a block diagram of a band pass filter constructed in accordance with the invention;  
         [0021]    [0021]FIG. 5 is a block diagram of a band pass filter constructed in accordance with an alternative embodiment of the invention; and  
         [0022]    [0022]FIG. 6 is a chart comparing filters made in accordance with the invention with filters of the prior art. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0023]    [0023]FIG. 1 is a schematic of a band pass filter known in the art. Filter  10  is known as a multiple feedback band pass circuit; see “ Electronic Filter Design Handbook”  by Williams and Taylor, Third Edition, McGraw-Hill, Inc., 1995, page 5.42-5.46.  
         [0024]    [0024]FIG. 2 is a schematic of a notch filter known as a twin-T filter with positive feedback; see the Williams and Taylor text, pages 6.38 and 6.39. This particular filter was chosen because of its simplicity, depth of notch, and because the gain can be adjusted easily.  
         [0025]    [0025]FIG. 3 illustrates an analog band pass filter constructed in accordance with a preferred embodiment of the invention. Band pass filter  30  includes a pair of filter channels coupled to a difference amplifier. Specifically, input  31  is coupled to filter  32  and filter  33 , which are the same type of filter, band pass or notch, but have slightly offset center frequencies. Preferably, the frequency response curve for filter  32  intersects the frequency response curve for filter  33  at −3 dB or less. This prevents the frequency response curve of filter  30  from having more than one peak. The output of filter  32  is coupled to a non-inverting input of filter  34  and the output of filter  33  is coupled to an inverting input of filter  34 . The resistors shown all have the same value, e.g. 10kΩ.  
         [0026]    Using a notch filter constructed as shown in FIG. 2 for each of filters  32  and  33 , one obtains the band pass filter described in cross-referenced application (1). Using a band pass filter constructed as shown in FIG. 1 for each of filters  32  and  33 , one obtains a band pass filter as described in cross-referenced application (2). FIGS. 1 and 2 illustrate filters that are preferred but are not the only filters suitable for implementing the invention.  
         [0027]    The signals from filters  32  and  33  are subtracted in amplifier  33 , producing a band pass frequency response having a narrower pass band and steeper skirts than analog filters of the prior art. Despite this improvement over the prior art, the frequency response can be further narrowed and the group delay improved by using the filter illustrated in FIG. 4.  
         [0028]    In FIG. 4, band pass filter  40  includes input  41  coupled to band pass filter  42  having an output coupled to notch filter  43 . Band pass filter  42  is preferably constructed as illustrated in FIG. 3, although the band pass filter illustrated in FIG. 1, or other analog band pass filters, could be used instead. Notch filter  43  has a notch frequency or center frequency below the pass band of filter  42 . Notch filter  44  is coupled to the output of notch filter  43  and has a notch frequency above the pass band of filter  42 . It does not matter what order filters  42 ,  43  and  44  are used.  
         [0029]    As noted in the Background of the Invention, the prior art definition of “Q” leaves something to be desired, as does the definition of “pass band.” One wants the frequency response to be as flat as possible within the pass band and the skirts to be as vertical as possible outside the pass band. Normalizing the response (setting maximum response to 0 dB) and defining the pass band as the region between the −3 dB points says nothing about the shape of the curve.  
         [0030]    When using a band pass filter constructed as illustrated in FIG. 3, notch filters  42  and  43  preferably have center frequencies slightly outside the −10 dB points on the response curve. Using an ordinary band pass filter for filter  41 , notch filters  42  and  43  preferably have center frequencies at least outside the −3 dB points on the response curve of the band pass filter.  
         [0031]    [0031]FIG. 5 illustrates an alternative embodiment of the invention. As noted above, the order in which the filters are placed does not matter. The results are the same. More specifically, all six permutations of the filters produce the same results.  
         [0032]    [0032]FIG. 6 illustrates the effect of passing a signal through filters  42 ,  43  and  44 . Curve  51  represents the frequency response of band pass filter  41 , constructed in accordance with FIG. 3. Curve  52  represents the signal at output  45 , i.e. the frequency response of band pass filter  40 . Curve  53  represents the group delay of band pass filter  42 . Curve  54  represents the group delay of band pass filter  40 , except for the notches near dashed lines  62  and  63 .  
         [0033]    The notches in curve  54  are artifacts of the simulation and arise because of the small amplitude of signal at the notch frequencies and because of a small sample size. Although each curve in FIG. 6 is based upon six hundred data points, this is not a very large sample compared to what the simulation software could provide. The data was reduced for conversion to a spreadsheet program from which the curves were drawn. Ten thousand or more points would exceed the resolution of a printer and take a great deal of time to process. The notches in curve  52  are real.  
         [0034]    As an aid to visualization, several straight, dashed lines are included in FIG. 6. The particular placement of these lines is not definitive of the invention. Line  61  shows the −20 dB level for curve  51 . Vertical lines  62  and  63  were placed at the intersections of line  61  and curve  52 , which is not normalized to zero dB. Horizontal line  64  is placed between curves  53  and  54  in the region between lines  62  and  63 .  
         [0035]    As can be seen, the range of the group delay is dramatically narrowed by the invention In the simulation upon which FIG. 6 is based, the ripple in curve  54  between lines  62  and  63  is less than 2 dB. In the art, a ripple of less than 3 dB is considered good. Note too that the uniformity in curve  54  extends past the −20 dB points on curve  52 . Thus, there is very little power in any signal having a frequency outside lines  62  and  63 . The slight increase in group delay is immaterial.  
         [0036]    A greater consistency within the pass band makes filter  40  useful in many applications, including telephones and telephone systems. Implemented as an integrated circuit, a filter constructed in accordance with the invention is much less expensive than an FIR filter, for example.  
         [0037]    The invention thus provides an analog band pass filter having short, relatively constant, group delay. The filter has higher Q than analog filters in the prior art and is relatively inexpensive despite improved performance when compared with analog filters of the prior art.  
         [0038]    Having thus described the invention, it will be apparent to those of skill in the art that many modifications can be made within the scope of the invention. For example, although only a filter is shown in each channel in FIG. 3, other circuitry can be included in each channel. The outputs of the channels would be summed if the signal in one channel were inverted without also inverting the signal in the other channel. The invention can be implemented in several different technologies, including analog filters, IIR filters, bi-quad filters, and switched-C filters. The invention can be used for band pass filters of any center frequency from sub-audio through radio frequency.