Patent Publication Number: US-10325586-B2

Title: Active noise reduction

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 13/899,073 filed May 21, 2013, now U.S. Pat. No. 9,583,090, issued Feb. 28, 2017, which claims priority from EP Application No. 12 168 685.1-2225 filed May 21, 2012, the disclosures of which are hereby incorporated in their entirety by reference herein. 
    
    
     TECHNICAL FIELD 
     Disclosed herein is an active noise reduction system and, in particular, a noise reduction system which includes a feedback and a feedforward loop. 
     BACKGROUND 
     An active noise reduction system, also known as active noise cancellation/control (ANC) system, generally use a microphone to pick up an acoustic error signal (also called a “residual” signal) after the noise reduction, and feeds this error signal back to an ANC filter. This type of ANC system is called a feedback ANC system. The ANC filter in a feedback ANC system is typically configured to reverse the phase of the error feedback signal and may also be configured to integrate the error feedback signal, equalize the frequency response, and/or to match or minimize the delay. Thus, the quality of a feedback ANC system heavily depends on the quality of the ANC filter. The same problem arises with ANC systems having a so-called feedforward or other suitable noise reducing structure. A feedforward ANC system generates by means of an ANC filter a signal (secondary noise) that is equal to a disturbance signal (primary noise) in amplitude and frequency, but has opposite phase. Thus, there is a general need for providing ANC systems with an improved performance. 
     SUMMARY 
     A noise reducing system comprises a first microphone that picks up noise signal at first location and that is electrically coupled to a first microphone output path; a loudspeaker that is electrically coupled to a loudspeaker input path and that radiates noise reducing sound at a second location; a second microphone that picks up residual noise at a third location and that is electrically coupled to a second microphone output path; a first active noise reducing filter that is connected between the first microphone output path and the loudspeaker input path; and a second active noise reducing filter that is connected between the second microphone output path and the loudspeaker input path; in which the first active noise reduction filter is a shelving or equalizing filter or comprises at least one shelving or equalizing filter or both. 
     These and other objects, features and advantages of the present invention will become apparent in light of the detailed description of the embodiments thereof, as illustrated in the accompanying drawings. In the figures, like reference numerals designate corresponding parts. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustration of a hybrid active noise reduction system in which a feedforward and feedback type active noise reduction system is combined; 
         FIG. 2  is a magnitude frequency response diagram representing the transfer characteristics of shelving filters applicable in the system of  FIG. 1 ; 
         FIG. 3  is a block diagram illustration of an analog active 1st-order bass-boost shelving filter; 
         FIG. 4  is a block diagram illustration of an analog active 1st-order bass-cut shelving filter; 
         FIG. 5  is a block diagram illustration of an analog active 1st-order treble-boost shelving filter; 
         FIG. 6  is a block diagram illustration of an analog active 1st-order treble-cut shelving filter; 
         FIG. 7  is a block diagram illustration of an analog active 1st-order treble-cut shelving filter; 
         FIG. 8  is a block diagram illustration of an ANC filter including a shelving filter structure and additional equalizing filters; 
         FIG. 9  is a block diagram illustration of an alternative ANC filter including a linear amplifier and a passive filter network; 
         FIG. 10  is a block diagram illustration of an analog passive 1st-order bass (treble-cut) shelving filter; 
         FIG. 11  is a block diagram illustration of an analog passive 1st-order treble (bass-cut) shelving filter; 
         FIG. 12  is a block diagram illustration of an analog passive 2nd-order bass (treble-cut) shelving filter; 
         FIG. 13  is a block diagram illustration of an analog passive 2nd-order treble (bass-cut) shelving filter; 
         FIG. 14  is a block diagram illustration of a universal ANC (active) filter structure that is adjustable in terms of, boost or cut equalizing falter with high quality and/or low gain; 
         FIG. 15  is a block diagram illustration of a digital finite impulse response filter (FIR) applicable in the system of  FIG. 1 ; 
         FIG. 16  is a Bode diagram depicting the transfer function of the primary path and the sensitivity function of the improved system; and 
         FIG. 17  is a diagram depicting the transfer function of the primary path and the sensitivity functions of the open loop system, the closed loop system and the combined, i.e. of the hybrid system. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , an improved noise reducing system includes a first microphone  1  that picks up at a first location a noise signal from, e.g., a noise source  4  and that is electrically coupled to a first microphone output path  2 . A loudspeaker  7  is electrically coupled to a loudspeaker input path  6  and radiates noise reducing sound at a second location. A second microphone  11  that is electrically coupled to a second microphone output path  12  picks up residual noise at a third location, the residual noise being created by superimposing the noise received via a primary path  5  and the noise reducing sound received via a secondary path  8 . A first active noise reducing filter  3  is connected between the first microphone output path  2  and via an adder  14  to loudspeaker input path  6 . A second active noise reducing filter  13  is connected to the second microphone output path  12  and via the adder  14  to the loudspeaker input path  6 . The second active noise reduction filter  13  is or comprises at least one shelving or equalizing (peaking) filter. These filter(s) may, for example, be a  2 nd order filter structure. 
     In the system of  FIG. 1 , an open loop  15  and a closed loop  16  are combined, forming a so-called “hybrid” system. The open loop  15  includes the first microphone  1  and the first ANC filter  3 . The closed loop  16  includes the second microphone  11  and the second ANC filter  13 . The first and second microphone output paths  2  and  12  and the loudspeaker input path  6  may include analog amplifiers, analog or digital filters, analog-to-digital converters, digital-to-analog converters or the like which are not shown for the sake of simplicity. The first ANC filter  3  may be or may comprise at least one shelving or equalizing filter. 
     The shelving or equalizing filter of the first ANC filter may be an active or passive analog filter or a digital filter. The shelving filter in the second ANC filter may be an active or passive analog filter. For example, the first ANC filter may be or may comprise at least one digital finite impulse response filter. Analog and digital filters which are suitable are described below with reference to  FIGS. 2-15 . 
     The system shown in  FIG. 1  has a sensitivity which can be described by the following equation:
 
 N ( z )=( H ( z )− W   OL ( z )· S   CL ( z )/(1− W   CL ( z )· S   CL ( z )),
 
in which H(z) is the transfer characteristic of the primary path  5 , W OL (z) is the transfer characteristic of the first ANC filter  3 , S CL (z) is the transfer characteristic of the secondary path  8 , and W CL (z) is the transfer characteristic of the second ANC filter  13 . Advantageously, the first ANC filter  3  (open loop) and the second ANC filter  13  (closed loop) can easily be optimized separately.
 
       FIG. 2  is a schematic diagram of the transfer characteristics  18 ,  19  of analog shelving filters applicable in the systems described above with reference to  FIG. 1 . In particular, a first order treble boost (+9 dB) shelving filter ( 18 ) and a bass cut (−3 dB) shelving filter ( 19 ) are shown. Although the range of spectrum shaping functions is governed by the theory of linear filters, the adjustment of those functions and the flexibility with which they can be adjusted varies according to the topology of the circuitry and the requirements that have to be fulfilled. 
     Single shelving filters are minimum phase (usually simple first-order) filters which alter the relative gains between frequencies much higher and much lower than the corner frequencies. A low or bass shelving filter is adjusted to affect the gain of lower frequencies while having no effect well above its corner frequency. A high or treble shelving filter adjusts the gain of higher frequencies only. 
     A single equalizer filter, on the other hand, implements a second-order filter function. This involves three adjustments: selection of the center frequency, adjustment of the quality (Q) factor, which determines the sharpness of the bandwidth, and the level or gain, which determines how much the selected center frequency is boosted or cut relative to frequencies (much) above or below the center frequency. 
     With other words: A low-shelving filter ideally passes ail frequencies, but increases or reduces frequencies below the shelving filter frequency by a specified amount. A high-shelving filter ideally passes all frequencies, but increases or reduces frequencies above the shelving filter frequency by a specified amount. An equalizing (EQ) filter makes a peak or a dip in the frequency response. 
     Reference is now made to  FIG. 3  in which one optional filter structure of an analog active 1st-order bass-boost shelving filter is shown. The structure shown includes an operational amplifier  20  having an inverting input (−), a non-inverting input (+) and an output. A filter input signal In is supplied to the non-inverting input of the operational amplifier  20  and at the output of the operational amplifier  20  a filter output signal Out is provided. The input signal In and the output signal Out are (in the present and all following examples) voltages Vi and Vo that are referred to a reference potential M. A passive filter (feedback) network including two resistors  21 ,  22  and a capacitor  23  is connected between the reference potential M, the inverting input of the operational amplifier  20  and the output of the operational amplifier  20  such that the resistor  22  and the capacitor  23  are connected in parallel with each other and together between the inverting input and the output of the operational amplifier  20 . Furthermore, the resistor  21  is connected between the inverting input of the operational amplifier  20  and the reference potential M. 
     The transfer characteristic H(s) over complex frequency s of the filter of  FIG. 3  is:
 
 H ( s )= Z   o ( s )/ Z   i ( s )=1+( R   22   /R   21 )·(1/(1+ sC   23   R   22 )),
 
in which Z i (s) is the input impedance of the filter, Z o (s) is the output impedance of the filter, R 21  is the resistance of the resistor  21 , R 22  is the resistance of the resistor  22  and C 23  is the capacitance of the capacitor  23 . The filter has a corner frequency f 0  in which f 0 =1/2πC 23 R 22 . The gain G 5  at lower frequencies (≈0 Hz) is G L =1+(R 22 /R 21 ) and the gain G H  at higher frequencies (≈∞ Hz) is G H =1. The gain GL and the corner frequency f 0  are determined, e.g., by the acoustic system used (loudspeaker-room-microphone system). For a certain corner frequency f 0  the resistances R 21 , R 22  of the resistors  21  and  22  are:
 
 R   22 =1/2π f   0   C   23  
 
 R   21   =R   22 /( G   L −1).
 
     As can be seen from the above two equations, there are three variables but only two equations so it is an over-determined equation system. Accordingly, one variable has to be chosen by the filter designer depending on any further requirements or parameters, e.g. the mechanical size of the filter, which may depend on the mechanical size and, accordingly, on the capacity C 23  of the capacitor  23 . 
       FIG. 4  illustrates an optional filter structure of an analog active 1st-order bass-cut shelving filter. The structure shown includes an operational amplifier  24  whose noninverting input is connected to the reference potential M and whose inverting input is connected to a passive filter network. This passive filter network is supplied with the filter input signal In and the filter output signal Out, and includes three resistors  25 ,  26 ,  27  and a capacitor  28 . The inverting input of the operational amplifier  24  is coupled through the resistor  25  to the input signal In and through the resistor  26  to the output signal Out. The resistor  27  and the capacitor  28  are connected in series with each other and as a whole in parallel with the resistor  25 , i.e., the inverting input of the operational amplifier  24  is also coupled through the resistor  27  and the capacitor  28  to the input signal In. 
     The transfer characteristic H(s) of the filter of  FIG. 4  is: 
                     H   ⁡     (   s   )       =       ⁢         Z   o     ⁡     (   s   )       /       Z   i     ⁡     (   s   )                       (   s   )     =       ⁢       (       R   26     /     R   25       )     ·     (       (     1   +     s   ⁢           ⁢       C   28     ⁡     (       R   25     +     R   27       )           )     /     (     1   +     s   ⁢           ⁢     C   28     ⁢     R   27         )       )                   
in which R 25  is the resistance of the resistor  25 , R 26  is the resistance of the resistor  26 , R 27  is the resistance of the resistor  27  and C 28  is the capacitance of the capacitor  28 . The filter has a corner frequency f 0 =1/2πC 28 R 27 . The gain G L  at lower frequencies (≈0 Hz) is G L =(R 26 /R 25 ) and the gain G H  at higher frequencies (≈∞ Hz) is G H =R 26 ·(R 25 +R 27 )/(R 25 ·R 27 ) which should be 1. The gain G L  and the corner frequency f 0  are determined, e.g., by the acoustic system used (loudspeaker-room-microphone system). For a certain corner frequency f 0  the resistances R 25 , R 27  of the resistors  25  and  27  are:
 
 R   25   =R   26   /G   L  
 
 R   27   =R   26 /( G   H   −G   L ).
 
     The capacitance of the capacitor  28  is as follows:
 
 C   28 =( G   H   −G   L )/2π f   0   R   26 .
 
     Again, there is an over-determined equation system which, in the present case, has four variables but only three equations. Accordingly, one variable has to be chosen by the filter designer, e.g., the resistance R 26  of the resistor  26 . 
       FIG. 5  illustrates an optional filter structure of an analog active 1st-order treble-boost shelving filter. The structure shown includes an operational amplifier  29  in which the filter input signal In is supplied to the non-inverting input of the operational amplifier  29 . A passive filter (feedback) network including a capacitor  30  and two resistors  31 ,  32  is connected between the reference potential M, the inverting input of the operational amplifier  29  and the output of the operational amplifier  29  such that the resistor  31  and the capacitor  30  are connected in series with each other and together between the inverting input and the reference potential M. Furthermore, the resistor  32  is connected between the inverting input of the operational amplifier  29  and the output of the operational amplifier  29 . 
     The transfer characteristic H(s) of the filter of  FIG. 5  is:
 
 H ( s )= Z   o ( s )/ Z   i ( s )=(1+ sC   30 ( R   31   +R   32 ))/(1+ sC   30   R   31 )
 
in which C 30  is the capacitance of the capacitor  30 , R 31  is the resistance of the resistor  31  and R 32  is the resistance of the resistor  32 . The filter has a corner frequency f 0 =1/2πC 30 R 31 . The gain G L  at lower frequencies (≈0 Hz) is G L =1 and the gain G H  at higher frequencies (≈∞ Hz) is G H =1+(R 32 /R 31 ). The gain G H  and the corner frequency f 0  are determined, e.g., by the acoustic system used (loudspeaker-room-microphone system). For a certain corner frequency f 0  the resistances R 31 , R 32  of the resistors  31  and  32  are:
 
 R   31 =1/2π f   0   C   30  
 
 R   32   =R   31 /( G   H −1).
 
     Again, there is an over-determined equation system which, in the present case, has three variables but only two equations. Accordingly, one variable has to be chosen by the filter designer depending on any other requirements or parameters, e.g., the resistance R 32  of the resistor  32 . This is advantageous because resistor  32  should not be made too small in order to keep the share of the output current of the operational amplifier flowing through the resistor  32  low. 
       FIG. 6  illustrates an optional filter structure of an analog active 1st-order treble-cut shelving filter. The structure shown includes an operational amplifier  33  whose non-inverting input is connected to the reference potential M and whose inverting input is connected to a passive filter network. This passive filter network is supplied with the filter input signal In and the filter output signal Out, and includes a capacitor  34  and three resistors  35 ,  36 ,  37 . The inverting input of the operational amplifier  33  is coupled through the resistor  35  to the input signal In and through the resistor  36  to the output signal Out. The resistor  37  and the capacitor  34  are connected in series with each other and as a whole in parallel with resistor  36 , i.e., inverting input of the operational amplifier  33  is also coupled through the resistor  37  and the capacitor  34  to the output signal Out. 
     The transfer characteristic H(s) of the filter of  FIG. 6  is: 
                     H   ⁡     (   s   )       =       ⁢         Z   o     ⁡     (   s   )       /       Z   i     ⁡     (   s   )                     =       ⁢       (       R   36     ⁢     /   35       )     ·       (     1   +     s   ⁢           ⁢     C   34     ⁢     R   37         )     /     (     1   +     s   ⁢           ⁢       C   34     ⁡     (       R   36     +     R   37       )           )                     
in which C 34  is the capacitance of the capacitor  34 , R 35  is the resistance of the resistor  35 , R 36  is the resistance of the resistor  36  and R 37  is the resistance of the resistor  37 .
 
     The filter has a corner frequency f 0 =1/2πC 34 (R 36 +R 37 ). The gain G L  at lower frequencies (≈0 Hz) is G L =(R 36 /R 35 ) and should be 1. The gain G H  at higher frequencies (≈∞ Hz) is G H =R 36 ·R 37 /(R 35 ·(R 36 +R 37 )). The gain G L  and the corner frequency f 0  are determined, e.g., by the acoustic system used (loudspeaker-room-microphone system). For a certain corner frequency f 0  the resistances R 35 , R 36 , R 37  of the resistors  35 ,  36  and  37  are:
 
 R   35   =R   36  
 
 R   37   =G   H   ·R   36 /(1− G   H ).
 
     The capacitance of the capacitor  34  is as follows:
 
 C   34 =(1− G   H )/2π f   0   R   36 .
 
     The resistor  36  should not be made too small in order to keep the share of the output current of the operational amplifier flowing through the resistor  36  low. 
       FIG. 7  illustrates an alternative filter structure of an analog active 1st-order treble-cut shelving filter. The structure shown includes an operational amplifier  38  in which the filter input signal In is supplied through a resistor  39  to the non-inverting input of the operational amplifier  38 . A passive filter network including a capacitor  40  and a resistor  41  is connected between the reference potential M and the non-inverting input of the operational amplifier  38  such that the capacitor  30  and the resistor  41  are connected in series with each other and together between the non-inverting input and the reference potential M. Furthermore, a resistor  42  is connected between the inverting input and the output of the operational amplifier  38  for signal feedback. 
     The transfer characteristic H(s) of the filter of  FIG. 7  is:
 
 H ( s )= Z   o ( s )/ Z   i ( s )=(1+ sC   40   R   41 )/(1+ sC   40 ( R   39   +R   41 ))
 
in which R 39  is the resistance of the resistor  39 , C 40  is the capacitance of the capacitor  40 , R 41  is the resistance of the resistor  41  and R 42  is the resistance of the resistor  42 . The filter has a corner frequency f 0 =1/2πC 40 (R 39 +R 41 ). The gain G L  at lower frequencies (≈0 Hz) is G L =1 and the gain G H  at higher frequencies (≈∞ Hz) is G H =R 41 /(R 39 +R 41 )&lt;1. The gain G H  and the corner frequency f 0  may be determined, e.g., by the acoustic system used (loudspeaker-room-microphone system). For a certain corner frequency f 0  the resistances R 39 , R 41  of the resistors  39  and  41  are:
 
 R   39   =G   H   R   42 /(1− G   H )
 
 R   41 =1− G   H )/2π f   0   R   42 .
 
     The resistor  42  should not be made too small in order to keep the share of the output current of the operational amplifier flowing through the resistor  42  low. 
       FIG. 8  depicts an ANC filter that is based on the shelving filter structure described above in connection with  FIG. 5  and that includes two additional equalizing filters  43 ,  44 , one of which (e.g.,  43 ) may be a cut equalizing filter for a first frequency band and the other may be a boost equalizing filter for a second frequency band. Equalization, in general, is the process of adjusting the balance between frequency bands within a signal. 
     The equalizing filter  43  includes a gyrator and is connected at one end to the reference potential M and at the other end to the non-inverting input of the operational amplifier  29 , in which the input signal In is supplied to the non-inverting input through a resistor  45 . The equalizing filter  43  includes an operational amplifier  46  whose inverting input and its output are connected to each other. The non-inverting input of the operational amplifier  46  is coupled through a resistor  47  to reference potential M and through two series-connected capacitors  48 ,  49  to the non-inverting input of operational amplifier  29 . A tap between the two capacitors  48  and  49  is coupled through a resistor  50  to the output of operational amplifier  46 . 
     The equalizing filter  44  includes a gyrator and is connected at one end to the reference potential M and at the other end to the inverting input of the operational amplifier  29 , i.e., it is connected in parallel with the series connection of the capacitor  30  and the resistor  31 . The equalizing filter  44  includes an operational amplifier  51  whose inverting input and its output are connected to each other. The non-inverting input of the operational amplifier  46  is coupled through a resistor  52  to reference potential M and through two series-connected capacitors  53 ,  54  to the inverting input of the operational amplifier  29 . A tap between the two capacitors  53  and  54  is coupled through a resistor  55  to the output of the operational amplifier  51 . 
     A problem with ANC filters in mobile devices supplied with power from batteries is that the more operational amplifiers that are used, the higher the power consumption is. An increase in power consumption, however, requires larger and thus more room consuming batteries when the same operating time is desired, or decreases the operating time of the mobile device when using the same battery types. One approach to further decreasing the number of operational amplifiers may be to employ the operational amplifier for linear amplification only and to implement the filtering functions with passive networks connected downstream (or upstream) of the operational amplifier (or between two amplifiers). An exemplary structure of such an ANC filter structure is shown in  FIG. 9 . 
     In the ANC filter of  FIG. 9 , an operational amplifier  56  is supplied at its noninverting input with the input signal In. A passive, non-filtering network including two resistors  57 ,  58  is connected to the reference potential M and the inverting input and the output of the operational amplifier  56  forming a linear amplifier together with the resistors  57  and  58 . In particular, the resistor  57  is connected between the reference potential M and the inverting input of the operational amplifier  56  and the resistor  58  is connected between the output and the inverting input of the operational amplifier  56 . A passive filtering network  59  is connected downstream of the operational amplifier, i.e., the input of the network  59  is connected to the output of the operational amplifier  56 . A downstream connection is more advantageous than an upstream connection in view of the noise behavior of the ANC filter in total. Examples of passive filtering networks applicable in the ANC filter of  FIG. 9  are illustrated below in connection with  FIGS. 10-13 . 
       FIG. 10  depicts a filter structure of an analog passive 1st-order bass (treblecut) shelving filter, in which the filter input signal In is supplied through a resistor  61  to a node at which the output signal Out is provided. A series connection of a capacitor  60  and a resistor  62  is connected between the reference potential M and this node. The transfer characteristic H(s) of the filter of  FIG. 10  is:
 
 H ( s )= Z   o ( s )/ Z   i ( s )=(1+ sC   60   R   62 )/(1+ sC   60 ( R   61   +R   42 ))
 
in which C 60  is the capacitance of the capacitor  60 , R 61  is the resistance of the resistor  61  and R 62  is the resistance of the resistor  62 . The filter has a corner frequency f 0 =1/2πC 40 (R 61 +R 62 ). The gain G L  at lower frequencies (≈0 Hz) is G L =1 and the gain G H  at higher frequencies (≈∞ Hz) is G H =R 62 /(R 61 +R 62 ). For a certain corner frequency f 0  the resistances R 61 , R 62  of the resistors  61  and  62  are:
 
 R   61 =(1− G   H )/2= f   0   C   60 ,
 
 R   62   =G   H /27π f   0   C   60 .
 
     One variable has to be chosen by the filter designer, e.g., the capacitance C 60  of the capacitor  60 . 
       FIG. 11  depicts a filter structure of an analog passive 1st-order treble (bass-cut) shelving filter, in which the filter input signal In is supplied through a resistor  63  to a node at which the output signal Out is provided. A resistor  64  is connected between the reference potential M and this node. Furthermore, a capacitor  65  is connected in parallel with the resistor  63 . The transfer characteristic H(s) of the filter of  FIG. 11  is:
 
 H ( S )= Z   o ( s )/ Z   i ( s )= R   64 (1+ sC   65   R   63 )/(( R   63   +R   64 )+ sC   65   R   63   R   64 )
 
in which R 63  is the resistance of the resistor  63 , R 64  is the resistance of the resistor  64  and C 65  is the capacitance of the capacitor  65 . The filter has a corner frequency f 0 =(R 63 +R 64 )/2πC 65 R 63 R 64 ). The gain G H  at higher frequencies (≈∞ Hz) is G H =1 and the gain G L  at lower frequencies (≈∞ Hz) is G L =R 64 /(R 63 +R 64 ). For a certain corner frequency f 0  the resistances R 61 , R 62  of the resistors  61  and  62  are:
 
 R   63 =1/2π f   0   C   65   G   L ,
 
 R   64 =1/2π f   0   C   65 (1− G   L ).
 
       FIG. 12  depicts a filter structure of an analog passive 2nd-order bass (treble-cut) shelving filter, in which the filter input signal In is supplied through series connection of an inductor  66  and a resistor  67  to a node at which the output signal Out is provided. A series connection of a resistor  68 , an inductor  69  and a capacitor  70  is connected between the reference potential M and this node. The transfer characteristic H(s) of the filter of  FIG. 12  is:\ 
                     H   ⁡     (   s   )       =       ⁢         Z   o     ⁡     (   s   )       /       Z   i     ⁡     (   s   )                     =       ⁢       (     1   +     s   ⁢           ⁢     C   70     ⁢     R   68       +       s   2     ⁢     C   70     ⁢     L   69         )     /     (     1   +     s   ⁢           ⁢       C   70     ⁡     (       R   67     +     R   68       )         +                         ⁢       s   2     ⁢       C   70     ⁡     (       L   66     +     L   69       )         )               
in which L 66  is the inductance of the inductor  66 , R 67  is the resistance of the resistor  67 , R 68  is the resistance of the resistor  68 , L 69  is the inductance of the inductor  69  and C 70  is the capacitance of the capacitor  70 . The filter has a corner frequency f 0 =1/(2π(C 70 (L 66 +L 69 )) −1/2 ) and a quality factor Q=(1/(R 67 +R 68 ))·((L 66 +L 69 )/C 70 ) −1/2 ). The gain G L  at lower frequencies (≈0 Hz) is G L =1 and the gain G H  at higher frequencies (≈∞ Hz) is G H =L 69 /(L 66 +L 69 ). For a certain corner frequency f o  resistance R 67 , capacitance C 70  and inductance L 69  are:
 
 L   69 =( G   H   L   66 )/(1− G   H ),
 
 C   70 =(1− G   H )/((2π f   0 ) 2   L   66 ), and
 
 R   68 =(( L   66   +L   69 )/ C   70 ) −1/2   −R   67   Q )/ Q.  
 
       FIG. 13  depicts a filter structure of an analog passive 2nd-order treble (bass-cut) shelving filter, in which the filter input signal In is supplied through series connection of an capacitor  71  and a resistor  72  to a node at which the output signal Out is provided. A series connection of a resistor  73 , an inductor  74  and a capacitor  75  is connected between the reference potential M and this node. The transfer characteristic H(s) of the filter of  FIG. 13  is: 
                     H   ⁡     (   s   )       =       ⁢         Z   o     ⁡     (   s   )       /       Z   i     ⁡     (   s   )                     =       ⁢         C   71     ⁡     (     1   +     s   ⁢           ⁢     C   75     ⁢     R   73       +       s   2     ⁢     C   75     ⁢     L   74         )       /     (       (       C   71     +     C   75       )     +                         ⁢       s   ⁢           ⁢     C   71     ⁢       C   75     ⁡     (       R   72     +     R   73       )         +       s   2     ⁢     C   71     ⁢     C   75     ⁢     L   74         )               
in which C 71  is the capacitance of the capacitor  71 , R 72  is the resistance of the resistor  72 , R 73  is the resistance of the resistor  73 , L 74  is the inductance of the inductor  74  and C 75  is the capacitance of the capacitor  75 . The filter has a corner frequency f 0 =((C 71 +C 75 )/(4π 2 (L 74 C 71 C 75 )) −1/2  and a quality factor Q=(1/(R 72 +R 73 ))·((C 71 +C 75 )L 74 /(C 71 C 75 )) −1/2 . The gain G H  at higher frequencies (≈∞ Hz) is G H =1 and the gain G L  at lower frequencies (≈0 Hz) is G L =C 71 /(C 71 +C 75 ). For a certain corner frequency f 0  resistance R 73 , capacitance C 75  and inductance L 74  are:
 
 C   75 =(1− G   L ) C   71   /G   L ,
 
 L   74 =1/((2π f   0 ) 2   C   71 (1− G   L )), and
 
 R   73 =(( L   74 /( C   70 (1 −G   L ))) −1/2   /Q )− R   72 .
 
     Inductors used in the examples above may be substituted by an adequately configured gyrator. 
     With reference to  FIG. 14 , a universal active filter structure is described that is adjustable in terms of boost or cut equalizing. The filter includes an operational amplifier  76  as a linear amplifier and a modified gyrator circuit. In particular, the universal active filter structure includes another operational amplifier  77 , the non-inverting input of which is connected to reference potential M. The inverting input of operational amplifier  77  is coupled through a resistor  78  to a first node  79  and through a capacitor  80  to a second node  81 . The second node  81  is coupled through a resistor  82  to the reference potential M, and through a capacitor  83  with the first node  79 . The first node  79  is coupled through a resistor  84  to the inverting input of operational amplifier  76 , its inverting input is further coupled to its output through a resistor  85 . The non-inverting input of operational amplifier  76  is supplied through a resistor  86  with the input signal In. A potentiometer  87  forming an adjustable Ohmic voltage divider with two partial resistors  87   a  and  87   b  and having two ends and an adjustable tap is supplied at each end with input signal In and the output signal Out. The tap is coupled through a resistor  88  to the second node  81 . 
     The transfer characteristic H(s) of the filter of  FIG. 14  is:
 
 H ( s )=( b   0   +b   1   s+b   2   s   2 )/( a   0   +a   1   s+a   2   s   2 )
 
in which
 
 b   0   =R   84   R   87a   R   88   +R   87b   R   88   R+R   87a   R   88   R+R   84   R   87b   R   88   +R   84   R   87b   R   82   +R   84   R   87a   R   82   +R   84   R   87a   R   87   b+R   87a   R   87b   R+RR   87b   R   82   +RR   87a   R   82 ,
 
 b 1 =R   87a   C   80   R   82   RR   88   +RC   83   R   88   R   82   R   87b   +R   84   R   87b   R   88   C   83   R   82   +R   87a   C   83   R   82   RR   88   +R   84   R   87a   R   88   C   83   R   82   +R   84   R   87a   R   87b   C   80   R   82   +R   84   R   87a   R   88   C   80   R   82   +R   84   R   87b   R   88   C   80   R   82   +R   87a   C   80   R   82   R   1   R   87b   +C   80   R   82   R   78   RR   87b   +R   80   R   88   R   82   R   87b   +R   84   R   87a   R   87b   C   83   R   82   +R   87a   C   83   R   82   RR   87b ,
 
 b 2 =R   87a   R   82   R   88   RC   80   C   83   R   78   +RR   87b   R   88   C   80   C   83   R   82   R   78   +R   84   R   87b   R   88   C   80   C   83   R   82   R   78   +R   84   R   87a   R   88   C   80   C   83   R   82   R   78   +R   84   R   87a   R   87b   C   80   C   83   R   82   R   78   +R   1   R   87a   R   87b   C   80   C   83   R   82   R   78 .
 
 a   0   =R   84   R   87b   R   82   +R   84   R   87a   R   82   +R   84   R   87b   R   88   +R   84   R   87a   R   88   +R   84   R   87a   R   87b ,
 
 a   1   =R   84   R   87b   R   88   C   80   R   82   +R   84   R   87a   R   88   C   83   R   82   +R   84   R   87a   R   88   C   83   R   82   +R   84   R   87a   R   88   C   80   R   82   +R   84   R   87a   R   87b   C   83   R   82   +R   84   R   87a   R   87b   C   80   R   82   −R   87a   R   82   C   80   RR   78 ,
 
 a   2   =R   84   R   87b   R   88   C   80   C   83   R   82   R   78   +R   84   R   87a   R   88   C   80   C   83   R   82   R   78   +R   84   R   87a   R   87b   C   80   C   83   R   82   R   78 .
 
in which a resistor X has a resistance Rx (X=78, 82, 84, 85, 86, 87a, 87b, 88), a capacitor Y has a capacitance C Y  (Y=80, 83) and R 85 =R 86 =R.
 
     Shelving filters in general and 2nd-order shelving filters in particular, beside equalization filters, require careful design when applied to ANC filters, but offer a lot of benefits such as, e.g., minimum phase properties as well as little space and energy consumption. 
       FIG. 15  illustrates a digital finite impulse response FIR filter which might be used as or in a first ANC filter  3  in the system of  FIG. 1 . The FIR filter includes, for instance, four series-connected delay elements  90 - 93  in which the first delay element in this series of delay elements  90 - 93  is supplied with a digital input signal X(z). The input signal x(z) and output signals of the delay elements  90 - 93  are fed through coefficient elements  94 - 98  each with a specific coefficient h( 0 ), h( 1 )-h( 4 ) to a summer or, as shown, to four summers  99 - 102  to sum up the signals from the coefficient elements  94 - 98  thereby providing an output signal Y(z). With the coefficients h( 0 ), h( 1 )-h( 4 ) the filter characteristic is determined, which may be a shelving characteristic or any other characteristic as, for instance an equalizing characteristic. 
     As can be seen from  FIG. 16 , by combining an open loop system with a closed loop system a more distinctive attenuation characteristic in a broader frequency range can be achieved. In the upper diagram shown in  FIG. 16 , an exemplary frequency characteristic for the combined system is depicted as magnitude over frequency. The lower diagram in  FIG. 16  depicts an exemplary phase characteristic as phase over frequency. Each diagram shows a) the passive transfer characteristic, i.e., the transfer characteristic H(z) of the primary path  5 , and b) the sensitivity function N(z) of the combined open and closed loop system. 
     The share of each of the open loop system  15  and the closed loop system  16  contributes to the total noise reduction is depicted in  FIG. 17 . The diagram depicts exemplary magnitude frequency responses of the transfer characteristic H(z) of the primary path and the sensitivity functions of the open loop system (N OL ), the closed loop system (N CL ) and the combined system (N OL+CL ). According to these diagrams, the closed loop system  16  is more efficient in the lower frequency range while the open loop system  15  is more efficient in the higher frequency range. 
     The system shown is suitable for a variety of applications such as, e.g., ANC headphones in which the second ANC filter is an analog filter and the first filter is an analog or digital filter. 
     Although various examples of realizing the invention have been disclosed, it will be apparent to those skilled in the art that various changes and modifications can be made which will achieve some of the advantages of the invention without departing from the spirit and scope of the invention. It will be obvious to those reasonably skilled in the art that other components performing the same functions may be suitably substituted. Such modifications to the inventive concept are intended to be covered by the appended claims. 
     While exemplary embodiments are described above, it is not intended that these embodiments describe all possible forms of the invention. Rather, the words used in the specification are words 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. Additionally, the features of various implementing embodiments may be combined to form further embodiments of the invention.