Patent Publication Number: US-2004054707-A1

Title: Multiplication coefficient supplement device, multiplication coefficient supplement method, and multiplication factor supplement program

Description:
FIELD OF THE INVENTION  
       [0001] The present invention relates to an apparatus for, a method of, and a computer program product for complementing a multiplication coefficient while multiplying an input signal by the multiplication coefficient.  
       BACKGROUND OF THE INVENTION  
       [0002] Up until now, there have been provided a wide variety of digital audio apparatuses for carrying out a volume adjusting function by way of multiplying an audio input signal by a multiplication coefficient in response to a volume level specified by a user. Here, as the multiplication coefficient is specified a discrete value determined in response to the volume level specified by the user. It is well known that the digital audio apparatus is operative to complement the multiplication coefficient by means of a time constant process while multiplying the audio input signal by the multiplication coefficient so as to obtain an audio output signal to be converted into a sound smoothly audible to a human ear, thereby eliminating an audible noise occurring due to a discontinuous waveform caused by the multiplication coefficient with the discrete value.  
       [0003] One typical example of the conventional multiplication coefficient complementary apparatus operative to carry out a four-channel volume adjusting function and forming part of the digital audio apparatus is exemplified and shown in FIG. 8. As shown in FIG. 8, the conventional multiplication coefficient complementary apparatus  110  comprises: four multiplication units  21 ,  22 ,  23 , and  24  each adapted to multiply an audio input signal by a multiplication coefficient; and four complementary units  31 ,  32 ,  33 , and  34 , respectively associated with the multiplication units  21 ,  22 ,  23 , and  24  in one-to-one relationship, and each adapted to carry out a coefficient complementary operation to complement the multiplication coefficient for a multiplication unit by means of a time constant process.  
       [0004] The complementary unit  31  forming part of the multiplication coefficient complementary apparatus is shown in FIG. 9. As shown in FIG. 9, the complementary unit  31  comprises an input section  31   a  adapted to input a target value of the multiplication coefficient therethrough, a first multiplication section  31   d  adapted to multiply the target value of the multiplication coefficient by (1−α), a delay section  31   g  adapted to delay the multiplication coefficient for one sampling period, and output the multiplication coefficient thus delayed to a delay signal output section  31   c , a second multiplication section  31   e  adapted to input the multiplication coefficient delayed for one predetermined sampling period from the delay signal output section  31   c , and multiply the multiplication coefficient delayed for one sampling period by α, and an adding section  31   f  adapted to add a value outputted from the first multiplication section  31   d  to a value outputted from the second multiplication section  31   e  to generate a multiplication coefficient to be outputted to an output section  31   b , wherein α is intended to mean a time constant. The conventional complementary unit  31  thus constructed is operative to carry out the aforesaid time constant process in response to the target value of the multiplication coefficient inputted from the input section  31   a  so to complement the multiplication coefficient from the current value to the target value, and to output the multiplication coefficient thus complemented from the output section  31   b  to the multiplication unit  21 . The four complementary units  31 ,  32 ,  33 , and  34  are the same in construction as one another, and operative to output the multiplication coefficients to the respective multiplication units  21 ,  22 ,  23 , and  24 .  
       [0005] Making the assumption that the multiplication coefficient is to be changed from, for example, a current value at “1” to a target value at “0” for a first channel, and the input section  31   a  of the first-channel complementary unit  31  is set at “0” (target value). The multiplication coefficient thus complemented for every sampling period and outputted from the output section  31   b  of the complementary unit  31  to the multiplication unit  21  is gradually declining from “1” and converging to “0” to form a curve locus gently running in accordance with the time constant α as shown in FIG. 10. The multiplication unit  21  is then operated to multiply the input signal by the multiplication coefficient thus complemented, thereby making it possible to output an audio output signal with a smooth waveform to be converted to a sound smoothly audible to a human ear. The time constant α is a value equal to or greater than “0” but less than “1”. The variation of the multiplication coefficients for every sampling period becomes smaller as the time constant α approaches to “1”, thereby enabling to output an audio output signal with a smooth waveform to be converted to a sound smoothly audible to a human ear while eliminating an audible noise due to a discontinuous waveform resulted from the multiplication coefficient with the discrete values.  
       [0006] The conventional multiplication coefficient complementary apparatus, however, encounters a drawback that the multiplication coefficient complementary apparatus comprises a plurality of multiplication units  21 ,  22 ,  23 , and  24 , and a plurality of complementary units  31 ,  32 ,  33 , and  34 , respectively associated with the multiplication units  21 ,  22 ,  23 , and  24  in one-to-one relationship, resulting in the fact that the conventional multiplication coefficient complementary apparatus requires the complementary units equal in number to the multiplication units. Furthermore, the conventional multiplication coefficient complementary apparatus encounters another drawback that the complementary units, which have finished the coefficient complementary operation or do not carry out the coefficient complementary operation, are still unnecessarily operating in a converging state. This means that all of the complementary units remain operating continuously for every sampling period regardless of whether carrying out the coefficient complementary operation or not, thereby consuming effective amount of operations for the digital audio apparatus, which can perform only a limited amount of operations.  
       [0007] In view of the foregoing problems, it is an object of the present invention to provide an apparatus for, a method of, and a computer program product for complementing a multiplication coefficient, which can reduce unnecessary operations performed during complementing a multiplication coefficient.  
       SUMMARY OF THE INVENTION  
       [0008] In accordance with a first aspect of the present invention, there is provided a multiplication coefficient complementary apparatus comprising: a plurality of multiplication units each for multiplying an input signal by a multiplication coefficient; a plurality of complementary units each for complementing the multiplication coefficient by means of a time constant process; and a control unit for changing states of connecting the multiplication units with the complementary units. This construction makes it possible for the multiplication coefficient complementary apparatus to comprise complementary units less in the number than the multiplication number as well as to reduce unnecessary operations performed during complementing the multiplication coefficient.  
       [0009] In accordance with a second aspect of the present invention, the control unit of the aforesaid multiplication coefficient complementary apparatus may connect a multiplication unit with a complementary unit upon starting to complement the multiplication coefficient. This construction makes it possible for the multiplication coefficient complementary apparatus to comprise only a minimum necessary number of complementary units in order to simultaneously complementing the multiplication coefficients as well as to further reduce unnecessary operations performed during complementing the multiplication coefficient.  
       [0010] In accordance with a third aspect of the present invention, the control unit of the aforesaid multiplication coefficient complementary apparatus is operative to disconnect the multiplication unit from the complementary unit when a predetermined time period elapses after the multiplication unit has been connected with the complementary unit. This construction makes it possible for the multiplication coefficient complementary apparatus to regard complementary units which have been operating for the predetermined time period as having finished their operations, and to connect them with other multiplication units for complementing other multiplication coefficients, thereby preventing the complementary units from being occupied by particular multiplication units as well as further reducing unnecessary operations performed during complementing the multiplication coefficient while maintaining the advantages of the multiplication units.  
       [0011] In accordance with a fourth aspect of the present invention, the control unit of the aforesaid multiplication coefficient complementary apparatus is operative to set the multiplication unit at a target value of the multiplication coefficient after the multiplication unit is disconnected from the complementary unit. This construction makes it possible for the multiplication coefficient complementary apparatus to disconnect the multiplication unit from the complementary unit and set the multiplication unit at the target value of the multiplication coefficient when the multiplication coefficient approaches to a value sufficiently close to the target value, thereby constantly carrying out a volume adjusting function by way of multiplying an audio input signal by the multiplication coefficient, which is equal to the target value, and eliminating an audible noise occurring due to a discontinuous waveform caused by the multiplication coefficient with the discrete values.  
       [0012] In accordance with a fifth aspect of the present invention, there is provided a multiplication coefficient complementary method comprising the steps of: connecting a multiplication unit for multiplying an input signal by a multiplication coefficient; with a complementary unit for complementing the multiplication coefficient by means of a time constant process; and disconnecting the multiplication unit from the complementary unit when a predetermined time period elapses after the multiplication unit has been connected with the complementary unit. This construction enables to reduce unnecessary operations performed during complementing the multiplication coefficient.  
       [0013] In accordance with a sixth aspect of the present invention, the aforesaid multiplication coefficient complementary method further comprises a step of: setting the multiplication unit at a target value of the multiplication coefficient after the multiplication unit is disconnected from the complementary unit. This construction enables to disconnect the multiplication unit from the complementary unit when the multiplication coefficient approaches to a value sufficiently close to the target value, and set the multiplication unit at the target value of the multiplication coefficient, thereby constantly carrying out a volume adjusting function by way of multiplying an audio input signal by the multiplication coefficient, which is equal to the target value, and eliminating an audible noise occurring due to a discontinuous waveform caused by the multiplication coefficient with the discrete values.  
       [0014] In accordance with a seventh aspect of the present invention, there is provided a multiplication coefficient complementary computer program product executable by a computer to perform a function of a control unit for changing states of connecting a plurality of multiplication units with a plurality of complementary units, whereby each of the multiplication units is operative to multiply an input signal by a multiplication coefficient; and each of the complementary units is operative to complement the multiplication coefficient by means of a time constant process. This construction enables to reduce unnecessary operations performed by the computer such as, for example, a digital signal processor, a microprocessor, or the like, during complementing a multiplication coefficient.  
       [0015] In accordance with an eighth aspect of the present invention, there is provided a multiplication coefficient complementary computer program product executable by a computer to perform a set of steps comprising: a step of connecting a multiplication unit for multiplying an input signal by a multiplication coefficient; with a complementary unit for complementing the multiplication coefficient by means of a time constant process; and a step of disconnecting the multiplication unit from the complementary unit when a predetermined time period elapses after the multiplication unit has been connected with the complementary unit. This construction enables to reduce unnecessary operations during complementing a multiplication coefficient.  
       [0016] In accordance with a ninth aspect of the present invention, the aforesaid multiplication coefficient complementary computer program product executable by a computer to perform a set of steps comprises a step of disconnecting the multiplication unit from-the complementary unit when a predetermined time period elapses after the multiplication unit has been connected with the complementary unit. This construction enables to disconnect the multiplication unit from the complementary unit when the multiplication coefficient approaches to a value sufficiently close to the target value, and set the multiplication unit at the target value of the multiplication coefficient, thereby constantly carrying out a volume adjusting function by way of multiplying an audio input signal by the multiplication coefficient, which is equal to the target value and eliminating an audible noise occurring due to a discontinuous waveform caused by the multiplication coefficient with the discrete values. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0017] The features and advantages of the multiplication coefficient complementary apparatus, the multiplication coefficient complementing method, and the multiplication coefficient complementing computer program product according to the present invention will more clearly be understood from the following description taken in conjunction with the accompanying drawings in which:  
     [0018]FIG. 1 is a block diagram showing a preferred embodiment of a multiplication coefficient complementary apparatus according to the present invention;  
     [0019]FIG. 2 is a block diagram showing a multiplication unit of the preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention;  
     [0020]FIG. 3 is a block diagram showing a complementary unit of the preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention;  
     [0021]FIG. 4 is a graph showing multiplication coefficient values outputted from the preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention;  
     [0022]FIG. 5 is a flowchart showing a process performed by a first preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention;  
     [0023]FIG. 6 is a block diagram showing a structure of a storage portion for use in a preferred embodiment of a multiplication coefficient complementing computer program product according to the present invention;  
     [0024]FIG. 7 is a flowchart showing a process performed by a second preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention;  
     [0025]FIG. 8 is a block diagram showing a conventional multiplication coefficient complementary apparatus;  
     [0026]FIG. 9 is a block diagram showing a multiplication unit of the conventional multiplication coefficient complementary apparatus; and  
     [0027]FIG. 10 is a block diagram showing a complementary unit of the conventional multiplication coefficient complementary apparatus.  
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
     [0028] Description of the preferred embodiment of the present invention will be made hereinlater with reference to the drawings.  
     [0029] Description hereinlater will be directed to a first preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention. The preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention will now be described with reference to the drawings shown in FIG. 1. The preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention comprises a plurality of multiplication units and a plurality of complementary units. The multiplication units forming part of the preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention are shown in FIG. 2. The complementary units of the preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention are shown in FIG. 3.  
     [0030] The multiplication coefficient complementary apparatus  10  shown in FIG. 1 is mounted on a digital audio apparatus for carrying out a volume adjusting function, as comprising a plurality of multiplication units  11  for multiplying a single-channel input signal by four respective multiplication coefficients to generate a four-channel audio output signal, a plurality of complementary units  12  for complementing the multiplication coefficients by means of a time constant process; and a control unit  13  for changing states of connecting the multiplication units  11  with the complementary units  12 .  
     [0031] The multiplication units  11 , as a whole constituting a multiplication unit group  11 , are shown in FIG. 2 as comprising a four multiplication units (a first multiplication unit  21 , a second multiplication unit  22 , a third multiplication unit  23 , and a fourth multiplication unit  24 ). The four multiplication units  21 ,  22 ,  23 , and  24  are the same in construction as one another, and adapted to input a single-channel input signal at an audio signal input  20 , and multiply the single-channel input signal by four multiplication coefficients  21   a ,  22   a ,  23   a , and  24   a  to generate a four-channel audio output signal, wherein the four multiplication coefficients  21   a ,  22   a ,  23   a , and  24   a , respectively correspond to four channels including a first channel, a second channel, a third channel, and a fourth channel.  
     [0032] The complementary units  12 , as a whole constituting a complementary unit group  12 , are shown in FIG. 3 as comprising two complementary units (a first complementary unit  31 , and a second complementary unit  32 ). The two complementary units  31  and  32  are the same in construction as each other, and comprise first multiplication sections  31   d ,  32   d  for respectively multiplying target values of the multiplication coefficients, inputted from input sections  31   a ,  32   a , by (1−α), second multiplication sections  31   e ,  32   e  for respectively inputting multiplication coefficients delayed for one predetermined sampling period from delay signal output sections  31   c ,  32   c , and multiplying the delayed multiplication coefficients by a, adding sections  31   f ,  32   f  for respectively adding values outputted from the first multiplication sections  31   d ,  32   d  to values outputted from the second multiplication sections  31   e ,  32   e  to respectively generate multiplication coefficients to be outputted to output sections  31   b ,  32   b , and delay sections  31   g ,  32   g  for respectively delaying the multiplication coefficient for one sampling period, and outputting the multiplication coefficients thus delayed to the delay signal output sections  31   c ,  32   c  wherein a is intended to mean a time constant.  
     [0033] It is assumed that the input value (target values of the multiplication coefficients) inputted to the input sections  31   a ,  32   a  is IN and the output value (multiplication coefficient after n sample periods) outputted from the  31   b ,  32  is OUTn. The relationship between IN and OUTn is defined by the following equation (1).  
       OUTn=IN× (1−α)+ OUTn− 1×α  (Equation 1)  
     [0034] Wherein OUTn−1 is intended to mean the delayed multiplication coefficient, which is one predetermined sampling period behind the multiplication coefficient OUTn. As the time constant α approaches to “1”, the variation of the multiplication coefficients for every sampling period becomes smaller, and accordingly, it takes a longer time until the multiplication coefficient OUTn converges to “0”. As the time constant α, on the other hand, approaches to “0”, the variation of the multiplication coefficients for every sampling period becomes greater, and accordingly, it takes a shorter time until the multiplication coefficient OUTn converges to “0”. It is assumed in the following description, that the time constant α is equal to 0.9, but it is of course needless to mention that the time constant α may be any value equal to or greater than “0” but less than “1”.  
     [0035] When a multiplication coefficient is required to be changed due to an instruction from, for example, a user specifying a volume level, the control unit  13  shown in FIG. 1 is operated to connect a multiplication unit of the multiplication unit group  11  with a complementary unit of the complementary unit group  12  upon starting to complement the multiplication coefficient. The control unit  13  is then operated to disconnect the multiplication unit from the complementary unit when a predetermined time period elapses after the multiplication unit has been connected with the complementary unit. It is assumed in the following description that the control unit  13  is operated to connect, by way of example, the first multiplication unit  21  shown in FIG.  2  and the first complementary unit  31  shown in FIG. 3.  
     [0036] The control unit  13  is operated to set the delay signal output section  31   c  of the first complementary unit  31  at an initial value of the multiplication coefficient, to set the input section  31   a  of the first complementary unit  31  at a target value of the multiplication coefficient, and to connect the output section  31   b  of the first complementary unit  31  with the multiplication coefficient input section  21   a  of the first multiplication unit  21 . Furthermore, the control unit  13  of the present embodiment is operated to disconnect the multiplication coefficient input section  21   a  of the first multiplication unit  21  from the output section  31   b  of the first complementary unit  31  when a predetermined time period elapses after the output section  31   b  of the first complementary unit  31  is connected with the multiplication coefficient input section  21   a  of the first multiplication unit  21 , and the multiplication coefficient approaches to a value sufficiently close to the target value.  
     [0037] The description hereinlater will be directed to the operation of the multiplication coefficient complementary apparatus thus constructed in the case that the multiplication coefficient is to be changed from, for example, a current value at “1” to a target value at “0” for the first-channel complementary unit  31 .  
     [0038] The control unit  13  is then operated to set the delay signal output section  31   c  of the first complementary unit  31  at an initial value (equal to “1”) of the multiplication coefficient, to set the input section  31   a  of the first-channel complementary unit  31  at a target value (equal to “0”) of the multiplication coefficient. After the initial value and the target value of the multiplication coefficient are thus specified for the first-channel complementary unit  31 , the multiplication coefficient outputted from the output section  31   b  of the complementary unit  31  is gradually declining from the initial value (equal to “1”) and converging to the target value (equal to “0”) by means of the time constant process carried out by the complementary unit  31  to form a curve locus as shown in FIG. 4.  
     [0039] When one sampling period, for example, elapses, the value of the multiplication coefficient outputted from the complementary unit  31  is calculated in accordance with equation 1 as follows.  
     0×(1−α)+1×α=α 
     [0040] When two sampling periods elapse, the value of the multiplication coefficient outputted from the complementary unit  31  is calculated in accordance with equation 1 as follows.  
     0×(1−α)+1×α×α=α 2    
     [0041] In a similar manner, when n sampling periods elapse, the value of the multiplication coefficient outputted from the complementary unit  31  results in α n .  
     [0042] The control unit  13  is operated to connect the output section  31   b  of the first complementary unit  31  with the multiplication coefficient input section  21   a  of the first multiplication unit  21  shown in FIG. 2 within the same sampling period, in which the control unit  13  specifies the initial value and the target value of the multiplication coefficient for the first-channel complementary unit  31 . This leads to the fact that an audio signal outputted from an audio signal output section  21   b  of the first multiplication unit  21  is changed smoothly in response to the variations of the multiplication coefficient values outputted from the complementary unit  31 .  
     [0043] At a time point (point B in FIG. 4) when hundred sampling periods elapse after a time point (point A in FIG. 4) at which the initial value and the target value of the multiplication coefficient are specified for the first-channel complementary unit  31 , the value of the multiplication coefficient results in α 100 =0.000026, which can be approximately regarded as the target value (equal to “0”). At this time point, the control unit  13  is operated to disconnect the multiplication coefficient input section  21   a  of the first multiplication unit  21  from the output section  31   b  of the first complementary unit  31 . The operation of the first complementary unit  31  becomes unnecessary until the multiplication coefficient is required to be changed again due to an instruction from, for example, a user specifying another volume level. While it has been described in the above that the control unit  13  disconnects the first multiplication unit  21  from the first complementary unit  31  when the time period of hundred sampling periods elapses after the multiplication unit  21  has been connected with the complementary unit  31 , the time period required to elapse after the multiplication unit  21  has been connected with the complementary unit  31  until the first multiplication unit  21  is disconnected from the first complementary unit  31  is not limited to the hundred sampling periods. According to the present invention, the time period required to elapse after the multiplication unit  21  has been connected with the complementary unit  31  until the first multiplication unit  21  is disconnected from the first complementary unit  31  may be a time period required to elapse after the multiplication unit  21  has been connected with the complementary unit  31  until the value of the multiplication coefficient approaches to the value, approximately equal to the target value, and determined in accordance with the time constant α.  
     [0044] The operations of the first complementary unit  31  in the case that the multiplication coefficient is to be changed from, for example, a current value at “1” to a target value at “0” for the second-channel, the third-channel, and the fourth-channel are the same as that in the case that the multiplication coefficient is to be changed from for the first-channel except for the fact that the output section  31   b  of the complementary unit  31  is connected with a different multiplication unit, thereby leading to the fact that the complementary unit  31  can complement the multiplication coefficients for four channels.  
     [0045] The multiplication coefficient, for example, for another channel, is required to be complemented while the first complementary unit  31  is complementing the multiplication coefficient for the first channel, the control unit  13  may control the second complementary unit  32  so as to complement the multiplication coefficient for the channel in a similar manner as described above, thereby enabling to simultaneously complement the multiplication coefficients for two channels.  
     [0046] The multiplication coefficients, for example, for more than three channels are required to be complemented, the multiplication coefficient complementary apparatus may complement the multiplication coefficients in a time division process.  
     [0047] Description hereinlater will be directed to a first preferred embodiment of the multiplication coefficient complementary method according to the present invention with reference to the flowchart shown in FIG. 5. The flowchart appearing in FIG. 5 shows steps of the first preferred embodiment of the multiplication coefficient complementary method according to the present invention.  
     [0048] When a multiplication coefficient is required to be changed due to an instruction from, for example, a user specifying another volume level, the control unit  13  is operated to judge whether the first complementary unit  31  is in use or not (S1). If it is judged that the first complementary unit  31  is in use, the control unit  31  is operated to judge whether the second complementary unit  32  is in use or not (S2). If it is judged that both the first complementary unit  31  and the second complementary unit  32  are in use, the control unit  31  is operated to wait until either of the complementary units has finished its operation.  
     [0049] When it is judged that either of the complementary units is not in use, the first control unit  31  is operated to select a multiplication unit to be used and determine a value of the multiplication coefficient to be changed (S11, S21). The description hereinlater will be directed to the operation in the case that the first complementary unit  31 , for example, is used to change the value of multiplication coefficient for the first multiplication unit  21 . The control unit  13  is operated to set a delay signal output section  31   c  of a first complementary unit  31  at an initial value of the multiplication coefficient and to set an input section  31   a  of the first complementary unit  31  at a target value of the multiplication coefficient (S12). The control unit  13  is then operated to connect an output section  31   b  of the first complementary unit  31  with an input section  21   a  of the first multiplication unit  21  (S13). The control unit  13  is operated to wait until predetermined sampling periods elapse, which are determined by the time constant α, after the first complementary unit  31  has been connected with the first multiplication unit  21  (S14), and to disconnect the output section  31   b  of the complementary unit from the input section  21   a  of the multiplication unit  21  (S15).  
     [0050] The operation in the case that the second complementary unit  32  is used to change the value of multiplication coefficient is similar to that in the case that the first complementary unit  31  is used except for the fact that the complementary unit  32  is not identical to the complementary unit  31  (S21 to S25).  
     [0051] Description hereinlater will be directed to a first preferred embodiment of the multiplication coefficient complementary computer program product according to the present invention with reference to the drawings shown in FIG. 6. The block diagram appearing in FIG. 6 shows a structure of a storage portion for use in the preferred embodiment of a multiplication coefficient complementing computer program product according to the present invention.  
     [0052] The multiplication coefficient complementary computer program product is executable by a computer such as, for example, a digital signal processor, a microprocessor computer, or the like, to perform a function of a control unit for changing states of connecting a plurality of multiplication units with a plurality of complementary units whereby each of the multiplication units is operative to multiply an input signal by a multiplication coefficient; and each of the complementary units is operative to complement the multiplication coefficient by means of a time constant process. As shown in FIG. 6, the computer such as, for example, a digital signal processor, a microprocessor computer, or the like, comprises a storage portion including memories  21   a ,  22   a ,  23   a , and  24   a  for storing multiplication coefficient values to be inputted to the respective multiplication units, memories  31   a  and  32   a  for storing values to be inputted to the input sections of the respective complementary units, memories  31   b  and  32   b  for storing values outputted from the output sections of the respective complementary units, and memories  31   c  and  32   c  storing values outputted from the delay sections of the respective complementary unit.  
     [0053] The multiplication coefficient complementary computer program product is executable by a computer to perform the coefficient complementary operation as described in the above with reference to the drawings shown in FIG. 5. The computer is operated to write the value stored in the memory  31   b  into the memory  21   a  while connecting the first complementary unit  31  with the first multiplication unit  21  (S13 in FIG. 5).  
     [0054] From the foregoing description, it is to be understood that the multiplication coefficient complementary method according to the present invention, makes it possible for the apparatus comprising, for example, four multiplication units, for carrying out a four-channel volume adjusting function, to complement the multiplication coefficients and output an audio output signal with a smooth waveform, with only two complementary units, which are less in the number than the multiplication units by two, as well as to reduce unnecessary operations performed during complementing a multiplication coefficient, in comparison with the apparatus comprising multiplication units and the complementary units, which are the same in the number as the multiplication units.  
     [0055] Description hereinlater will be directed to a second preferred embodiment of the multiplication coefficient complementary apparatus according to the present invention with reference to the drawings shown in FIGS. 1, 2, and  3 . The present embodiment is different from the first embodiment in that the present embodiment of the multiplication coefficient complementary apparatus is operative to directly set the multiplication unit at a target value of the multiplication coefficient after the multiplication unit is disconnected from the complementary unit. The elements and the parts of the second embodiment entirely the same as those of the first embodiment will be omitted from description for avoiding repetition.  
     [0056] At the time point (point B in FIG. 4) when the hundred sampling periods elapse after a time point at which the multiplication unit is connected with the complementary unit, and the multiplication unit is disconnected from the complementary unit, the value of the multiplication coefficient outputted from the output section  31   b  of the complementary unit  31  to the multiplication coefficient input section  21   a  of the first multiplication unit  21  results in α 100 =0.000026, which can be approximately regarded equal to the target value (equal to “0”). The present embodiment of the multiplication coefficient complementary apparatus is operative to set the multiplication coefficient input section  21   a  of the first multiplication unit  21  at the target value (equal to “0”) after the multiplication unit is disconnected from the complementary unit so that the value of the multiplication coefficient becomes completely equal to the target value (equal to “0”). At the time point when the hundred sampling periods elapse after the time point at which the multiplication unit is connected with the complementary unit, the value of the multiplication coefficient outputted from the output section  31   b  of the complementary unit  31  to the multiplication coefficient input section  21   a  of the first multiplication unit  21  results in α 100 =0.000026, which can be approximately regarded as the target value (equal to “0”). As will be seen from the foregoing description, the present embodiment of the multiplication coefficient complementary apparatus, which is operative to directly set the multiplication coefficient input section  21   a  of the first multiplication unit  21  at the target value (equal to “0”) when the multiplication unit is disconnected with the complementary unit, does not output an output signal with a discontinuous waveform causing an audible noise to a human ear, thereby eliminating an audible noise occurring due to a discontinuous waveform caused by the multiplication coefficient with the discrete values.  
     [0057] Description hereinlater will be directed to a second preferred embodiment of the multiplication coefficient complementary method according to the present invention with reference to the flow chart shown in FIG. 7. The flow chart appearing in FIG. 7 shows steps of the second preferred embodiment of the multiplication coefficient complementary method according to the present invention.  
     [0058] The present embodiment is different from the first embodiment in that the present embodiment of the multiplication coefficient complementary method has a step of directly setting the multiplication unit at a target value of the multiplication coefficient after the multiplication unit is disconnected from the complementary unit (S16, S26). The other steps of the second embodiment entirely the same as those of the first embodiment will be thus omitted from description for avoiding repetition.  
     [0059] Description hereinlater will be directed to a second preferred embodiment of the multiplication coefficient complementary computer program product according to the present invention with reference to the drawings shown in FIG. 6. The block diagram appearing in FIG. 6 shows a structure of a storage portion for use in the preferred embodiment of a multiplication coefficient complementing computer program product according to the present invention. The present embodiment is different from the first embodiment in that the present embodiment of the multiplication coefficient complementary computer program product is executable by a computer to perform a step of directly setting the multiplication unit at a target value of the multiplication coefficient after the multiplication unit is disconnected from the complementary unit. The computer is operated to write the target value into the memories  21   a ,  22   a ,  23   a , and  24   a  while setting the multiplication unit at a target value of the multiplication coefficient. The other steps of the second embodiment entirely the same as those of the first embodiment will be thus omitted from description for avoiding repetition.  
     [0060] As will be seen from the foregoing description, it is to be understood that the present embodiment can constantly carry out a volume adjusting function by way of multiplying an audio input signal by a multiplication coefficient, which is equal to the target value corresponding to a volume level specified by a user, and eliminate an audible noise occurring due to a discontinuous waveform caused by the multiplication coefficient with a discrete value.  
     [0061] While it has been described in the above that the multiplication coefficient complementary apparatus is mounted on a digital audio apparatus, and is operative to input a single-channel input signal and to carry out a four-channel volume adjusting function, according to the present invention, the numbers of channels, the multiplication units, and the complementary units are not limited to the numbers described above, and the number of complementary units may be less than that of the multiplication units.  
     [0062] As will be seen from the foregoing description, it is to be understood that the multiplication coefficient complementary apparatus, the multiplication coefficient complementary method, and the multiplication coefficient complementary computer program product according to the present invention can reduce unnecessary operations performed during complementing a multiplication coefficient while the number of the complementary units may be less than that of the multiplication units.