Abstract:
An analog calculation circuit in a filter circuit is corrected in the calculation error by estimating the error from a calculation result of known inputs and known multiplier. A multiplier is changed according to the estimated error. The filter circuit has a voltage to current converter at an input side and a current to voltage converter at an output side and a calculation of current is performed therein.

Description:
FIELD OF THE INVENTION 
     The present invention relates to a filter circuit applicable to a matched filter for a spread spectrum communication system. 
     BACKGROUND OF THE INVENTION 
     A matched filter judges whether two signals are the same. In a spread spectrum communication system, such as mobile cellular radio or wireless local area network (LAN), each user processes a received signal by the matched filter having a spreading code allocated. A correlation peak is detected from the output of the matched filter so that synchronization, acquisition and holding are performed. 
     When the spreading code is PN(i), chip time is Tc, spreading ratio is M, and an input signal and correlation output are S(t) and R(t) at a time t, the following formula (1) is given.                R        (   t   )       =       ∑     i   =   0       M   -   1              PN        (   i   )       ·     S        (     t   -     i   ·   Tc       )                   (   1   )                                
     Here, PN(i) is a sequence of one bit data. 
     Double sampling or higher order over sampling is necessary for acquisition, so a plurality of matched filters are needed. The calculation of formula (1) is performed in a plurality of matched filters simultaneously, and one of the calculation results is selectively output or a plurality of outputs are added. The matched filter is constructed by a digital circuit or a surface acoustic wave (SAW) device. The former has large circuit size and consumes a lot of electrical power. Therefore it is inadequate for a mobile phone. The latter has a low S/N ratio and it is difficult to incorporate it with other circuits within one large scale integrated circuit (LSI). 
     The inventors of the present invention have considered the filter circuits above based on an analog calculation circuit. The analog calculation circuit has an inverting amplifier, and input capacitance connected to an input of the amplifier and a feedback capacitance connected between the input and an output of the amplifier. A sampling and holding circuit, adder, multiplication circuit, integration circuit and other circuits of high speed, low power and high accuracy circuits are realized. 
     FIG.  18 ( a ) shows an example of such an analog calculation circuit. V 1  and V 2  are input terminals, Vo is an output terminal and INV is an inverting amplifier. The inverting amplifier INV consists of CMOS inverters working in an area of transition of output from high level to low level or from low level to high level. An odd number of CMOS inverters, shown as three stages of CMOS inverters  201 ,  202  and  203  in the figure, are serially connected. A serial circuit of resistance R and a capacitance C is connected between an input and output of the CMOS inverter  202 . This serial circuit works as a negative feedback circuit as well as a load of the CMOS  202  for decreasing the gain of the inverting amplifier INV. A capacitance Cg is connected to the inverting amplifier INV for phase compensation so that unexpected oscillation is prevented. 
     Input capacitances C 1  and C 2  are connected between a point B at the input of INV and the input terminal V 1 , and between the point B and V 2 , respectively. A feedback capacitance Cf is connected between the output terminal Vo and the point B. 
     The gain of the inverting amplifier is very high, so the voltage at the point B is a constant value Vb. The point B is connected to the gate of the transistors of the CMOS inverter  201  and is a floating point or insulated point from any electrical source. 
     Assuming that the electrical charge of the capacitances is zero at the initial condition, the total charge at point B is zero after voltages V 1  and V 2  are input. Thus resulting in the following formula (2) of “preservation of electrical charge”. 
     
       
         C 1 (V 1 −Vb)=C 2 (V 2 −Vb)+Cf(V 0 −Vb)=0  (2) 
       
     
     When V 1  and V 2  are voltages from the voltage Vb with point B as a reference point, and defining V(1)=V1−Vb, V(2)=+V2−Vb and Vout=Vo−Vb provides formula (3) which is obtained from the formula (2).              Vout   =     -     (           C   1     Cf          V        (   1   )         +         C   2     Cf          V        (   2   )           )               (   3   )                                
     A voltage Vout is output as an inverted voltage of a summation of input voltages V(i) (i=1,2) multiplied by a coefficient (Ci/Cf), a ratio of the input capacitance Ci and the feedback capacitance Cf. 
     The voltage Vb at the point B is usually Vdd/2 for maximizing the dynamic range. This voltage is called Vref, hereinafter. and Vref=+Vb=Vdd/2. 
     If C1=C2=Cf, the output voltage Vout=−{V(1)+V(2)}. A summation of both input voltages is thus obtained and, an adder is realized. 
     As shown in FIG.  18 ( b ), a similar relationship to the above is applicable when more input voltages are input. Then, the formula (4) is obtained.              Vout   =     -     (           C   1     Cf          V        (   1   )         +         C   2     Cf          V        (   2   )         +   …   +         C   i     Cf          V        (   i   )         +   …   +         C   n     Cf          V        (   n   )           )               (   4   )                                
     If the input capacitances Ci (i=1 to n) are equal to Cf, that is, Ci=Cf (i=1 to n), an output voltage is obtained as a summation of input voltages. An adder of a plurality of inputs is realized. 
     A sampling and holding circuit using the above analog circuit is shown in FIG.  19 . Vin is an input voltage, SW is a sampling switch, Cin is an input capacitance connected to the input of the inverting amplifier INV, Cf is a feedback capacitance and Vout is an output voltage. The input capacitance and the feedback capacitance have equal values. The sampling switch SW is for example a switching circuit consisting of a MOS transistor such as CMOS transmission gate. 
     The sampling and holding circuit corresponds to a circuit shown in FIG.  18 ( a ) wherein the number of inputs is reduced to one. Since Cin and Cf are equal to each other, Vout=−Vin. At first the sampling switch SW is closed so as to sample the input signal. When SW is opened, an inverted voltage of the input voltage at the time is output from the ouput terminal The voltage is held until the sampling switch SW is closed. Accordingly, a sampling and holding circuit is realized. 
     An analog digital multiplication circuit using the above analog calculation circuit is shown in FIG.  20 . Vin is an input voltage, Vref is the reference voltage and Vref=Vdd/2=Vb. MUX 1  to MUX n  are multi-plexers for switching capacitances having the first input terminals connected to V 1 , the second input terminals connected to Vref and output terminal connected to C 1  to C n , respectively. Control signals d 1  to d n  are input to the multi-plexers MUX 1  to MUX n , respectively. Vin is selected to be input to C1 when di (i=1 to n) is “1”, and Vref is selected when di (i=1 to n) is “0”. 
     The capacitances C 1  to C n  have capacity ratios that are powers of “2”, as defined by formula (5) 
     
       
         C N =2C N−1 = . . . =2′C H−i = . . . =2 n−1  C 1   (5) 
       
     
     The formula for holding electrical charge is defined by equation (6).                    ∑     i   =   1     n            C   i            d   i          (       V   IN     -   Vb     )           +       ∑     i   =   1     n              C   i          (     1   -     d   i       )            (       V   ref     -   Vb     )         +     Cf        (     Vout   -   Vb     )         =   0           (   6   )                                
     The output voltage Vout is defined by formula (7), wherein Vref=Vb.              Vout   =         -                1   Cf              ∑     i   -   1     n            C   i          d   i          V     i                 n             =         C   1     Cf          V     i                 n              ∑     i   -   1     n            2     n   -   i            d   i                     (   7   )                                
     Vin multiplied by a binary number on n-bits corresponding to d 1  to d n  is obtained as Vout. Therefore, a multiplication circuit for multiplying an analog data by a digital data is realized. 
     Various analog calculation circuits can be constructed by the above analog calculation circuit. The analog calculation circuit is a voltage driven type, so the electrical power consumption is very low. The circuit is easy to incorporate within an LSI. Various circuits other than the filter circuit (ADF: analog digital filter) can be realized using the sampling and holding circuit, multiplication circuit and adder above. 
     The above analog calculation circuit has a calculation error due to an error of the capacity ratio (inclination) caused by parasitic capacitance of wiring and manufacturing deviation of capacitances. In mass-production, it is difficult to correct the error by additional resistance or additional capacitance because each LSI may have differing errors from others and adjacent circuits within one LSI may have different errors. 
     SUMMARY OF THE INVENTION 
     The present invention has an object to provide a filter circuit of smaller circuit size and lower power consumption than the conventional filter. 
     The present invention has another object to provide a filter circuit of higher accuracy than the conventional circuit. 
     According to the present invention, an analog calculation circuit in a filter circuit corrects the calculation error by estimating the error from a calculation result of known inputs and a known multiplier. A multiplier is changed according to the estimated error. 
     According to the present invention, a filter circuit has a voltage to current converter at an input side and a current to voltage converter at an output side and a calculation of current is performed therein. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS 
     FIG. 1 is a block diagram of the first embodiment of the filter circuit of the present invention; 
     FIG. 2 is a circuit diagram of a sampling and holding circuit of the first embodiment; 
     FIG. 3 is a circuit diagram of a scaling circuit of the first embodiment; 
     FIGS.  4 ( a ) to ( c ) are circuit diagrams showing performance of the sampling and holding circuit; 
     FIG. 5 is a circuit diagram of a multiplication circuit of the first embodiment; 
     FIG. 6 is a circuit diagram of an adder of the first embodiment; 
     FIG. 7 is a diagram showing frequency response of the first embodiment; 
     FIG. 8 is a block diagram of the second embodiment of the present invention; 
     FIG. 9 is a circuit diagram of the sampling and holding circuit of the second embodiment; 
     FIG. 10 is a circuit diagram of a constant current source in FIG. 9; 
     FIG. 11 is a circuit diagram of a multi-plexer in FIG. 8; 
     FIG. 12 is a circuit diagram of an adder in FIG. 8; 
     FIG. 13 is a circuit diagram of an inverter in FIG. 8; 
     FIG. 14 is a circuit diagram of a voltage-current converter in FIG. 8; 
     FIG. 15 is a circuit diagram of a current-voltage converter in FIG. 8; 
     FIG. 16 is a circuit diagram of another voltage-current converter; 
     FIG. 17 is a circuit diagram of another current-voltage converter; 
     FIGS.  18 ( a ) and ( b ) are circuit diagrams of a conventional adder, 
     FIG. 19 is a circuit diagram of a conventional sampling and holding circuit, and 
     FIG. 20 is a circuit diagram of the conventional multiplication circuit. 
    
    
     DETAILED DESCRIPTION 
     The first embodiment of a filter circuit according to the present invention is described, below. 
     In FIG. 1, there is shown in filter circuit having a group  10  of N stages of serial sampling and holding circuits  11   n  to  11   N−1 , a group  20  of N stages of coefficient registers  21   0  to  21   N−1  corresponding to the sampling and holding circuits and a group  30  of N stages of multiplication circuits  31   0  to  31   N−1  corresponding to the sampling and holding circuits. An input signal Ain is input to the first stage  11   0 , and a sampling clock of a period T is provided to the total sampling and holding circuits. The sampling and holding circuits transfer the input signal Ain in response to the sampling clock one after another toward the last stage  11   N−1 . 
     The input signal held by each sampling and holding circuit is multiplied in the corresponding multiplication circuit by a coefficient stored in the corresponding coefficient register. The group of the coefficient registers consists of a shift register of N stages, each stage storing a coefficient h by which the signal Ain in the corresponding sampling and holdiong circuit is multiplied. 
     Each multiplication circuit is an analog-digital multiplication circuit receiving an output signal (analog signal) from the corresponding sampling and holding circuit and a coefficient (digital signal) from the corresponding coefficient register. The multiplication circuits  31   0  to  31   N−1  multiply the discrete input signals Ain by the coefficients h, respectively. 
     An adder  40  is connected to the multiplication circuits  31   0  to  31   N−1  for adding the outputs of the multiplication circuits together. An addition result y is output from the adder to a scaling circuit  50  for adjusting y to be a predetermined level and transferring an output to the following circuits. 
     An output from scaling circuit  50  is input into a measuring circuit  60  so that a measured value of the output can be obtained. The measured value is fed into a comparator  70  to be compared with a theoretical value based on a formula μγ/N. A comparison result is input into a determining circuit  80  to determine whether there is an agreement between the comparison result and a coefficient h. A determination result is then fed into coefficient registers  21   0 . 
     As shown in FIG. 2, each of the sampling and holding circuits  11   0  to  11   N−1  consists of a sampling circuit and a holding circuit serially connected. The sampling circuit includes an input switch connected to an input signal Vi, an input capacitance Cis connected to an output of the input switch, an inverting amplifier INV connected to an output of the input capacitance and a feedback capacitance Cfs for connecting an output of INV to its input. The holding circuit includes an input switch connected to an output of the sampling circuit, an input capacitance Cih connected to an output of the input switch, and inverting amplifier INV connected to an output of the input capacitance and a feedback capacitance Cfh for connecting an output of INV to its input. The capacity ratio fo (Cfs/Cis)=(Cih/Cfh)−1. The input switch of the sampling circuit is controlled by a sampling control signal and the input switch of the holding circuit is controlled by a holding control signal on an inverted signal of the sampling control signal. When the sampling control signal is at a high level and the holding control signal is at a low level, the input voltage Vi is input to the sampling circuit. An inverter signal of the sampled signal is output from the inverting amplifier INV. The inverted signal is input to the holding circuit and its inverted signal, that is, the same signal as the input signal Vi is output from the holding circuit. 
     FIG. 3 shows a scaling circuit  50  for adjusting a level of input signal Vi according to 5 bit digital data A[0, . . . , 4] and B[0, . . . , 4]. The digital data B[0, . . . , 4] controls the input capacitance, and the digital data A[0, . . . , 4] controls the feedback capacitance. The input capacitance consists of capacitances C B0  to C B4  and C BC , and the feedback capacitance consists of capacitances C A0  to C A4  and C AC . Each input of the capacitances C B0  to C B4  is alternatively connected to the input signal or a reference voltage Vref through switches B 0  to B 4 . These switches are controlled by the signal B[0, . . . , 4]. Each output of the capacitances C B0  to C B4  is connected to an input of an inverting amplifier INV and the switches alternatively connect the output of the inverting amplifier to the feedback capacitances or the reference voltage Vref. When a composite capacity of the input capacitances is C B0  a composite capacity of the feedback capacitances is C Am  C Am  is 2 m  (m=0 to 4) and C Bn  is 2 n  (n=0 to 4). An output voltage Vout is output from the scaling circuit  50 , as in the formula (8).              Vout   =       (         C   BC     +       ∑     i   =   0     4          Bi   ·     C   Bi               C   AC     +       ∑     i   =   0     4          Ai   ·     C   Ai             )     ·   Vin             (   8   )                                
     Therefore, the output of the scaling circuit can be adjusted according to a scaling factor defined by the input capacitances and feedback capaitances. 
     The filter circuit in FIG. 1 performs a calculation of FIR filter as in the formula (9).                y        (   kT   )       =       ∑     n   =   0       N   -   1              h        (   nT   )       ·     x        (     kT   -   nT     )                   (   9   )                                
     Here, T is the sampling interval, N is the number of taps, k is an integer from − ∞ to + ∞ , x is an input signal, y is an output signal and h is the coefficient. 
     In the formula (9), errors are neglected such as errors in the capacity ratio (inclination) of input capacitances and feedback capacitances due to floating capacity, manufacturing deviation and so forth. These errors are hereinafter represented by a capacity error factor. Errors caused by offset voltage in the operational amplifier or other circuit components are hereinafter represented by an offset factor. When the capacity error factor is defined as “α n ” and the offset factors as “β n ” formula (9) becomes formula (10), which includes these error factors. The formula (9) is rewritten to be formula (10) when these errors are included.          y        (   kT   )       =         ∑     n   =   0       N   -   1              h        (   nT   )       ·     {       α   n     ·     x        (     kT   -   nT     )         }         +       ∑     n   =   0       N   -   1              n        (   nT   )       ·     β   n                                  
     Since the second term of the total sum of “h(nT)β n ” is constant in a predetermined filter with predetermined coefficients, the total error can be decreased by correcting only the first term in response to the input signal when the second term is evaluated in advance. Here, α n  is the capacity error factor and is calculated as in the formula (11) when the sampling and holding circuits  11   0  to  11   N−1  have errors of a 0  to a N−1 .                      α   0     =     a   0                   α   1     =       a   0     ×     a   1                     α   2     =       a   0     ×     a   1     ×     a   2                     α   3     =       a   0     ×     a   1     ×     a   2     ×     a   3                 ⋮               α     N   -   1       =       a   0     ×     a   1     ×     a   2     ×     a   3     ×   …   ×     a     N   -   1                       (   11   )                                
     The errors can be corrected by amending the coefficient h as in the formula (12).                  1     α   n       ·     h        (   nT   )                         (       n   =   0     ,   1   ,   2   ,   …   ,     N   -   1       )             (   12   )                                
     By the error correction of formula (12), the output is similar to that of formula (9) free from the errors, as in formula (13).                y        (   kT   )       =       ∑     n   =   0       N   -   1              1     α   n       ·     h        (   nT   )       ·     α   n     ·     x        (     kT   -   nT     )                   (   13   )                                
     The error α n  is predicted by the following 5 steps. 
     Step 1: Changing the coefficient of the first tap to be maximum, for example “127” and changing other coefficients to be “0”. 
     Step 2: Setting the scaling factor to be “1” so that the output is equal to the input. 
     Step 3: Inputting a predetermined input signal and recording the output signal in response to the input signal. 
     Step 4: Changing the coefficient of the second to the last taps to be maximum, successively, and repeat Steps 2 and 3. 
     Step 5: Comparing the theoretical inclination and the measured inclination so as to obtain the error in the inclination. Then, the error α n  os obtained. 
     FIGS.  4 ( a )- 4 ( c ) show the error prediction process. FIG.  4 ( a ) is a circuit without error. When the inclination is “1”, that is, the ratio Cis and Cfs is “1” as in formula (14). The following formula (15) is given.                Cis   Cjs     =   1           (   14   )                               Vo=−(Vi−Vb)+Vb=−Vi+2Vb  (15) 
     When an error occurs as in FIG.  4 ( b ), that is, Cis/Cis≠1, and an error B is included in the bias voltage, the output is as shown in the formula (16).              Vo   =         -                Cis   Cfs          Vi     +       (       Cis   Cfs     +   1     )          (     Vb   +   B     )                 (   16   )                                
     α and β are defined as in the formulae (17) and (18).                Cis   Cfs     =     α   s             (   17   )                 β   s     =         (       Cis   Cfs     +   1     )          (     Vb   +   β     )       -     2      Vb               (   18   )                                
     The output of the sampling circuit in FIG.  4 ( b ) is as in the formula (19). 
     
       
         Vo=−α S Vi+2Vb+β s   (19) 
       
     
     When the holding circuit of FIG.  4 ( c ) has an error α h in the inclination, the formula (20) is given. 
     
       
         Vo=−α h Vi+2Vb+β h   (20) 
       
     
     The output of the sampling circuit shown in the formula (19) is input to the holding circuit which outputs an output as in the formula (21). 
     
       
         Vo=−α h (−α s Vi+2Vb+β R )+2Vb+β h   
       
     
     
       
         φ=α s α h Vi−α h 2Vh−α h β s +2Vb+β h   (21) 
       
     
     When α and β are rewritten as in the formula (22) and (23), the output of the holding circuit is as in the formula (24). 
     
       
         α=α s α b   (22) 
       
     
     
       
         β=α h 2Vb−α h β s +2Vb+β h   (23) 
       
     
      Vo=αV1+β  (24) 
     The output of the holding circuit is one of the inputs to the multiplication circuits  31   0  to  31   N−1 . 
     Next, the error propagation in the multiplication circuit is discussed with reference to FIG.  5 . When an error in the bias voltage of the multiplication circuit is e, the output of the multiplication circuit is given as in the formula (25).                    Vo   =                  -       ∑     n   =   0       N   -   1                Cin   ·   bn     Cfm        Vin         +       ∑     n   =   0       N   -   1                Cin   ·   bn     Cfm          (     Vb   +   e     )         +   Vb   +   e   +                                ∑     n   =   0       N   -   1                Cin   ·     bn   _       Cfm        e                   =                  -       ∑     n   =   0       N   -   1                Cin   ·   bn     Cfm        Vin         +       ∑     n   =   0       N   -   1                Cin   ·   bn     Cfm        Vb       +   Vb   +   e   +       ∑     n   =   0       N   -   1              Cin   Cfm        e                       (   25   )                                
     Here, Vref=+Vb, and b is the control signal of the multiplication circuit, that is, multipliers. 
     γ is defined in the formula (26).              γ   =       ∑     n   =   0       N   -   1              Cn   ·   bn     Cfm               (   26   )                                
     The multiplication circuit has an error δ in its inclination that is independent from γ. The output voltage Vo can be expressed as in the formula (27).              Vo   =         -   δ                   γ                 Vi     +       (       δ                 γ     +   1     )        Vb     +       (         ∑     n   =   0       N   -   1            Cin   Cfm       +   1     )        e               (   27   )                                
     When the input voltage Vi of the multiplication circuit is substituted by the output of the sampling and holding circuit, the output is as in the formula (28).                    Vo   =                    -   δ                   γ                   (       α                 Vi     +   β     )       +       (       δ                 γ     +   1     )        Vb     +       (         ∑     n   =   0       N   -   1            Cin   Cfm       +   1     )        e                   =                    -   δ                   γα                 Vi     -   δγβ   +       (     δγ   +   1     )        Vb     +       (       ∑     n   =   0       N   -   1            Cin   Cfm       )        e                     (   28   )                                
     When ζ is defined as in the formula (29), the output voltage Vo is given by the formula (30). This output is input to the adder following the multiplication circuit.              ζ   ≃       -   δγβ     +       (         ∑     n   =   0       N   -   1            Cin   Cfm       +   1     )        e               (   29   )                               Vo=−δγαVi+(δγ+1)Vb+ζ  (30) 
     Next, the error propagation in the adder  40  is discussed with reference to FIG.  6 . When input voltages are Vi 1  to ViN, input capacitances are Ci 1  to CiN and a feedback capacitances is Cfa, the theoretical output of the adder is as in the formula (31).              Vo   =         -       C   i1       C   fa              V   i1       -         C   i2       C   fa            V   i2       -   …   -         C   iN       C   fa            V   iN       +           C   i1     +     C   i2     +   …   +     C   iN     +     C   fa         C   fa          Vb               (   31   )                                
     When the error in the bias voltage of the adder  40  is H, the output of the multiplication circuit having the maximum coefficient is Vi1 and the outputs of other multiplication circuits having the coefficient of “0” are Vi2 to ViN, Vi1 can be expressed as in the formula (30). Vi2 to ViN are Vb−ζj (j=2 to N). Then, the output of the adder  40  is as in the formula (32).                    Vo   =                    -       C   i1       C   fa              (         -   δ                   γα                 Vi     +       (     δγ   +   1     )        Vb     +     ζ   1       )       -         C   i1       C   fa            (     Vb   +     ζ   2       )       -   …   -                                    C   iN       C   fa            (     Vb   +     ζ   N       )       +           C   i1     +     C   i2     +   …   +     C   iN     +     C   fa         C   fa            (     Vb   +   H     )                     =                      C   i1       C   fa          δγα                 Vi     -         C   i1       C   fa            (         (     δγ   +   1     )        Vb     +     ζ   1       )       -         C   i1       C   fa            (     Vb   +     ζ   2       )       -   …   -                                    C   iN       C   fa            (     Vb   +     ζ   N       )       +       (           C   i1     +     C   i2     +   …   +     C   iN         C   fa       +   1     )          (     Vb   +   H     )                       (   32   )                                
     In the formula (32), the terms not including Vi are constant and can be expressed by ζ. The ratio of Ci1 and Cfa is defined as in the formula (33).                  C   i1       C   fa       =     θ                   1   N               (   33   )                                
     Here, θ is the error in the inclination of the adder  40  and N is the number of inputs of the adder. The output of the adder  40  is as in the formula (34).              Vo   =       θ                   1   N        δγα                 Vi     +   η             (   34   )                                
     The output is input to the scaling circuit  50 . 
     When the scaling factor is μ, its error independent from μ is κ and an offset voltage and its error is λ, the output of the scaling circuit is as in the formula (35).              Vo   =       μκθ                   1   N        δγα                 Vi     +   λ             (   35   )                                
     From the formula (35), the error of the inclination is κθδα in one tap. 
     Therefore, the final output can be corrected in error by multiplying the multiplier γ of the multiplication circuit  31   i  by          1   κθδα     .                          
     As mentioned above, the tap coefficients are changed to be maximum one after another, a ramp wave is input and the inclination is measured from the output. The measured inclination is compared with the theoretical inclination            μ                 γ     N     .                          
     The error is the above xθδα. 
     FIG. 7 is a simulation result of frequency response showing the effect of the error correction. In the simulation, the number of taps is 32, coefficient accuracy is 8 bit, the sampling frequency is 48 kHz. The error of the sampling and holding circuit is assumed as an attenuation of          31   32     .                          
     Therefore, the attenuation of the 32th tap is            31   32       32   32       .                          
     The input signal is a M-system including a white noise. The curve B is the case including the attenuation. There occurs attenuation through the total frequencies. The curve C of the case of corrected coefficients is equivalent to the theoretical wave in the passband and has similar attenuation in the stopband. 
     As mentioned above, the error of the analog calculation circuit can be corrected by charging the multipliers according to the correction data without adding electrical elements such as resistance, capacitance etc. The calculation result is accurate. 
     The error correction can be applied to other circuits including analog-digital multiplication such as the filter circuit above. 
     FIG. 8 shows the second embodiment ofa matched filter circuit for a code division multiple access communication system according to the present invention. 
     The filter circuit includes a voltage-current converter V- 1  for converting a voltage signal into a current signal. The current signal is held by a plurality of sampling and holding circuits SH 1  to SHn successively in response to a system clock CLK 0 . The data held by the sampling and holding circuits are not transferred through the sampling and holding circuits, so the transfer error is prevented. The outputs of the sampling and holding circuits are input to corresponding multi-plexers MUX 1  to MUXn having two outputs. Each multi-plexer selectively outputs the input from the corresponding sampling and holding circuit from one of the two outputs in response to a control signal, that is, spreading code or PN code. The PN code is a 1 bit binary multiplier corresponding to two outputs. One of the outputs is introduced to the first adder ADD 1  and the other is introduced to the second adder ADD 2 . An output of the second adder ADD 2  is inverted by an inverter INV and is input to the third adder ADD 3 . An output of ADD 1  is also input to ADD 3  so as to be added to the inverted output of ADD 2 . An output of ADD 3  is converted to a voltage signal by a current-voltage converter I-V. 
     FIG. 9 shows the sampling and holding circuit SH 1  in FIG.  8 . SH 1  has a pair of MOS transistors T 21  and T 22  which are connected at their one terminal through constant current sources S 21  and S 22 , respectively, to a high voltage Vdd. The other terminals are connected to a low (ground) voltage. Gates of the transistors T 21  and T 22  are connected through a control switch SW 2  with each other. A grounded capacitance C 7  is connected to a line between the switch SW 2  and T 22 . An input current Iin 2 , an output of V-I, is input to a line between T 21  and S 21 . An output current Iout 2  is output from a line between S 22  and T 22 . When T 21  and T 22  are substantially equivalent and SW 2  is closed, SH 1  becomes a current mirror circuit generating currents Iout 2  equal to -Iin 2 . C 7  is charged when SW 2  is closed. A voltage caused by the electrical charge in C 7  is put on the gate of T 22 , the output current Iout 2  is kept even when SW 2  is opened. Then, the analog current signal is held. A current between T 21  and T 22  is prevented by opening SW 2 . So, the electrical power consumption is low. The circuit size is much smaller than a circuit for holding a digital signal of a plurality of bits. 
     Description of SH 2  to SH 1  is neglected because these are similar to SH 1 . 
     FIG. 10 shows the current source S 21  in FIG.  9 . S 21  consists of a MOS transistor a gate of which is connected with a terminal t 31  of higher voltage. A terminal t 32  of lower voltage is connected with T 21  in FIG.  9 . The current source S 22  is similar to S 21 , so the description therefor is omitted. 
     In FIG. 11, the multi-plexer MUX 1  includes a pair of switches SW 41  and SW 42  which are connected to an input current Iin 4 . The switches are alternatively closed so that the input is introduced to one of outputs Io 41  and Io 42 . The switches SW 41  and SW 42  are controlled by a PN code and its inversion, respectively. The multi-plexers MUX 2  to MUXn are similar to MUX 1 , so descriptions are omitted. 
     FIG. 12 shows the first adder ADD 1 . ADD 1  is a current mirror circuit having a pair of MOS transistors T 51  and T 52 , which are connected at their one terminals through constanct current sources S 51  and S 52 , respectively, to a high voltage Vdd. The other terminals are connected to a low (ground) voltage. A plurality of input currents lin 51  to li 5 k are connected to a line between T 51  and S 51  as well as to gates of T 51  and T 52 . An output current Iout 5  is output from a line between T 52  and S 52 . When T 51  and T 52  have equivalent performance, Iout 5  is an inversion of a summation of the input currents Iin 51  to Iin 5 k as in the formula (36).              Iout5   =     -       ∑     i   =   1     k        Iin5i               (   36   )                                
     The adders ADD 2  and ADD 3  are similar to ADD 1 , the description therefor is omitted. 
     As shown in FIG. 13, the inverter INV is a current mirror circuit having a pair of MOS transistors T 61  and T 62  which are connected at one terminal of T 61  and one terminal of T 62  through constant current sources S 61  and S 62 , respectively, to a high voltage Vdd. The other terminals are connected to a low (ground) voltage. An input current lin 6  is connected to a line between T 61  and S 61  as well as to gates of T 61  and T 62 . An output current Iout 6  is output from a line between T 62  and S 62 . When T 61  and T 62  have equivalent performance, Iout 6  is an inversion of the input current Iin 6 . 
     In FIG. 14, the voltage current converter V-I has an operational amplifier OP 1  receiving at its non-inverted input an input voltage Vin 7  through a resistance R 3 . A reference voltage (ground voltage) is connected through a resistance R 1  to the inverted input. An output of the operational amplifier OP 1  is fed back to the inverted input through a resistance R 2 . OP 1  outputs an output current Iout 7  through a resistance R 5 . The output current is input to a non-inverted input of an operational amplifier OP 2 . An output of the operational amplifier OP 2  is fed back to an inverted input of OP 2  as well as input through a resistance R 4  to the non-inverted input of OP 1 . 
     When output voltages of OP 1  and R 5  are V 71  and V 72 , respectively, and R1=R2=R3=R4, the following formulae (37) and (38) are given. 
     
       
         V71=V72+Vin7  (37) 
       
     
     
       
         
           
             
               
                 
                   Iout7 
                   = 
                   
                     
                       
                         V71 
                         - 
                         V72 
                       
                       R5 
                     
                     = 
                     
                       Vin7 
                       R5 
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     Therefore, the voltage Vin7 is converted into the current Iout7 
     FIG. 15 shows a current-voltage converter I-V having an operational amplifier OP 3 . An output current Iin8 is input at the inverted input of OP 3  and an output of OP 3  is fed through a resistance R8 back to the inverted input. The relationship between the input and output of I-V is as in the formula (39). 
     
       
         Vout8=Iin8×R8  (39) 
       
     
     FIG. 16 is another voltage-current converter in which OP 1  and OP 2  in FIG. 14 are substituted by inverting amplifiers NO 1  and NO 2 , respectively, each consisting of an odd number of serial CMOS inverters. An input voltage Vin9 is input through an input capacitance C 3  to NO 1 , and an output of NO 1  is connected through a feedback capacitance C 8  to its input. A resistance R 5  is connected to the output of NO 1 . The output of R 5  is connected through a capacitance C 4  to an input of NO 2 . An output of NO 2  is connected through a capacitance C 6  to the input of NO 1  as well as through a capacitance C 5  to its input. 
     When C8=C3=C4=C5=C6, the relationship between the input and output voltages are as in the formula (40). 
     
       
         Vin9=V92−V91  (40) 
       
     
     Then, the output current is as in the formula (41).              Iout9   =       -       V91   -   V92     R5       =     Vin9   R5               (   41   )                                
     FIG. 17 is another current-voltage converter. An input current Iin10 is input to an inverting amplifier NO 10  and an output of NO 10  is fed through a resistance R 10  back to its input. The relationship between the input and output is as in the formula (42). 
     
       
         Vout10=−Iin10×R10  (42)