referring first to fig1 a charge - transfer - device ( ctd ) transversal filter 10 is shown connected to tap weight adjustment circuitry 12 which includes a reference transversal filter 14 . the function of the ctd transversal filter 10 is to process analog input signals received on the line 24 in order to produce a filtered output signal on the line 18 . digital input test signals appear on line 16 and are converted to analog signals for processing by the digital - to - analog converter 40 which is a part of the test assembly . the function of the adjustment circuitry 12 is to adjust the signal - processing performance of the ctd transversal filter 10 . the ctd transversal filter 10 includes a charge - transfer - device ( ctd ) delay line 22 which consists of a plurality of charge - storage cells which are connected in series so that a signal placed on the input line 24 to the delay line 22 will propagate down the delay line 22 at a rate determined by an external clock ( not shown ). the delay line 22 consists of charge - storage cells which are of a standard construction and which exhibit charge - transfer inefficiency ( cti ) and fixed - pattern noise ( fpn ). the number of charge - storage cells in the delay line 22 is equal to the number m . each of the charge - storage cells of the delay line 22 is tapped and connected to a weighting - coefficient - gain stage , of which the stages 26 , 28 , 30 and 32 are typical . the number of tap - weighting stages is equal to the number of charge - storage cells in the delay line 22 . the number m is chosen to provide enough stages to accomplish the type of filtering required from the transversal filter 10 in accordance with well - known transversal - filter design techniques . although four stages ( 26 , 28 , 30 and 32 ) are shown in the drawing , more or fewer stages may be provided depending on the filtering task to be accomplished by the filter 10 . each of the tap - weighting stages 26 , 28 , 30 and 32 may consist of a simple amplifier , wherein the gain of each amplifier may be individually varied in order to provide selected weighting for each of the taps on the delay line 22 . the output of each of the tap - weighting stages 26 , 28 , 30 and 32 is added together or summed in the adder 34 in order to produce the output signal 36 for the transversal filter 10 . the output signal on the line 36 is brought out to the terminal 18 which presents the signal which is denoted as the filtered output of the transversal filter 10 . a signal is also provided on the line 38 which is connected to the output of the last charge - storage element on the delay line 22 . the signal on the line 38 is not a filtered - signal output but instead is a signal which may be used by the tap - coefficient - adjustment circuitry 12 for setting the coefficients or gains used by the stages 26 , 28 , 30 and 32 . the coefficient tap - weight - adjustment circuitry 12 , illustrated in fig1 is shown in block - diagram form and may be constructed using conventional electronic - circuit - design techniques or may be constructed using analogous programmed - computer techniques in which the operations symbolized by the blocks in the diagram are performed by computer software operations analogous to the block functions . the circuitry 12 includes an analog - to - digital converter 42 which is connected through gain and delay stages 44 and 46 to the input 48 of the reference transversal filter 14 . the function of the converter 42 is to change the analog signals on the line 38 into digital signals which may be used by the adjustment circuitry 12 . the gain stage 44 and delay stage 46 perform operations on the digital signal produced by the converter 42 in accordance with the mathematical techniques described in further detail below . the function of the stage 46 is to delay the signal passing from the line 38 to the line 48 so that the filters 14 and 10 operate in synchronism . the stage 46 is set so that d = p + m , wherein p is the period of the pseudo - random - noise - sequence test signal provided to the input 16 in order to allow adjustment of the tap coefficients in the ctd filter 10 . m is the number of tap coefficients in the filter 10 , and t is the period of the clocking signal used in the filter 10 . the reference transversal filter 14 includes a plurality of delay elements 50 , 52 and 54 which are one less in number than the number m . tap coefficient stages 56 , 58 , 60 and 62 have inputs connected to taps of the transversal filter 14 . the number of stages ( such as 56 , 58 , 60 and 62 ) is equal to the number m . the outputs of the stages 56 , 58 , 60 and 62 are added together or summed in the adder 64 which produces the reference - transversal - filter 14 output on the line 66 . the transversal filter 14 also provides unweighted tap outputs on the line 68 , 70 , 72 , 72a and 74 . a gain stage 76 is connected to the transversal filter 10 output line 36 and provides an input signal to the analog - to - digital converter 78 which provides a digital output signal on the line 80 . a summation stage 82 has a non - inverting input connected to the line 66 and an inverting input connected to the line 80 in order to produce an error - function - output signal on the line 84 . the function of the summation stage 82 is to compare the output ( on line 66 ) of the transversal filter 14 with the output ( as conditioned on line 80 ) of the ctd transversal filter 10 . a performance criterion stage 86 receives the error function signal input on line 84 and produces an output signal on the line 88 . the operation of the performance - criterion stage 86 may provide for minimization of the mean - square error or minimization of the mean - average error in the signal presented on the line 84 . the function of the performance - criterion stage 86 is to evaluate how closely the output provided from the ctd - transversal filter 10 compares with the output provided from the reference transversal filter 14 . the signal on the line 88 is provided as an input to the multiplier stages 90 , 92 , 94 and 96 . the multiplier stages 90 , 92 , 94 and 96 are representative of the plurality of multipliers ( m in number ) which are provided in the coefficient - adjustment circuitry 12 . accumulator stages 98 , 100 , 102 and 104 have inputs connected to the outputs of the multiplier stages 90 , 92 , 94 and 96 , respectively . the accumulators 98 , 100 , 102 and 104 have their outputs connected to the tap weighting stages 26 , 28 , 30 and 32 , respectively of the ctd - transversal filter 10 . the function of the accumulator stages 98 , 100 , 102 and 104 is to generate the proper weighting which is to be provided by the stages 26 , 28 , 30 and 32 , respectively . the accumulator stages ( 98 , 100 , 102 and 104 ) also serve as integrators in responding to the inputs from the multiplier stages 90 , 92 , 94 and 96 . summation stages 106 , 110 and 114 provide outputs which are connected to inputs of the multiplier stages 90 , 92 , and 94 . the line 74 from the transversal filter 14 is connected to an input of the multiplier stage 96 . gain stages 108 , 112 and 116 have outputs connected to the inverting inputs of summation stages 106 , 110 and 114a , respectively , and correspond to the charge - transfer inefficiencies of individual charge - storage cells of the delay line 22 . the inputs of gain stages 108 , 112 and 116 are connected to the lines 70 , 72 and 74 , respectively . the non - inverting inputs of summation stages 106 , 110 and 114 are connected to the lines 68 , 70 and 72a . the multiplier stages 90 , 92 , 94 and 96 have inputs connected to the lines 118 , 120 , 122 and 124 , each of which is provided with inputs corresponding to numbers representing the values u o k p , 1 , u o k p2 , u o k p , 2 , u o k p , 3 and u o k p , m , as shown . although the ctd - transversal filter 10 shown in fig1 is shown as having four taps , additional taps and coefficient - weighting stages may be added . such additional stages are omitted in the drawing and replaced by horizontal dashed lines for clarity . similarly , additional circuit elements similar to those shown may be added to the tap - weight coefficient - adjustment circuitry 12 in the region denoted with dashed horizontal lines . referring next to fig2 the charge storage cell 126 is a block - diagram model describing the operation and performance of a charge - storage cell in the delay line 22 of fig1 . this charge - transfer - device cell model is the same as that shown in a published technical paper : buss , d . d ., and bailey , w . h ., &# 34 ; applications of charge - coupled devices to communications &# 34 ;, technical paper digest , ccd applications conference , san diego , calif ., september 1973 , page 83 . the model includes an input line 128 ( labeled x k - 1 ), an output line 130 ( labeled x k ) and a tap line 132 ( labeled y k ). the model also includes summation stages 134 and 136 , a delay stage 138 , and gain stages 140 and 142 . the summation stage 134 has non - inverting inputs connected to the input line 128 and the output of the stage 142 . the delay stage 138 has its input connected to the output of the stage 134 , and has its output connected to the input of summation stage 136 . the stage 142 corresponds to the charge - transfer inefficiency of the charge - storage element 126 and has its input connected to the output of the delay stage 138 . the stage 140 corresponds to the fixed - pattern noise ( actually one minus the fixed - pattern - noise parameter f k ) and has its input connected to the output of the delay stage 138 . the output of the stage 140 is connected to the line 132 . the summation stage 136 has a non - inverting input connected to the output of the delay stage 138 , and an inverting input connected to the output of the stage 142 in order to produce an output on the line 130 . the model shown in fig2 is presented as a block diagram for simulation of the performance of an actual charge - storage cell in the delay line 22 . the following explanation of equations is presented in order to better explain the theory of operation of the invention . the explanation refers to the numbered equations which follow and which are further explained by the list of definitions which follow . equation ( 1 ) expresses the transfer function for the model of fig2 showing the relationship between the output produced on line 130 and the input on line 128 . equation ( 2 ) expresses the relationship for the model of fig2 between the output - tap signal produced on the line 132 and the output signal produced on the line 130 . equation ( 3 ) expresses the transfer function from the ctd input ( line 24 of fig1 ) to the nth tap output of the delay line 22 in which x 0 indicates the input on line 24 and y n indicates the tap output signal ( corresponding to the signal on the line 132 in fig2 ). as with all of the equations in this description , one sample time of delay is indicated by the z - 1 transform operator . equation ( 4 ) expresses the overall transfer function g ( z ) for the ctd - transversal filter 10 of fig1 in which g ( z ) expresses the ratio between the output signal on the line 36 and the input signal on the line 24 . the transfer function g ( z ) may be expressed as the ratio of two polynomials in the operator z - 1 , a numerator polynomial n ( z ), and a denominator polynomial d ( z ). the equation ( 5 ) represents the numerator characteristics of the transfer function g ( z ) in which the polynomial coefficients are expressed as α n . equation ( 6 ) expresses the denominator characteristics of the transfer function g ( z ). if the transversal filter 10 were ideal , the denominator polynomial , d ( z ), would be identically equal to unity . equation ( 6 . 5 ) is an expression for the value of each coefficient of the numerator polynomial n ( z ) defined in equation ( 5 ) and shows the relationship which may be determined by connecting a plurality of charge - storage elements in series , each of which has a construction like the cell 126 shown in fig2 . equation ( 7 ) illustrates the important fact that the effective tap weights ( see equation ( 6 . 5 )), are each composed of a weighted sum of the actual tap weight , c n , and the preceding actual tap weight , c m - 1 c n - 1 . the relationship expressed in equation ( 7 ) is very important to the invention and expresses the important relationship between the polynomial coefficients for the numerator function expressed in equation ( 5 ) and the physical tap weights , c n , of the ctd - transversal filter 10 . equation ( 8 ) expresses the relationship which is observed to the construction of the ctd transversal filter 10 , i . e ., there is no input top weight . equation ( 9 ) is an expression for the pulse gain from the ctd - transversal filter input 24 to the output line for the nth tap output . note that the actual value for the gain expressed in the equation ( 9 ) is measured by propagating an isolated pulse down the delay line 22 and measuring the ratio between the pulse maximum applied to the input line 24 and the pulse maximum measured at each of the taps on the line 22 ( the inputs to the weighting stages 26 , 28 , 30 and 32 ). the equation ( 10 ) expresses the zero frequency gain from the transversal filter input 24 to the nth tap output . the zero frequency gain is measured by transmitting a test dc signal on the line 24 and measuring the dc signal level at each of the taps along the delay line 22 . equation ( 11 ) combines equations ( 9 ) and ( 10 ) in order to express the pulse gain in terms of the zero - frequency gain for each charge transfer cell 126 of the delay line 22 . equation ( 12 ) is an expression for the charge - transfer inefficiency ( cti ) of the n th cell . equation ( 13 ) expresses the fact that the zero - frequency gain and pulse gain for the delay line 22 cell zero is equal to one ( cell zero is defined as equal to the same signal as the line 24 before any delay . equation ( 14 ) defines the magnitude of a modified frequency - response reference in terms of the product between the magnitude of the desired frequency response for the transversal filter 10 and the magnitude of the denominator function d ( z ) as defined in equation ( 6 ). equation ( 16 ) places the expression of equation ( 14 ) in the frequency domain . equation ( 17 ) expresses the magnitude of the modified frequency - response reference in terms of a modified reference transversal filter having tap coefficients b n . the magnitude response of the reference transversal filter defined by equation ( 17 ) is to closely match the magnitude response of equation ( 16 ). the reference transversal filter defined in equation ( 17 ) is produced in the circuit of fig1 by the reference transversal filter 14 . equation ( 18 ) defines an auxiliary variable u in terms of its z transform u ( z ). equation ( 19 ) is an expression for the output of the transversal filter 10 , y ( z ), in terms of the auxiliary variable , u . equation ( 20 ) defines a reference signal r ( z ) corresponding to the output of the reference transversal filter 14 on the line 66 . equation ( 21 ) defines an error signal corresponding to the error signal present on the line 84 . the error signal is defined in terms of the difference between the inverse transforms of r ( z ) and y ( z ) as defined in equations ( 19 ) and ( 20 ). a convergence - controlling parameter is used in equation ( 22 ) to control the rate of convergence of the individual tap - weight coefficient c k . equation ( 22 ) is an adjustment equation for the tap - weight coefficients in the ctd transversal filter 10 . the equation ( 22 ) calls for adjustment of the tap - weight coefficients , the c k , through the use of the method of steepest decent by taking the gradient of a performance criterion , j ( e n ), wherein the performance criterion is a single valued , unimodal function of the error signal defined in equation ( 21 ). the performance criterion p n is equal to the derivative of the performance criterion j with respect to the error signal e n . equation ( 23 ) is a definition for the performance criterion p n such that the adjustment circuitry 12 will operate to minimize the mean - squared error of the error signal e n as presented on the line 84 . equation ( 24 ) is an alternative definition for the performance criterion p n ( alternative to the definition of the equation ( 23 )). the equation ( 24 ) is a definition for the performance criterion that will result in a minimization of the mean absolute , or magnitude of error in the error signal presented on the line 84 . equation ( 25 ) is an expression for the inverse transformation of equation ( 19 ) above . equation ( 26 ) is an expression for the partial derivative of y n , as expressed in equation ( 25 ), with respect to the tap weight coefficient , c k . equation ( 27 ) expresses the relationship between the effective tap weight and the actual tap weight for the ctd transversal filter 10 , as defined in equation ( 7 ). equation ( 28 ) expresses the amount by which the ctd filter 10 tap - weight coefficients are to be adjusted , based on the equations ( 22 ) and ( 26 ). the tap - weight - coefficient adjustment circuitry 12 of fig1 implements the adjustments defined by equation ( 28 ). that is , for example , multiplier 90 in fig1 performs the operation suggested by equation ( 28 ) by multiplying together the signals obtained on lines 118 , 88 and the output line of summation block 106 . the summation stage 106 performs the differencing operation defined between the brackets on the right hand side of equation ( 28 ). the performance criterion , p n is provided to the multiplication stage 90 on the signal line 88 . the convergence - controlling parameter and pulse - gain figure are provided as inputs on the line 118 to the multiplication stage 90 . similar functions are performed by the stages 92 , 94 and 96 . that is , the adjustments to be applied to each of the tap - weight coefficient stages 26 , 28 , 30 and 32 is defined by the equation ( 28 ). equations ( 29 ) and ( 30 ) express a simplification which may be used with the adjustment circuitry 12 in which the inputs to the lines 118 , 120 , 122 and 124 are each made the same , thus effecting only the relative convergence rates for the tap - weight coefficients of the stages 26 , 28 , 30 and 32 . equation ( 31 ) provides another simplification in the operation of the adjustment circuitry 12 in which the charge - transfer inefficiency parameters used in the stages 108 , 112 and 116 are each made equal to a single effective value of charge - transfer inefficiencies . however , the simplification shown in equation ( 31 ) is not advisable for ctd transversal filters 10 which have significant variations in charge - transfer inefficiencies between the charge - storage cells of the delay line 22 . k p , n is the ratio of the peak amplitude of the pulse measured at the filter tap n to the peak amplitude of the pulse provided at the filter input as a step in the tap - weight - adjustment method . k dc , n is the ratio of the dc signal level at the filter tap n to the dc signal level provided at the filter input as a step in the tap - weight - adjustment method . r ( ω ) is the desired frequency response to be produced by the ctd transversal filter . ω s sampling or clocking frequency of the ctd transversal filter in radians / second . c n is the tap weight coefficient for the ctd transversal filter element n . b n is the tap - weight coefficient for a reference transversal filter element n . f n is the fixed - pattern noise for the ctd transversal - filter element n . ω is the frequency of the input signal provided to the ctd - transversal filter during use of the filter . α n is the effective tap weight of the ctd transversal filter element n . n ( z ) and d ( z ) are the numerator and denominator functions , respectively , for the function g ( z ). the following equations express the relationships disclosed in the preceding description and point out the theory of operation of the invention . the number enclosed in parentheses to the right of each equation is the equation number referred to in the preceding text . ## equ1 ##