a first embodiment of the invention is illustrated in fig1 in the environment of raster distortion and convergence correction circuitry in a television signal display device . both digital and analog television receivers are subject to raster and distortion errors . horizontal convergence errors and raster distortion , such as side pincushion distortion , may be corrected by selectively delaying one or more of the individual color signals in a given scan line . this delay may be accomplished by clocking samples of the signal into a memory device at the input sample rate , and clocking the samples out of the memory with clock signals of varying phase to produce incremental sample delays . alternatively , as described in u . s . pat . no . 4 , 771 , 334 , respective ones of the color signals may be effectively selectively delayed by interpolating successive signal samples . that is , the amplitude values of a number of successive samples are scaled and combined in such fashion to generate a sample value having an amplitude representing a pixel spatially located between respective ones of the pixels represented by actual sample values . successive interpolated samples are respectively generated by different interpolation functions . this is accomplished simply by changing the scaling coefficients in the interpolator for successive sample value computations . interpolators of this type are in effect programmable adaptive filters which have an impulse response h i ( nt ), where the index i connotes one of many impulse responses that the interpolator may be programmed to exhibit . fig1 shows , in block form , an example of convergence and distortion circuitry that may be implemented in the blue signal path of a television receiver . similar circuitry ( not shown ) is incorporated in the red and green signal paths except that the respective interpolating filters in the respective paths are programmed to exhibit different signal delays . in this example separated analog blue signal is applied to an analog - to - digital converter 51 which develops digital samples representing the analog signal . the digital samples are coupled to a buffer memory 55 such as a first - in - first - out memory ( fifo ). samples in the fifo are supplied to the horizontal interpolating filter 56 as needed by the filter 56 . the interpolating filter 56 generates samples corresponding to samples exhibiting more or less delay depending on the instantaneous location of the current pixel along the horizontal scan line . that is , interpolated samples at the extremities of the line exhibit relatively large effective delays and samples near the center of the line exhibit no delay . the samples provided by the interpolating filter 56 are coupled to a dac 57 which converts the digital samples to analog form and applies same to kinescope driver circuitry . the interpolating filter 56 is conditioned to provide each of the successive interpolation functions h i ( nt ) under the control of the control circuitry 53 . the control circuitry 53 includes timing circuitry which is programmed to condition the fifo 55 to output the appropriate signal samples in accordance with respective interpolating functions . in addition it includes counting circuitry that is reset to zero by each horizontal synchronizing pulse hs , and which counts pulses of the sampling clock fs . respective count values are an indication of the current location along a horizontal scan line . the count values are applied as address codes to a coefficient memory 54 . the coefficient memory is programmed with scaling coefficients used to program the interpolating filter and thereby condition it to exhibit a particular function h i ( nt ). thus the interpolating filter 56 is reprogrammed every sample interval ( though it may be programmed to perform the same function for a number of successive sample intervals , particularly in the center of a line ). each function h i ( nt ) is defined by a set of coefficients h i1 , h i2 , . . . h in stored in the memory 54 . a set of coefficients is provided for each address value . desirably the dac 57 should have a flat frequency response over the range of frequencies exhibited by the digital signal to be converted . in this arrangement however it is known a priori that the particular dac used in the apparatus will distort the signal during digital to analog conversion . that is , the dac has an impulse response g ( nt ) different from unity . the impulse response g ( nt ) is a consequence of at least the sin ( πft )/ πft output characteristic of the dac , and may include other contributions . to compensate the non ideal frequency characteristics of the dac 55 , the design of the interpolating filter 56 is modified . let h i ( ω ) represent the fourier transform of the nominal impulse response h i ( nt ) of the interpolating filter 56 , and let g ( ω ) represent the fourier transform of the impulse response g ( nt ). the respective impulse responses h i &# 39 ;( nt ) of the modified interpolating filter correspond to the inverse fourier transform , if (. ), of the ratio of h i ( ω ) and g ( ω ), or ; where the asterisk designates convolution , and g - 1 ( nt ) is a time response function which has an amplitude and phase response that is the reciprocal of g ( nt ). thus to compensate for the undesirable roll - off of the dac , the programming coefficients stored in the coefficient memory 54 correspond to the coefficients that define the respective impulse responses h i &# 39 ;( nt ) rather than h i ( nt ). note that no extra hardware is required to perform the compensation . fig2 illustrates a further embodiment in the environment of a television signal deghosting apparatus . in certain geographical areas broadcast television signals will reflect off solid objects , and then recombine with the direct signal . the result on demodulation and display of the received signal is the occurrence of phantom - like replicas of the transmitted image appearing spatially displaced from the desired or direct image . these images may be removed by incorporating deghosting apparatus . in fig2 transmitted television signals are received by antenna and applied to a tuner and if circuit 10 . signal from the circuitry 10 is applied to a detector 12 which develops a analog baseband composite television signal . the composite signal is coupled to an analog - to digital convertor 14 , which develops digital representations of the analog composite signal . the digital composite signal is applied to deghosting apparatus including an equalizing filter 15 , an analyzer 16 and a source of reference values 22 . deghosted signal output from the equalizing filter is applied to the digital - to - analog convertor 18 which restores the signal to analog form . the deghosted analog composite signal is then applied to processing circuitry 20 , which may be a conventional television receiver , or rebroadcasting apparatus etc . deghosting apparatus fall into the class of circuitry known as equalizing filters . in a typical equalizing or deghosting implementation , a model of the signal transmission channel is determined . an equalizing filter is then configured to render the transmission channel transparent to the transmitted signal . a detailed explanation of ghost cancelling , using frequency transform techniques , may be found in the u . s . pat . no . 4 , 897 , 725 by t . tanaka etal , entitled &# 34 ; ghost cancelling circuit &# 34 ;. assume that the broadcast signal contains regularly recurring training signals which are precisely defined by an impulse response characteristic v ( nt ), ( having a corresponding frequency transform v ( ω )). the received training signal has an impulse characteristic x ( nt ), which is equal to the convolution of the function v ( nt ) with the impulse response characteristic of the transmission channel . upon reception of a repetition of the training signal , the analyzer 16 isolates and stores it for computations . the computations include generating a frequency transform , x ( ω ) of the received training signal . the transform , v ( ω ), of an uncorrupted training signal is accessed from memory , and divided by the transform , x ( ω ). an inverse transform is performed on the quotient to produce the function h ( nt ) which defines the required impulse response of an equalizing filter to compensate for distortions ( or ghosts ) introduced into the signal by the transmission channel . the analyzer is conditioned to program the equalizing filter to exhibit the impulse response h ( nt ). in the fig2 example , assume that the dac 18 exhibits an impulse response g ( nt ) corresponding to sin ( πft )/ πft ( with a corresponding frequency transform g ( ω )). the equalizing or deghosting filter 15 can be programmed to correct for both the signal distortions incurred in transmission channel and the signal distortion to be incurred by the dac . this may be accomplished by incorporating the transform g ( ω ) in the computation of the impulse response h &# 39 ;( nt ) for the equalizing filter 15 . there are at least two approaches to these computations . g ( ω ). one is to multiply the transform x ( ω ) by g ( ω ), and then dividing the transform v ( ω ) by the resulting product . the inverse transform h &# 39 ;( nt ), of the quotient is the desired composite impulse response for the equalizing filter 15 . a second approach , which requires less computation by the analyzer 16 is to incorporate the transform g ( ω ) within the transform of the undistorted training signal . that is to utilize a training signal transform v &# 39 ;( ω ) given by the equation ; the function h &# 39 ;( nt ) is then generated from the inverse transform of the quotient v &# 39 ;( ω )/ x ( ω ). in the foregoing examples , the impulse response for the programming equalizing filter was calculated in the frequency domain using frequency transforms , for example fast fourier transforms . it will be appreciated by those skilled in the art of adaptive equalizing ( or deghosting ) filter design , that the impulse response h ( nt ) may be generated in the time domain using convolution of the appropriate functions including the impulse response of the received training signal , the impulse of the undistorted training signal and the impulse response of the dac . a detailed explanation of these techniques may be found in u . s . pat . no . 4 , 864 , 403 entitled &# 34 ; adaptive television ghost cancellation system including filter circuitry with non - integer sample delay .&# 34 ; fig3 illustrates a third embodiment in the context of an audio signal processing system . in the figure a portion of one channel of a digital stereo audio processor is shown . similar circuitry would be implemented for the other stereo channel . element 89 is a source for providing , for example , the left channel digital stereo signal , and may include tuning , demodulating and signal matrixing circuitry . the signal is coupled to the cascade connection of a volume and balance circuit 92 , a treble and bass circuit 90 , a dac 93 and an analog low pass filter 95 . the volume and balance circuit , and the treble and bass circuit , are both controlled via user inputs applied through a user control interface 91 . assume in this example that the dac 93 imparts a sin ( πft )/ πft frequency response characteristic to the signal converted . also assume that the low pass filter should have a frequency response b ( ω )= l ( ω ) m ( ω ), but in fact is limited to the frequency response l ( ω ). typically digital treble and bass circuitry are implemented with programmable filters including delay elements for concurrently providing a plurality of relatively delayed samples , scaling circuits for weighting the plurality of relatively delayed samples by selectable weighting factors and summing means for combining the weighted samples to produce the output signal . each set of weighting coefficients , corresponding to respective bass or treble response characteristics , defines an impulse response h i ( nt ). respective sets of coefficients are stored in the user interface 91 . responsive to user stimuli a set of coefficients is selected by the user according to his listening preference , and applied to program the treble and bass circuit 90 . as in the previous examples , the undesirable frequency response of the dac 93 may be compensated in the circuitry preceding the dac , i . e ., in the programmable filter function of the treble and bass circuit . in addition the deficiency of the lowpass filter 95 may also be compensated in the treble and bass circuit . this is accomplished by altering the coefficients stored in the user interface for programming the treble and bass circuit . the stored coefficients will define impulse responses h &# 39 ; i ( nt ). rather than h i ( nt ). where m ( nt ) is the impulse response corresponding to the deficiency m ( ω ) in the desired frequency response of the low pass filter 95 , g - 1 ( nt ) is the reciprocal time response of the undesired impulse response of the dac 93 , and the asterisk connotes the convolution function .