Abstract: There is provided an interpolation method for the Volume-of-Fluid (VOF) applied to a two-phase incompressible fluid, in particular, which makes it possible to cause time evolution of a shape-describing function based on the Volume-of-Fluid (VOF) method while preserving a sharpness of a shape described by the function. The method defines a function F on a one-dimensional structured grid formed on a one-dimensional real region, the function being defined through definition of a value thereof at a center of each cell within the one-dimensional structured grid, as an interpolation function H. With respect to a cell of interest on the one-dimensional structured grid, a slope is set to zero if a forward difference and a backward difference of the function f have different signs, and to a value twice as large as a smaller one of absolute values of the forward difference and the backward difference if the forward difference and the backward difference have the same sign.

Abstract: Various approaches for motion search refinement in a processing element are discussed. A k/2+L+k/2 register stores an expanded row of an L×L macro block. A k-tap filter horizontally interpolates over the expanded row generating horizontal interpolation, results. A transpose storage unit stores the interpolated results generated by the k-tap filter for k/2+L+k/2 entries, wherein rows or columns of data may be read out of the transpose storage unit in pipelined register stages. A k-tap filter vertically interpolates over the pipelined register stages generating vertical interpolation results.

Abstract: Systems and methods for improving Ct determination in PCR amplification curves by correcting PCR data for temperature shifts that may occur during the PCR process. A double sigmoid function with parameters determined by a Levenberg-Marquardt (LM) regression process is used to find an approximation to the portion of the curve in the region after the temperature shift, termed “CAC”, the cycle where the temperature shift occurred. A robust linear approximation is determined for the portion of the curve in the region before the temperature shift. Values of the fluorescent intensity for the cycle CAC or CAC+1 are determined using both the linear approximation and the LM process, and a difference in these values is subtracted off of the portion of the data set representing the portion of the curve before the temperature shift occurred to produce a shift-corrected data set. The shift-corrected data set may be displayed or otherwise used for further processing.

Abstract: A voice signal interpolation apparatus is provided which can restore original human voices from human voices in a compressed state while maintaining a high sound quality. When a voice signal representative of a voice to be interpolated is acquired by a voice data input unit 1, a pitch deriving unit 2 filters this voice signal to identify a pitch length from the filtering result. A pitch length fixing unit 3 makes the voice signal have a constant time length of a section corresponding to a unit pitch, and generates pitch waveform data. A sub-band dividing unit 4 converts the pitch waveform data into sub-band data representative of a spectrum. A plurality of sub-band data pieces are averaged by an averaging unit 5 and thereafter a sub-band synthesizing unit 6 converts the sub-band data pieces into a signal representative of a waveform of the voice by a sub-band synthesizing unit 6.

Abstract: An asynchronous sample rate converter interpolates and filters a digital audio input signal to produce a filtered, up-sampled first signal. A FIFO memory receives the first signal and stores samples thereof at locations determined by a write address and presents stored samples from locations determined by a read address. The presented samples are passed through an interpolation and resampling circuit to produce a continuous-time signal which is re-sampled to produce a signal that is up-sampled relative to a desired output. That signal then is filtered and down-sampled to produce the output signal. Sample rate estimating circuitry computes a difference signal representative of a time at which a data sample of the audio input signal is received and a time at which a corresponding audio output sample is required, and address generation circuitry generates the read and write addresses.

Abstract: A compressing device comprises plural stages of delay circuits (1?1 to 4?1) and multiplying/adding circuits (5?1 to 10?1) that performs weighted addition of output data from the delay circuits (1?1 to 4?1) according to the value of a digital basic function and thereby determines thinned-out data from sampling data sequentially inputted. Since the thinned-out data is determined by the compression part using a digital basic function serving as the original of a sampling function of infinite supports defferentiable once or more times over the whole range, a compression ratio of at lease 8 can be achieved only by the simple four operations. Further, since interpolation data is determined by the decompression part by using the same digital basic function, the original data before the compression can be reproduced with substantial fidelity by only the simple four operations.

Abstract: A method for an accurate approximation to Slerp function that is much faster to compute on current processors. Specifically, the present invention provides a method for obtaining an interpolated quaternion comprising forming a first product of a first quaternion and a first scaling function; forming a second product of a second quaternion and a second scaling function; and forming a sum of the first product and the second product, wherein the first scaling function is approximated by obtaining a first polynomial and wherein the second scaling function is approximated by obtaining a second polynomial, thus obtaining an interpolated quaternion that is in between the first quaternion and the second quaternion.

Abstract: Interpolation techniques are described for use with data that may not be uniform and may be characterized as scattered. Such data may be obtained in instances where data acquisition may not be easily controlled such as in obtaining experimental data for use with models. Data interpolation techniques may be used in connection with the experimental data to produce a more complete and accurate data set representative of a variety of conditions using as input the non-uniform or scattered data. Such data sets may be used in a variety of applications including providing a realistic and complete set of data for training and verifying neural networks.

Abstract: A system and method are disclosed for processing a signal that includes receiving encoded data including a plurality of input symbols; generating an input symbol set from the plurality of input symbols; looking up a plurality of output samples for the input symbol set; and outputting the plurality of output samples.

Abstract: A scaling method is to scale source data to destination data, wherein three reference points of the source data denoted as ?1, 0, and 1. Function f(x)=ax2+bx+c are used to describe the destination data within 0 and 1. The method includes setting a midpoint 0.5 with a quantity of f(0.5)=[f(0)+f(1)]/2 and f?(0)=f?(1)=DG; wherein D is a slope of [2f(0)?f(?1)?f(1)], and G is a gain factor to adjust the slope. Curve f(x) passes through the points of 0, 0.5, and 1. The coefficients of a, b, and c for f(x) are solved by a range of 0?x<0.5 and a range of 0.5?x<1, so that the f(x) is symmetric or substantially symmetric to the midpoint Curve is set to have: f(x)=2[f(1)?f(0)?DG]x2+(DG)x+f(0) for 0?x<0.5; and f(x)=2[DG+f(0)?f(1)]x2+[4f(1)?4f(0)?3DG]x+[DG?f(1)+2f(0)] for 0.5?x<1.

Abstract: A method is for scaling data from a source data to a destination data, wherein a function f(x) is determined to describe the destination data, in which x is a deviation from a current reference point 0. Two source data of f(0) and f(1) with respect to the point 0 and the point 1 are used as reference data. The method is performed by setting an initial condition about a primary slope D =f(1)?f(0), f(0.5)=[f(1)+f(0)]/2, a gain factor G>1, and f?(0.5)=DG=[f(1)?f(0)]G The f(x) is taken by a quadratic equation of f(x)=ax2+bx+c, which should pass f(0), f(1), f(0.5) and satisfy the slope of f?(0.5). Coefficients of a, b, and, c, are respectively solved in two ranges of 0?x<0.5 and 0.5?x<1, so as to obtain the function f(x) being about symmetric to the middle point at 0.5. The same procedure is applied for a next source data. Preferably, the function is symmetric to the middle point at (0.5, f(0.5)). Also and, a Z transformation of Z(z)=X(x)?0.

Abstract: A system and method interpolates a full color image from an array of single color sensors. Each sensor measures a single color, e.g., red, green or blue. The measured color values are stored as an array of data. For each data element, a plurality, e.g., four, gradients are computed that specify the color and/or luminance difference along different linear paths extending through the data element. At least some of the gradients are computed using a first order color differential and a second order color or luminance differential along the selected path. One or more gradients are then selected based on a comparison of the gradients to a computed threshold. Using the data elements along the path of the selected gradient or gradients, the missing color values are interpolated. The interpolation algorithm also utilizes first and second order color differentials.

Abstract: A decimation system and decimation circuit for decimating waveform data on an oscilloscope. The decimation circuit is implemented using sixteen parallel 16-to-1 multiplexers connected in parallel to a data bus which selectively captures samples based on control signals generated by a sample counting circuit. Decimation factor and phase values can be input to program the amount of decimation performed by the circuit. The decimation system provides even more flexibility in controlling the decimation and is formed by combining several of the decimation circuits with corresponding analog-to-digital converters and memory segments.

Abstract: An apparatus which processes a digital image and a method therefor which can reduce an error when calculating an output value obtained by interpolating pixel values of the input digital image. The apparatus includes an interpolation processing unit which interpolates an input digital image, and a controller which measures an interpolation interval of pixel values of the digital image, calculates a coefficient by substituting the interpolation interval for a coefficient equation stored in a register, and calculates an interpolation node for the digital image by substituting the coefficient and an output pixel position value of the digital image for an interpolation node calculation equation. The controller controls the interpolation processing unit so as to interpolate the digital image to the interpolation node. As a result, it is possible to reduce an error between an interpolated output pixel position value and an output pixel position value for the pixel values of the input digital image.

Abstract: A calculating apparatus comprises a memory and a calculating section. The memory is stored with table data for referencing a value of a variable x by using a value of a variable y and a value of a solution z. The calculating section inputs x_in and y_in, reads two values y_a and y_b corresponding to y_in from the memory, reads two values x_aa and x_ab corresponding to x_in from the memory in a line corresponding to y_a, reads two values x_ba and x_bb corresponding to x_in from the memory in a line corresponding to y_b, and calculates a solution z corresponding to x_in and y_in in an interpolation by using x_in and y_in and the read values y_a, y_b, x_aa, x_ab, x_ba, and x_bb.

Abstract: A controller that eliminates an error caused by acceleration/deceleration control, and controls the velocity of drive axes which is not represented by a rectangular coordinate system such that maximum allowable values of velocity, acceleration, and jerk of the drive axes are not exceeded. A program is analyzed in a command analysis section, and an interpolated position on a motion path in the rectangular coordinate system is determined in a first interpolation section, and then converted by means of a transformation section into drive axes' positions not in the rectangular coordinate system. In a tangential acceleration calculating section, a tangential acceleration is determined. In a velocity limit calculating section, a velocity limit at the time of each position being reached is determined which does not exceed maximum allowable values of velocity, acceleration, and jerk of the drive axes.

Abstract: Methods and apparatus, including computer program products, implementing and using techniques for using a color table defining a mapping from a source color space representing colors in source color coordinates to a destination color space representing colors in destination color coordinates. An input color in the source color space is received. A location of the input color in a cell of the color table is determined in terms of cell coordinate values in a cell coordinate system. The cell coordinate values are ordered to determine a processing order of the dimensions of the source color space. The cell coordinate values are used to calculate an output color in the destination color space, making no more interpolation calculations than the number of source color space dimensions multiplied by the number of destination color space dimensions.

Abstract: Disclosed are a method and apparatus for forming a color transform lookup table which helps output a smooth image having no pseudo contour and excellent in granularity. On the basis of a previously formed table, a color space is expressed by a basic triangle of white-primary color-black, and output signal values corresponding to lattice points in this basic triangle are calculated by linear interpolation. Black ink and cyan ink are replaced by setting a straight line AB, as a boundary line, connecting two points immediately before black ink begins to be introduced on two sides of the basic triangle.

Abstract: An interpolation filter having a first gain multiplexer, a second gain multiplexer, an adder and a multiplexer. The interpolation filter uses neighboring input discrete-time signals to generate interpolation signals having the desired sampling rate.

Abstract: This invention is a method and apparatus for interpolation which enables simpler and cost efficient implementation in hardware or software. A function table stores values of the function at addresses corresponding to the argument points where the function is known. The input value enables identification of the function values for arguments immediately below and above the input value. Respective bits of the absolute value of the difference between these two function values enables corresponding gradient value tables. A set of gradient values are stored in these gradient value tables. The least significant bits of the input value, those bits less significant than the arguments of the stored function values, address entries in the enabled gradient value tables. The desired interpolation value is the sum of the first function value and the gradient value recalled from the gradient tables.

Abstract: A system for updating a control coefficient to a target value during a prescribed number of periodic incremental update increments. The system divides the desired change in the value of the coefficient by the number of update increments. Specifically, the number of increments by the number of increments is limited to powers of two, so that the division can be accomplished simply by demarking the change in value according to the portion of number of increments, thereby separating the change into a quotient and a remainder. The value of each update increment is nominally equal to the quotient, with the remainder being distributed relatively evenly by adding one to selected updates.

Abstract: A data interpolating device comprises plural stages of delay circuits (1?1, 2?1, 3?1) for delaying discrete data sequentially inputted and multiplication/addition circuits (4?1 to 16?1) that performs weighted addition of data outputted from the output stages of the plural stages of delay circuits (1?1, 2?1, 3?1) according to the value of a digital basic function (?1, 1, 8, 8, 1, ?1) and thereby determine interpolation data. Since a sampling function of finite supports differentiable once or more times over the whole range.

Abstract: In the process of interpolation of video and/or audio digital data Sn, an interpolated value is chosen depending on whether or not an edge is detected. The edge detection is performed as follows. Let L=|S2n?S2n?2|, C=|S2n+2?S2n|, and R=|S2n+4?S2n+2|. An edge is detected when R>9(C+L) or L>9(C+R). A predictor P2n+1=K1S2n+K2S2n+2 provides the interpolated value for S2n+1 when an edge is detected, where K1=kL/(kL+kR), K2=kR/(kL+kR), where kL=1/(1+L), kR=1/(1+R) or kL=d2n+1,2n+2/(1+L) and kR=d2n,2n+1/(1+R). A different predictor (e.g. a cubic predictor) is used when no edge is detected. Other embodiments are also provided.

Abstract: Method and apparatus for determining at least one characteristic of a digital data signal. The method includes identifying at least one region of a waveform such as an Eye Diagram that contains information for determining at least one characteristic of interest of the digital data signal. Sufficient samples of the digital data signal are then taken to fully construct only the identified at least one region of the Eye Diagram without fully constructing the entire Eye diagram, and the at least one characteristic of interest is then determined from the fully constructed at least one region of the Eye Diagram.

Abstract: An apparatus and method for adaptively introducing a compensating signal latency related to a signal latency of a data symbol decision circuit. Adaptive timing control circuitry, including an interpolating mixer implemented as a tapped delay line with correlated tap coefficients, introduces a latency adaptively and substantially matching the latency of the data decision circuit for use within an adaptive equalizer, thereby minimizing the mean-squared error of such decision circuit. This adaptive latency is used in generating the feedback error signal which, in turn, can be used by the feedforward equalizer for dynamically adjusting its adaptive filter tap coefficients.

Abstract: A signal interpolator comprises a fractional interpolator and a numeric controlled oscillator. The numeric controlled oscillator may generate a control signal for controlling the fractional interpolator. The numeric controlled oscillator generally comprises a register, a modulo-M device, and an adder. The register may hold a count value, and the modulo-M device may apply a modulo-M function to the count value to generate the control signal therefrom. The adder may add an increment value to the modulo-M signal from the modulo-M device, to update the count value in the register.

Abstract: A frequency interpolating device for restoring an audio signal compressed at high ratio while keeping the high sound quality. An input digital signal to be subjected to frequency interpolation is converted to a spectrum signal representing the spectrum of the time-series signal by an analyzer. A spectrum analyzing section specifies, as an interpolating band, a deletion band not containing any spectrum among the bands defined by dividing the spectrum of the signal. A frequency interpolating section deduces the envelope of a digital signal and scales the spectrum of the spectrum distribution in the interpolating band specified by the spectrum analyzing section so that the spectrum matches with the function of the envelope and performs addition. The past spectra used for the scaling and addition are read out of a spectrum storage section. A synthesizer converts back the signal having the spectrum after the addition to the time-series signal.

Abstract: A system and method for performing trajectory generation, interpolation, and control for a motion control application, where the trajectory generation, interpolation, and control are performed in parallel with each other. In one embodiment, an FPGA in a motion control device may be configured to perform the trajectory generation, interpolation, and control in parallel. Performing trajectory generation, interpolation, and control in parallel on an FPGA may increase the efficiency of the motion control application.

Abstract: A digital sampling instrument for multi-channel interpolatative playback of digital audio data stored in a waveform memory provides improved interpolation of musical sounds by use of a cache memory.

Abstract: A decimation system and decimation circuit for decimating waveform data on an oscilloscope. The decimation circuit is implemented using sixteen parallel 16-to-1 multiplexers connected in parallel to a data bus which selectively captures samples based on control signals generated by a sample counting circuit. Decimation factor and phase values can be input to program the amount of decimation performed by the circuit. The decimation system provides even more flexibility in controlling the decimation and is formed by combining several of the decimation circuits with corresponding analog-to-digital converters and memory segments.

Abstract: A simulation device is provided with a speed ratio determining portion and a speed determining portion for calculating the maximum feeding speed of an operative part from an interference detecting distance and an interpolation period, and replacing the feeding speed of the operative part, which is read out by a program analyzing portion, with the maximum feeding speed; and an interpolating portion for determining interpolated points of a moving path of the operative part from the feeding speed of the operative part, which is replaced by the maximum feeding speed by the speed ratio determining portion and the speed determining portion, and the interpolation period. An interference check on the operative part is made at an interpolated point determined by the interpolating portion.

Abstract: A system, method and computer program product are provided for branching during programmable processing in a computer graphics pipeline. Initially, data is received. Programmable operations are then performed on the data in order to generate output. Such operations are programmable by a user utilizing instructions from a predetermined instruction set. When performing the programmable operations in the foregoing manner, programmable branching may take place between the programmable operations. Subsequently, the output is stored in memory. Also included is a system, method and computer program product for directly executing a function in the computer graphics pipeline. Initially, input data is received in the computer graphics pipeline. A mathematical function is directly performed on the input data in order to generate output data. It should be noted that the mathematical function is directly performed in the computer graphics pipeline without a texture look-up or aid from a central processing unit.

Abstract: A method of interpolating data for a waveform or vector display provides a variable interpolation rate based upon a distance between consecutive samples of input data. The distance is used to access a coefficient look-up table from among a plurality of coefficient look-up tables, the number of look-up tables being a function of the number of interpolation rates desired. The distance is also used to control a clock for reading out the coefficients from the coefficient look-up table. The distance is variable between consecutive samples. A finite impulse response (FIR) filter receives the coefficients from the coefficient look-up table and provides interpolated data between each set of consecutive samples. The distance may also be used to control the intensity of an electronic beam for a display device upon which the interpolated data is displayed.

Abstract: A method and software are disclosed for processing data values of a data array at equally spaced locations in two dimensions where the desired data values are nulls in the data array. The method and software first searches for linear ranges of contiguous nulls, and then performs incidental interpolation of all points in such range.

Abstract: A method for representation, interpolation and/or compression of data includes identifying a two-dimensional interpolation function s(z) based on a sampling function a(z). A Cauchy integral theorem is applicable for the interpolation function s(z). The interpolation function s(z) is used for the representation, interpolation and/or compression of the data.

Abstract: A trigonometric interpolator interpolates between two data samples at an offset &mgr;, where the two data samples are part of a set of N data samples. The trigonometric interpolator fits a trigonometric polynomial to the N data samples and evaluates the trigonometric polynomial at the offset &mgr;. The trigonometric inteprolator can be utilized for data rate changing and to correct mismatches between received samples and transmitted symbols. Simulations demonstrate that the trigonometric interpolater attains better performance than “conventional” interpolators, while simultaneously reducing the required hardware. In embodiments, the filter response of the trigonometric interpolator can be modified to achieve an arbitrary frequency response in order to enhance the interpolator performance. More specifically, the frequency response of the interpolator can be shaped to effectively correspond with the frequency response of the input data samples and the offset &mgr;.

Abstract: A method for approximating a base 2 logarithm of a binary input and the circuit to implement the method are disclosed. The circuit comprises means for determining the integer portion of the logarithm, a lookup table module, a residual function module, an adder module and a register. This circuit performs the approximation in one system clock cycle time.

Abstract: A data interpolating device comprises plural stages of delay circuits (1−1, 2−1, 3−1) for delaying discrete data sequentially inputted and multiplication/addition circuits (4−1 to 16−1) that performs weighted addition of data outputted from the output stages of the plural stages of delay circuits (1−1, 2−1, 3−1) according to the value of a digital basic function (−1, 1, 8, 8, 1, −1) and thereby determine interpolation data. Since a sampling function of finite supports differentiable once or more times over the whole range.

Abstract: Interpolation techniques are described for use with data that may not be uniform and may be characterized as scattered. Such data may be obtained in instances where data acquisition may not be easily controlled such as in obtaining experimental data for use with models. Data interpolation techniques may be used in connection with the experimental data to produce a more complete and accurate data set representative of a variety of conditions using as input the non-uniform or scattered data. Such data sets may be used in a variety of applications including providing a realistic and complete set of data for training and verifying neural networks.

Abstract: Linear interpolators that are both accurate and cost effective to implement in hardware are presented. These interpolators use a multi-bit value approach that permits adders to be used instead of multipliers. The inherent error known in multi-bit value approaches is corrected by using a more accurate approximation for a distance ratio used in interpolation calculations.

Abstract: A frequency interpolation apparatus is provided which reproduces a signal similar to an original signal by approximately recovering suppressed frequency components, from an input signal having the suppressed frequency components in a specific frequency band of the original signal. The input signal is divided into a plurality of signal component sets each having frequency components in a frequency band among a plurality of frequency bands, and a signal component set in the band with the suppressed signal components is synthesized from the plurality of divided signal component sets and added to the input signal. Each of the plurality of divided signal component sets is frequency-converted to a signal component set in the same frequency band, and the signal component set in the band with the suppressed signal components is synthesized through linear combination of the frequency-converted signal component sets.

Abstract: There is provided an interpolation method for the Volume-of-Fluid (VOF) applied to a two-phase incompressible fluid, in particular, which makes it possible to cause time evolution of a shape-describing function based on the Volume-of-Fluid (VOF) method while preserving a sharpness of a shape described by the function. The method defines a function F on a one-dimensional structured grid formed on a one-dimensional real region, the function being defined through definition of a value thereof at a center of each cell within the one-dimensional structured grid, as an interpolation function H. With respect to a cell of interest on the one-dimensional structured grid, a slope is set to zero if a forward difference and a backward difference of the function f have different signs, and to a value twice as large as a smaller one of absolute values of the forward difference and the backward difference if the forward difference and the backward difference have the same sign.

Abstract: An apparatus (20) and method (22) for transparently accessing and interpolating data are provided. Consecutive data values (24) of a function are generated and indexed. Even-indexed data values (24) are stored in an even-indexed table (30) and odd-indexed data values (24) are stored in an odd-indexed table (32). Adjacent-indexed data values (24) are acquired substantially simultaneously from even- and odd-indexed tables (30,32) with the first-indexed value (Gn) extracted from the even-indexed table (30) when an integral portion (A[N]) of a memory address (A[N+F]) is even and from the odd-indexed table (32) when the integral portion (A[N]) is odd. A fractional portion (A[F]) of the memory address (A[N+F]) is converted into an incremental value (&Dgr;).

Abstract: A data interpolating method capable of reducing an operation volume without the occurrence of a truncation error. Each of four step function generators generates a preset step function. Multipliers each multiply step function values output from relative step function generators by discrete data values held cyclically in data holding sections. An adding unit adds together the multiplied results output from respective multipliers in response to the respective four discrete data and the added values is integrated twice by integrators, an interpolation value between the discrete data being then output from the second-stage integrator.

Abstract: An implicit function field of a nonmanifold is held in a form of volume data; a value of an implicit function at a point between lattice points is decided by interpolation; and if a difference in code distances between two adjacent voxels to be interpolated is larger than a fixed width, no surface is formed between the voxels. Furthermore, an entered curved surface is broken down into curved surface patches which enable determination of a front and a back; numbers are given to the front and the back, respectively, to be distinguished from each other; and a space is classified into a plurality of regions by using the number of a surface of a nearest point.

Abstract: A method for forming an actuating variable to be output periodically by a control unit in output periods for controlling an apparatus, in particular the ignition or fuel injection of internal combustion engines, includes reading output signals of at least two sensors into the control unit and ascertaining individual components of the actuating variable based on the output signals. The sensor output signals are read-in and the individual components are determined periodically at intervals of one read-in period or one determination period being equal to or a multiple of the output period of the actuating variable. The read-in period of a sensor output signal is dependent on a speed of variation of the sensor output signal, and in particular it increases as the maximum speed of variation of the sensor output signal decreases. The determination period of each individual component is dependent on the read-in periods of the sensor output signals involved in each individual component.

Abstract: A method for producing a plurality of successive output data values defining an output curve that approximates an input curve defined by a plurality of input sample values, the output data values having a higher sampling frequency than the input sample values, the method comprising the steps of: pre-emphasizing the plurality of input sample values; defining successive and overlapping intervals including at least three of the pre-emphasized input sample values; interpolating a plurality of the output data values in an interpolation interval by calculating a moving average of a linear interpolation curve based on the at least three pre-emphasized input sample values, each of the output data values being influenced by the at least three pre-emphasized input sample values; and, emphasizing differently the influence of the at least three pre-emphasized input sample values for determining different ones of the output data values in the interpolation interval, whereby the pre-emphasizing step brings the output curve

Abstract: A method for generating a convergence correction curve from a plurality of successive output data values determined from a plurality of input sample values smaller in number than the plurality of output data values, the method comprising the steps of: defining successive and overlapping intervals including exactly three of the input sample values; interpolating a plurality of the output data values in an interpolation interval by calculating a moving average of a linear interpolation curve based on the three input sample values, each of the output data values being influenced by the three input sample values; emphasizing differently the influence of the three input sample values for determining different ones of the output data values in the interpolation interval; and, adjusting the input sample values to control convergence correction, whereby each incremental slope of the correction curve between adjacent output data values varies smoothly.

Abstract: A signal interpolator comprises a fractional interpolator and a numeric controlled oscillator. The numeric controlled oscillator may generate a control signal for controlling the fractional interpolator. The numeric controlled oscillator generally comprises a register, a modulo-M device, and an adder. The register may hold a count value, and the modulo-M device may apply a modulo-M function to the count value to generate the control signal therefrom. The adder may add an increment value to the modulo-M signal from the modulo-M device, to update the count value in the register.

Abstract: A linear interpolation operator for determining the value y of a function of x when one knows the value y1 corresponding to x1, and a value y2 corresponding to x2 (where x2<x≧x1), comprises a first calculation circuit which determines the equation (xm+xM)/2; a second calculation which determines the equation (ym+yM)/2; a comparison circuit which compares x with (xm+xM)/2 so as to determine which one of the intervals [xm,(xm+xM)2], [(xm+xM)/2, xM] contains x and to feed back the limits of the selected interval into the first calculation circuit and the limits of the interval corresponding in y into the second calculation circuit.