# Function generation

## Subclass of:

## 708 - Electrical computers: arithmetic processing and calculating

## 708100000 - ELECTRICAL DIGITAL CALCULATING COMPUTER

## 708200000 - Particular function performed

### Patent class list (only not empty are listed)

#### Deeper subclasses:

Class / Patent application number | Description | Number of patent applications / Date published |
---|---|---|

708270000 | Function generation | 52 |

20140344322 | QUANTUM PROCESSOR BASED SYSTEMS AND METHODS THAT MINIMIZE A CONTINUOUS VARIABLE OBJECTIVE FUNCTION - Computational techniques for mapping a continuous variable objective function into a discrete variable objective function problem that facilitate determining a solution of the problem via a quantum processor are described. The modified objective function is solved by minimizing the cost of the mapping via an iterative search algorithm. | 11-20-2014 |

20140351306 | METHOD OF GENERATING CORRELATION FUNCTION, METHOD OF TRACKING SIGNAL AND SIGNAL TRACKING SYSTEM - A method of generating a correlation function, a method of tracking a signal, and a signal tracking apparatus are provided. The method of generating a correlation function involves receiving a CBOC(6,1,1/11) signal, interpreting a subcarrier pulse period of the CBOC(6,1,1/11) signal as a subcarrier pulse period of BOC | 11-27-2014 |

20090013020 | Method and device for restoring degraded information - The present invention provides a technology which can perform a precise restoration to a distribution of original information by carrying out an iterative calculation using only a distribution of degraded information. The method according to the present invention performs the restoration to original information based only on degraded information. The method according to the present invention considers the distribution of the degraded information and the distribution of the original information as distributions of probability density functions, and considers a transfer function of a transfer system as a probability density function of a conditional probability. The most probable estimations of the distribution of the original information with respect to the distribution of the degraded information and the most probable estimations of the distribution of the transfer function are alternately carried out to finally restore the original information by means of the iterative calculation based on the Bayes' theorem for probability density functions. | 01-08-2009 |

20090287754 | SYSTEMS AND METHODS FOR STEP DISCONTINUITY REMOVAL IN REAL-TIME PCR FLUORESCENCE DATA - Systems and methods for removing jump discontinuities in PCR or growth data. A first approximation to a curve that fits a received data set is determined by applying a non-linear regression process to a non-linear function that models the data set to determine parameters, including a step discontinuity parameter, of the non-linear function. One example of a non-linear function is a double sigmoid equation. A second approximation to a curve that fits the data set is also determined by applying a regression process to a second non-linear function to determine parameters, including a step discontinuity parameter, of the second function. One of the first or second approximations is then selected based on an information coefficient determined for each of the first and second approximations. If a confidence interval calculated for the step discontinuity parameter includes the value zero, no step correction is made. If the confidence interval does not include the value zero, then a step correction is made. If a step correction is made, the portion of the data curve prior to the step change is replaced with appropriate portion of the selected approximation to produce a shift-corrected data set. In certain aspects, the portion of the data curve up to the first point after the step change is corrected. In certain aspects, if the approximation does not satisfy a goodness of fit criterion, no step correction is made. The shift-corrected data set is returned and may be displayed or otherwise used for further processing. | 11-19-2009 |

20120016920 | DIRECT CURRENT COMPENSATION SYSTEM AND METHOD FOR SCATTERING PARAMETER RATIONAL FUNCTIONS - A direct current compensation method for S-parameter rational functions reads S-parameters f(sk), which are generated at given frequency sk, from a storage unit. An S-parameter, which is generated at frequency sk=0 is supplemented into the S-parameters f(sk), upon the condition that there is no S-parameter which is generated at the frequency sk=0. An S-parameter ration function is generated according to the S-parameters f(sk). A DC level of the S-parameter rational function is compensated to generate a compensated S-parameter rational function. | 01-19-2012 |

20100198897 | DERIVING A FUNCTION THAT REPRESENTS DATA POINTS - A function that represents data points is derived by creating a matrix (e.g., a Hankel matrix) of an initial rank, where the matrix contains the data points. Singular values are derived based on the matrix, and it is determined whether a particular one of the singular values satisfies an error criterion. In response to determining that the particular singular value does not satisfy the error criterion, the rank of the matrix is increased and the deriving and determining tasks are repeated. In response to determining that the particular singular value satisfies the error criterion, values of parameters that approximate the function are computed. | 08-05-2010 |

20110078223 | APPROXIMATION PROCESSING METHOD AND APPROXIMATION PROCESSING DEVICE - An approximation processing method for approximating a point group using a curve or a surface defined by control points includes a step of forming an approximated curve (surface) using control points that retain features of a shape; a first calculation step of calculating a closest point closest to each of the data points on the approximated curve (surface); a second calculation step of calculating an error vector that joins the closest point, obtained in the first calculation step, to the data point; and a third calculation step of calculating a corrected control point by moving each of the control points based on the error vector obtained by the second calculation step. The step of forming an approximated curve (surface) and the first to third calculation steps are repeated to make the approximated curve (surface) respectively approximate the curve (surface) of an object configured by the data points. In correcting control points, a simple geometrical algorithm is used for calculating control points to reduce the number of control point convergence operations and thereby to quickly generate a curve or a surface, which approximates the data points of a point group, without having to solve a linear system. | 03-31-2011 |

20090216820 | FAST COMPUTATION OF COMPACT POSET ISOMORPHISM CERTIFICATES - Two methods and systems for fast construction of poset isomorphism certificates are provided. Posets (partially-ordered sets) generalize graphs. The invented certificates are number sequences such that two posets are isomorphic if and only if their corresponding certificates coincide. The first method yields the (Omicron,Iota) poset isomorphism certificate. The minimal Phi-isomorphism certificate can be constructed by partitioning vertices of the graphs into Phi-ranked symmetry clusters and constructing a topological Phi-vertex ranking. Thus, symmetries in posets are detectable at low cost. In addition, the Phi-vertex ranking and a poset isomorphism certificate provide a pair of separate one-dimensional keys for poset encoding. Data objects representable as posets, which are commonly used in automated design, safety and security applications, biocomputing, management of semi-structured data, and other fields, can be stored, analyzed, indexed, and accessed using the isomorphism certificates requiring much less storage and computation time. | 08-27-2009 |

20110153703 | SYSTEM AND METHOD OF GENERATING COMPLEX WAVEFORMS - Methods for generating complex waveforms, including step functions, impulse functions, and gate pulses are provided, as well as methods for generating modulated waveforms employing a number of known and newly developed modulation formats. The methods of the present invention employ a continuous linear function, wherein all output points are defined. Discontinuities and singularities are eliminated, yet pulses having nearly instantaneous transitions may be achieved. Thus, gate pulses step functions, binary waveforms and the like may all be generated from a single function, where they entire output range of the function is defined over a continuous input domain. | 06-23-2011 |

20100191789 | METHOD FOR REGULATING AN ACTUAL VALUE OF A VARIABLE CHARACTERIZING A POSITION OF AN ACTUATOR, COMPUTER PROGRAM PRODUCT, COMPUTER PROGRAM, AND RECORDING MEDIUM - A method is provided for regulating an actual value of a variable, which characterizes a position of an actuator, to a setpoint value using a regulator, which method makes it possible to optimize regulation in terms of bandwidth, stability, accuracy, and sturdiness. A predefined time characteristic of the setpoint value is transformed into a desired time characteristic of the actual value. A first transfer function is formed in the frequency domain and is approximated using one or more factors, in particular delay elements, to transform the predefined time characteristic of the setpoint value into the desired time characteristic of the actual value. A nonintegral exponent is selected for at least one of the factors. | 07-29-2010 |

20120059865 | ANALYSIS METHOD USING FINITE ELEMENT METHOD, AND ANALYTICAL COMPUTATION PROGRAM USING FINITE ELEMENT METHOD - An analysis method using a finite element method includes: selecting an analysis domain to be analyzed; dividing the analysis domain into elements as calculation objects; creating a matrix of each element; integrating a general function term as a product of a Galerkin weight function and a general function; creating simultaneous equations, based on the sum of matrices of respective elements and the sum of values obtained by integrating the general function term, and obtaining a numerical solution from the simultaneous equations. In integrating the general function term, the concept of a nodal domain defined based on a result of discretization of a second-order differential term according to a Galerkin finite element method is introduced, and the general function term using a typical value of the element is integrated. | 03-08-2012 |

20120072476 | IDENTIFICATION CIRCUIT AND METHOD FOR GENERATING AN IDENTIFICATION BIT USING PHYSICAL UNCLONABLE FUNCTIONS - An embodiment of the present invention is an identification circuit installed on an integrated circuit for generating an identification bit, comprising a first circuit to generate a first output signal that is based on random parametric variations in said first circuit, a second circuit to generate a second output signal that is based on random parametric variations in said second circuit, a third circuit capable to be operated in an amplification mode and in a latch mode, wherein in said amplification mode the difference between the first output signal and the second output signal is amplified to an amplified value and, wherein in said latch mode said amplified value is converted into a digital signal. | 03-22-2012 |

20140310325 | MODEL CALCULATION UNIT, CONTROL UNIT AND METHOD FOR CALIBRATING A DATA-BASED FUNCTION MODEL - A model calculation unit for calculating a data-based function model in a control unit is provided, the model calculation unit having a processor core which includes: a multiplication unit for carrying out a multiplication on the hardware side; an addition unit for carrying out an addition on the hardware side; an exponential function unit for calculating an exponential function on the hardware side; a memory in the form of a configuration register for storing hyperparameters and node data of the data-based function model to be calculated; and a logic circuit for controlling, on the hardware side, the calculation sequence in the multiplication unit, the addition unit, the exponential function unit and the memory in order to ascertain the data-based function model. | 10-16-2014 |

20140289296 | SYSTEM AND METHOD OF GENERATING COMPLEX WAVEFORMS - Systems and methods for generating complex waveforms, including step functions, impulse functions, and gate pulses are provided, as well as methods for generating modulated waveforms employing a number of known and newly developed modulation formats. The systems and methods of the present invention employ a continuous linear function, wherein all output points are defined. Discontinuities and singularities are eliminated, yet pulses having nearly instantaneous transitions may be achieved. Thus, gate pulses step functions, binary waveforms and the like may all be generated from a single function, where they entire output range of the function is defined over a continuous input domain. | 09-25-2014 |

20110238719 | METHOD FOR DECOMPOSING AN ANHARMONIC PERIODIC SIGNAL AND CORRESPONDING COMPUTER PROGRAM - This method for decomposing an anharmonic periodic signal, the general form of which may be expressed as x(t)=x | 09-29-2011 |

20140297705 | METHOD AND SYSTEM FOR THE DIGITAL SYNTHESIS OF A WAVEFORM - A method for digital synthesis of a waveform, wherein: samples of a reference waveform that is divided into a plurality of contiguous time segments are stored in a digital memory; the duration of each time segment is set at a respective desired value; the time segments are scanned in an orderly manner as a function of a clock signal so as to select one time segment at a time; for the time segment selected, a relative time that has elapsed from the start of the time segment is calculated as a function of the clock signal; the memory is addressed as a function of said relative time and of a ratio between the number of the samples and the desired duration of the time segment in order to read at least part of the samples of the time segment; and a digital-to-analog conversion of the samples read from the memory is carried out. | 10-02-2014 |

20100138462 | Method for Encoding Information Using Non Linear Evenly Distributed Functions and Computer Software for Implementing Said Method - The invention related to a method for encoding information using non-linear evenly distributed functions, that comprises the following steps for building such a function: selecting a first natural integer n, a first set En of cardinal n, a group G operating on said first set En, a second natural integer q and a second set Eq of cardinal q; defining a set OG of the orbits of the group G operating on vectors of n elements in the set Eq, a function II that, for each vector of the n elements of the set Eq, associates the corresponding orbit and a second function Φ allocating to each orbit of the group G a value of the set Eq; evenly distributing into a number q of sections the sums of the cardinals of the orbits of the group; defining a third function F comprising the first and second functions Φ | 06-03-2010 |

20150074159 | METHODS FOR DETERMINING A RESULT OF APPLYING A FUNCTION TO AN INPUT AND EVALUATION DEVICES - According to various embodiments, a method for determining a result of applying a first function to an input may be provided. The method may include: determining a second function; and applying the second function to a value based on the input to determine a first intermediate value; applying the second function to a value based on the intermediate value to determine the result. | 03-12-2015 |

20120226726 | SYSTEM AND METHOD FOR GENERATING DISCRETE-TIME MODEL (DTM) OF CONTINUOUS-TIME MODEL (CTM) FOR A DYNAMICAL SYSTEM - Method and apparatus for processing continuous-time models (CTM) in a digital processing architecture is disclosed. The discrete state-space technique maps the CTM into the discrete-time model (DTM) and stores the states of the system in a sample time independent discrete state space set of matrices. The resulting state-space matrices can be processed in software or directly in hardware. The method disclosed is particularly suited to be used in automatic synthesis algorithms where a digital circuit is generated from an algorithm described in a high level language or model representation such as, for example, data flow or bond graph into a hardware description language (HDL), and the HDL model can be synthesized using system specific tools to generate an application specific integrated circuit (ASIC) or an FPGA configuration. | 09-06-2012 |

20100131579 | SETTING CORDIC ITERATION COUNTS - This disclosure relates to setting the iteration count of a Cordic module as a function of a signal characteristic of an input signal provided to the Cordic module. | 05-27-2010 |

20110219053 | RECURSIVE TAYLOR SERIES-BASED COMPUTATION OF NUMERICAL VALUES FOR MATHEMATICAL FUNCTIONS - A recursive method for computing numerical values for mathematical functions includes providing a recursive Taylor series representation of a mathematical function f(x) of a variable x evaluated around a given operating point a. The recursive Taylor series representation includes a plurality of derivative derived terms that include ratios of derivatives of f(x) evaluated at the operating point a. Coefficient data is determined from ones of the derivative derived terms stored in a tangible memory device evaluated at the operating point a over a predetermined range. An approximation for the mathematical function f(x) is computed using the recursive Taylor series representation evaluated with the coefficient data. | 09-08-2011 |

20150074158 | METHOD AND SYSTEM FOR PRINCIPAL COMPONENT ANALYSIS - A method of constructing a set of basis functions is disclosed. The method comprises: receiving a set of data vectors describing a physical object or a physical phenomenon; using a data processor for calculating a set of eigenvalues for an objective matrix defined as a sum of a first matrix corresponding to the set of data vectors and a second matrix corresponding to a Laplace-Beltrami operator, the objective matrix being a positive definite matrix; and constructing the set of basis functions based on at least a subset of the eigenvalues. | 03-12-2015 |

20120030269 | Generating Filter Coefficients for a Multi-Channel Notch Rejection Filter - Provided is a system for generating coefficient values. The system may include a base function generator and a series of accumulators including a leading and a last accumulator. In the series of accumulators, the data output of each accumulator, except the last, may be coupled to the data input of a successive adjacent accumulator. The base function generator may be configured to output, to the leading accumulator, a series of data values that may correspond to a base function that is a specified order derivative of a filter function. Each accumulator may be configured to: add a data value currently at its data input to a currently stored data value to produce an updated data value that may correspond to a respective value of a specified order integral of the base function; store the updated data value in the accumulator; and output the updated data value at its data output. | 02-02-2012 |

20130212141 | Computing Time-Decayed Aggregates Under Smooth Decay Functions - Aggregates are calculated from a data stream in which data is sent in a sequence of tuples, in which each tuple comprises an item identifier and a timestamp indicating when the tuple was transmitted. The tuples may arrive at a data receiver out-of-order, that is, the sequence in which the tuples arrive are not necessarily in the same sequence as their corresponding timestamps. In calculating aggregates, more recent data may be given more weight by a decay function which is a function of the timestamp associated with the tuple and the current time. The statistical characteristics of the tuples are summarized by a set of linear data summaries. The set of linear data summaries are generated such that only a single linear data summary falls between a set of boundaries calculated from the decay function and a set of timestamps. Aggregates are calculated from the set of linear data summaries | 08-15-2013 |

20140250161 | FUNCTION APPROXIMATION BASED ON STATISTICAL PROPERTIES - Embodiments of techniques and systems for approximating a function are described. In embodiments, a computing device may receive one or more statistical properties associated with application of an approximation function of a function over a target domain. The computing device may formulate one or more constraints on one or more parameters of a functional form of the approximation function, based at least in part on the one or more statistical properties. The computing device may then determine the one or more parameters subject to the constraints and out put results of the determination. In embodiments, the one or more parameters may be determined through application of an optimization procedure. Other embodiments, may be described and claimed. | 09-04-2014 |

20130031151 | INCORPORATING NOISE AND/OR JITTER INTO WAVEFORM GENERATION - Methods and apparatus disclosed herein operate, for example, to derive a non-ideal received signal from an ideal signal, to compute, from the non-ideal received signal, at least one probability density function of amplitude and time values representing deviations from the ideal signal, to derive at least one amplitude noise component and at least one timing jitter component from the at least one probability density function, and to generate a non-ideal waveform by applying the at least one amplitude noise component and the at least one timing jitter component to an ideal waveform. | 01-31-2013 |

20100293213 | Method and apparatus for approximating a function - Embodiments described herein provide techniques for computing an approximation of a function. These embodiments provide an iterative method that avoids the computation of the normal matrix and/or the coefficients, as is typical in the prior art. (See diagram | 11-18-2010 |

708271000 | Direct digital frequency synthesizer | 6 |

20150106416 | SIGNAL PROCESSORS AND METHODS FOR ESTIMATING TRANSFORMATIONS BETWEEN SIGNALS WITH PHASE ESTIMATION - A phase estimation method estimates the phase of signal components using a point spread function. The method obtains a point spread function that expresses complex frequencies at a non integer location in terms of integral frequencies, for a complex frequency of a signal at a non integer location in a complex frequency domain. It obtains complex frequencies of the signal for the integral frequencies, and computes a sum of products of the complex frequencies of the signal at the integral frequencies with the corresponding complex values of the point spread function to provide an estimate of phase of the signal at the non integer location. | 04-16-2015 |

20090248772 | Single-Level Parallel-Gated Carry/Majority Circuits And Systems Therefrom - A carry/majority circuit, comprising a plurality of differential transistor pairs coupled in parallel and forming a pair of output nodes, with a single parallel gated level. Current is steered through a leg of the transistor pair having a higher input voltage. | 10-01-2009 |

20080256154 | Method and Apparatus for Synthesizing a User Defined Pre-Emphasized Arbitrary Waveform for High Speed Serial Data Technologies - The embodiments herein provide a device and method to generate Pre-emphasized signal. In one embodiment herein an input file containing digital data representing a digital data pattern waveform is received and up-sampled by an Fs/Fd rate. The up-sampled digital data is used for generating step response. The generated step response is differentiated to generate coefficients of a pre-emphasis filter which are convolved with the digital data pattern waveform input signal to generate a pre-emphasized digital data pattern waveform file. | 10-16-2008 |

20140222882 | Phase-to-Amplitude Converter for Direct Digital Synthesizer (DDS) with Reduced AND and Reconstructed ADD Logic Arrays - A sine wave generator for a Direct Digital Synthesizer (DDS) converts a digital phase input into a digital sine wave output. Sine values and slopes are stored in read-only memory (ROM) for coarse upper phase bits in a first quadrant. A quadrant folder and phase splitter reflects and inverts values from the first quadrant to generate amplitudes for all four quadrants. Each sine value and slope is stored for a range of lower phase bits. A Delta bit separates upper and lower phase bits. Delta conditionally inverts the lower phase bits, the sine value, and the final polarity. A reduced AND logic array multiplies the slope by the conditionally inverted lower phase bits. A reconstructed ADD logic array then adds the conditionally inverted sine value. The conditionally inverted polarity is added to generate the final sine value. Sine generation logic is streamlined with conditional inversion based on the Delta bit. | 08-07-2014 |

20090094302 | Incorporating Noise and/or Jitter into Waveform Generation - One or more embodiments are disclosed that involve computer implementable techniques for generating simulate-able waveforms without the need for repeatedly including and simulating a full channel model or testing the waveforms on a physical channel. Techniques according to such embodiments the invention comprise simulating the sending of a waveform across a channel and recording deviations from a simulated received waveform, which comprise differences between the ideal waveform as sent and the simulated received waveform. These deviations are then used to create simulate-able waveforms, which include the effects of noise and jitter, without the need for additional channel simulation. As an alternative to using channel simulation, deviations may also be collected from sending a waveform across a physical channel. Thus, a received signal sent across the physical channel may be sampled at sample points to record deviations, which are then used to create simulate-able waveforms without sending additional signals across the physical channel. Other embodiments include deriving and recording signal deviations from a simulated or measured system pulse response, and tabulating the deviations in the system pulse response when it occurs within a set of pre-determined bit patterns. | 04-09-2009 |

20110276613 | Efficient Function Generator Using Case Detection and Output Selection - A function generator for a digital system includes a plurality of sub-function generators. Each sub-function generator has an input that receives a respective input value and has an output that provides a respective output value responsive to the respective input value. A case detector receives a system input value and selectively routes at least a first portion of the system input value to the input of at least one selected sub-function generator. The case detector selects the selected sub-function generator in response to at least a second portion of the system input value. The case detector further suppresses transitions of data on the input of at least one non-selected sub-function generator. The case detector further selects the respective output value provided by the at least one selected sub-function generator and provides the selected respective output value as a function generator output value. | 11-10-2011 |

708274000 | Linear | 6 |

20100281089 | SIGNAL MAPPING - A circuit includes a signal processing circuit for accepting an input and for generating a set of outputs. The input is provided in an input range that has a set of representative values, and each output represents a measure of an association of the input with one or more of the representative values. The signal processing circuit includes a group of output sections, each output section being responsive to the input of the signal processing circuit. Each output section includes one or more sigmoid generators. Each sigmoid generator is responsive to an input of the output section to generate an output that represents a sigmoid function of the input of the output section. Each output section also includes a circuitry for combining the outputs of the one or more sigmoid generators to form one of the set of outputs of the signal processing circuit. An input transformation circuit is coupled to the plurality of output sections. The input transformation circuit is configurable to transform the input of the signal processing circuit for controlling a mapping characteristic from the input to the set of outputs. | 11-04-2010 |

20090106340 | Generation of schedule by which physical items to be manufactured are assigned into production slots via reducing non-zero factors within coefficient matrix clusters - A schedule is generated by which physical items to be manufactured are assigned into production slots. The physical items have constraints governing manufacture of the physical items. The method generates coefficient matrix clusters from a mathematical programming problem based on an actual scheduling problem. Each coefficient matrix cluster defines a variable cluster-constraint cluster pair. A variable cluster of each coefficient matrix cluster defines production slot-physical item pairs. A constraint cluster of each coefficient matrix cluster defines a group of constraints. Each coefficient matrix cluster includes coefficient-binary variable pairs, each pair having a binary variable multiplied by a coefficient. For each coefficient matrix cluster, the method reduces non-zero factors within the cluster. Each non-zero factor within the coefficient matrix cluster is defined as a coefficient-binary variable pair such that the binary variable of the pair multiplied by the coefficient of the pair is non-zero. The schedule is then generated. | 04-23-2009 |

20100191790 | SYSTEM AND METHOD FOR CORRELATION SCORING OF SIGNALS - Systems, methods and computer readable storage media are provided for identifying, in a signal of interest, signal segments matching a reference signal segment. A processor coupled to memory is adapted to perform operations including: converting the reference signal segment to a first vector characterized by n pairs of data points, wherein n is an integer greater than zero and each pair of data points comprises a data point having a value along the first axis and a value along a second axis normal to the first axis. Segment of the signal of interest are converted to additional vectors, wherein each of the segments of the signal of interest has a first length in a direction along the first axis and has n pairs of data points. A correlation value is calculated between the reference signal segment and each of the segments of the signal of interest, using the first vector and the additional vectors, respectively. An estimation of the magnitude of the reference signal segment relative to at least a subset of the segments of the signal of interest for which correlation values have indicated relatively similar correlation is calculated. | 07-29-2010 |

20090172059 | Computing time-decayed aggregates in data streams - Aggregates are calculated from a data stream in which data is sent in a sequence of tuples, in which each tuple comprises an item identifier and a timestamp indicating when the tuple was transmitted. The tuples may arrive out-of-order, that is, the sequence in which the tuples arrive are not necessarily in the sequence of their corresponding timestamps. In calculating aggregates, more recent data may be given more weight by multiplying each tuple by a decay function which is a function of the timestamp associated with the tuple and the current time. The tuples are recorded in a quantile-digest data structure. Aggregates are calculated from the data stored in the quantile-digest data structure. | 07-02-2009 |

20090172058 | Computing time-decayed aggregates under smooth decay functions - Aggregates are calculated from a data stream in which data is sent in a sequence of tuples, in which each tuple comprises an item identifier and a timestamp indicating when the tuple was transmitted. The tuples may arrive at a data receiver out-of-order, that is, the sequence in which the tuples arrive are not necessarily in the same sequence as their corresponding timestamps. In calculating aggregates, more recent data may be given more weight by a decay function which is a function of the timestamp associated with the tuple and the current time. The statistical characteristics of the tuples are summarized by a set of linear data summaries. The set of linear data summaries are generated such that only a single linear data summary falls between a set of boundaries calculated from the decay function and a set of timestamps. Aggregates are calculated from the set of linear data summaries | 07-02-2009 |

20090172057 | Computer system for predicting the evolution of a chronological set of numerical values - The invention relates to a computer system for assisting prediction of the future of a chronological set (J) of numerical values which are stored in the memory (H) of a computer (O), such as to enable the generation of a topological structure, which can be displayed (V), using an algorithm-based analyzer (A). The topological structure comprises a dense network of regression-based curves in which characteristic figures, which can be used for prediction (P) purposes, can manifest. | 07-02-2009 |

708276000 | Trigonometric | 7 |

20090006514 | METHOD AND DEVICE FOR NUMERICALLY GENERATING A FREQUENCY - To generate a digital signal at a given frequency, a step of calculating at least one trigonometric function for consecutive phases separated by a phase gap φ | 01-01-2009 |

20110004645 | APPARATUS AND PROGRAM FOR ARCTANGENT CALCULATION - An arctangent calculation apparatus includes a phase angle memory unit in which a phase angle is stored in advance, the phase angle corresponding to a two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; a vector rotation unit that performs a vector rotation operation on a two-dimensional vector value corresponding to in a range of 0° to 360° and converts the two-dimensional vector value corresponding to in a range of 0° to 360° into a two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; an arctangent calculation unit that outputs, from the phase angle memory unit, a phase angle that corresponds to the two-dimensional vector value corresponding to in a range of 0° to substantially 22.5°; and a phase angle conversion unit that converts the phase angle into a phase angle in a range of 0° to 360°. | 01-06-2011 |

20090157783 | NUMERICALLY-CONTROLLED OSCILLATOR CAPABLE OF GENERATING COSINE SIGNAL AND SINE SIGNAL ONLY USING COSINE LOOK UP TABLE AND OPERATING METHOD OF THE NUMERICALLY-CONTROLLED OSCILLATOR - A numerically-controlled oscillator (NCO) and an operating method of the NCO are provided. According to the NCO and the operating method of the NCO, it is possible to reduce the size of a lookup table memory by using a lookup table, which stores a plurality of phase compensation values for different phases obtained by using a cosine function or a sine function. Thus, it is possible to easily calculate cosine and sine addresses and cosine and sine signs and to quickly provide a cosine phase compensation signal and a sine phase compensation signal. | 06-18-2009 |

20150127695 | PROCESSOR TRIGONOMETRIC COMPUTATION - A method for a processor computing a first trigonometric function to use an alternative trigonometric function for certain ranges of the operand. A modulo function may be used to provide an operand with a reduced range, and the modulo function may subtract in multiple steps in a manner that preserves low-order bits. | 05-07-2015 |

20090327383 | SINUSOIDAL WAVE GENERATION CIRCUIT - There are provided a coefficient ROM | 12-31-2009 |

20090300088 | SINE/COSINE GENERATOR | 12-03-2009 |

20110055303 | Function Generator - One embodiment relates to a method for generating a periodic function in response to an argument in a digital signal processing system, where the periodic function can be represented as functions of two or more components of the argument. The method may include: obtaining a first operand from one of two or more lookup tables in response to a first component of the argument; obtaining a second operand from one of the lookup tables in response to a second component of the argument; conditionally mirroring the first and second operands in response to a quadrant of the argument; and calculating a value of the periodic function in response to the operands with a linear algebra unit without using conditional code execution. | 03-03-2011 |

708277000 | Logarithmic/exponential | 6 |

20130110896 | LOGARITHMIC/INVERSE-LOGARITHMIC CONVERSION CIRCUIT | 05-02-2013 |

20100332576 | APPARATUS AND METHOD OF CALCULATING SQUARE ROOT IN FINITE EXTENSION FIELD - Disclosed is an apparatus and a method of calculating the square root of an element a, which is not zero, belonging to a finite extension field F | 12-30-2010 |

20090037504 | Exponent Processing Systems and Methods - Embodiments of exponent processing systems and methods are disclosed. One method embodiment, among others, comprises performing a first table lookup using a first address to provide a first value corresponding to the first component part, setting an integer exponent to provide an integer-based value corresponding to the integer component, performing a second table lookup using a second and third address to provide a second value and a third value corresponding to the second component part and the third component part, respectively, expanding and normalizing the second and third values to provide expanded and normalized second and third values, combining the expanded and normalized second and third values to produce a first product, and computing the exponential function by combining the first value, the integer-based value, and the first product. | 02-05-2009 |

20090222503 | Melting Curve Analysis with Exponential Background Subtraction - A system and methods are provided for melting curve genotyping analysis of nucleic acids. Melting curves are generated by plotting fluorescence of a sample as a function of temperature. In one illustrative example, an exponential algorithm is employed to remove the background from generated melting curves and thereby perform comparative analysis to other melting curves. Additional illustrative examples provide for measuring the differences between two or more melting curves and clustering the genotypes of the provided sample nucleic acids. | 09-03-2009 |

20090083351 | EXPONENTIATION CALCULATION APPARATUS AND EXPONENTIATION CALCULATION METHOD - A exponentiation calculation apparatus includes a dividing unit which divides an input value as an element of a torus T | 03-26-2009 |

20140351307 | CALCULATING NODE CENTRALITIES IN LARGE NETWORKS AND GRAPHS - Embodiments related to calculating node centralities in large and complex networks and graphs. An aspect includes approximating a product of a matrix exponential and a random probe vector of an adjacency matrix, wherein the adjacency matrix represents a graph. A diagonal of the adjacency matrix is computed based on the product of the matrix exponential and the random probe vector. The node centralities are then calculated based on the computed diagonal until a designated number of central nodes has been detected according to embodiments. | 11-27-2014 |