Abstract: This method for decomposing an anharmonic periodic signal, the general form of which may be expressed as x(t)=x0+x1 cos(?(t)), wherein ?(t) is the phase of the signal, is characterized in that it consists of: determining an expression of the phase equation F ? ( ? ) = ? ? ? t , determining an expression of the phase ?(t) as a function of de parameters (r, rk, ?1, pk) measuring the anharmonicity of the signal and its morphology, from p cosn and p sinn functions defined by: p ? ? cos n ? ( t , r ) = ? k = 1 ? ? cos ? ( kt ) ? r k k n ? ? and ? ? p ? ? sin n ? ( t , r ) = ? k = 1 ? ? sin ? ( kt ) ? r k k n .

Abstract: Tensor linear Laplacian discrimination for feature extraction is disclosed. One embodiment comprises generating a contextual distance based sample weight and class weight, calculating a within-class scatter using the at least one sample weight and a between-class scatter for multiple classes of data samples in a sample set using the class weight, performing a mode-k matrix unfolding on scatters and generating at least one orthogonal projection matrix.

Abstract: 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.

Abstract: The present invention is an incremental umbrella sampling method to improve the performance of established sampling methods. It is sampling the state space by iteratively generating states xi,t and their weighting factors represented by Formula (a) by fitting the sampling distribution function ?j(x) of the next iteration to at least one weighted property of the already sampled states. This means that ?j(x) is fitted to the product represented by Formula (b), in which Formula (a) is the weighting factor and O(x,i) is a function respectively a property of the states xi,t. The number of states xi,t and the number of weighting factors (see Formula (a)) is incremented with each iteration. In order to have a consistent set of weighting factors (see Formula (a)), the weighting factors are recalculated in each iteration for all, respectively for a set of selected, states. By fitting ?j(x) in the state space it is possible to use all the information of Formula (a) and O(xi,t) for the states xi,t generated so far.

Abstract: 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.

Abstract: Interpolators for quadratic approximation for sinusoids are described. A sample source providing first order derivatives of sub-sampled sets of phase factor samples is used. A differentiator is coupled to receive the first order derivatives and configured to provide second order derivatives of the first order derivatives. A first scaling device is coupled to receive each of the first order derivatives. A second differentiator is coupled to receive each of the first order derivatives and configured to respectively provide second order derivatives of the first order derivatives. A second scaling device is coupled to receive the second order derivatives. A first integrator is coupled to receive output from the first scaling device for preloading, and to receive output from the second scaling device for integration. A third scaling device is coupled to receive output from the first integrator. A second integrator is coupled to receive output from the third scaling device.

Abstract: 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.

Abstract: One embodiment of the present invention is a microcontroller (24) including an embedded memory (42), waveform control circuitry (44) operatively coupled to the memory (42), several terminals (52), and a programmable processor (30). Processor (30) is responsive to execution of the first sequence of instructions to store a waveform bit pattern in memory (42) with a desired transmission timing. Waveform circuitry (44) is responsive to processor (30) to control transmission of the waveform bit pattern stored in memory (42) through one or more of the terminals (52) in accordance with the timing while processor (30) executes the second sequence of instructions to perform a different process.

Abstract: Systems, devices and methods of automatic diverse software generation are disclosed. In an embodiment, a method includes providing a base algorithm implementation related to a first hardware profile of a hardware resource, automatically generating a diverse algorithm implementation related to a second hardware profile different from the first hardware profile using the base algorithm implementation and information about the hardware resource, and executing the base algorithm implementation and the diverse algorithm implementation. Embodiments of systems and devices, including microprocessors and compilers, are also disclosed.

Abstract: The present invention relates to a direct digital frequency synthesizer using a variable sine wave-weighted digital to analog converter with improved size and efficiency and a synthesizing method thereof. The direct digital frequency synthesizer and the synthesizing method thereof are capable of simplifying a configuration for matching output data of a phase accumulator to sine wave amplitude without increase in complexity of a DAC by applying a nonlinear DAC for directly generating a current corresponding to base points with sine weights and a variable sine wave-weighted DAC for generating fine currents to be combined with variable weights based on the base points. Accordingly, it is possible to provide a high quality output, reduce a size and power consumption, and increase a speed.

Abstract: A method and a processing device may be provided for performing efficient weighted consistent sampling. A group of sets having multiple elements with associated weights may be provided. A single hash function may be applied to each of the elements of the group of sets to produce consistent uniformly distributed non-negative random numbers. Transformed values corresponding to each of the elements may be produced by determining a wth root of a value based on applying the hash function to a respective element, where w may be based on a weight associated with the respective element. A minimum transformed value or a maximum transformed value may be determined for each of the sets. Sets having matching ones of the minimum transformed value or the maximum transformed value may be determined. The determined sets may be considered to be similar.

Abstract: 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.

Abstract: System, methods, and apparatuses produce simulated human physiological waveforms such as electrocardiograph (ECG) and blood pressure signals where the microcontroller and/or digital-to-analog converters may be switched to a lower power-consuming state by programmable instructions and switched on in response to a programmable sleep timer.

Abstract: A phase calculation apparatus using a binary search is provided. The phase calculation apparatus includes a quarter surface preprocessor determining the bigger one between an absolute value of I component data and an absolute value of Q component data as horizontal component data and the smaller one as perpendicular component data, and detecting information on a phase region indicating an mth (m=1 to 8) phase region (the mth phase region is between (m?1) ?/4 and m ?/4 in which the I/Q component data are located; a phase representative value detector detecting phase representative values x corresponding to the horizontal component data and the perpendicular component data; and a quarter surface postprocessor calculating phase values of the I/Q component data based on the detected information about the phase region and the detected phase representative values x. The phase can be calculated using a limited memory, low complexity of calculation and regardless of the number of bits of I/Q component data.

Abstract: 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 600, for example.) The iterative method works on the functions directly. At each iteration, the approximating function is computed directly. (See diagram 200.) Since there is no need to compute the normal matrix or the coefficients of the basis functions, this approach avoids the overhead associated with them, and therefore, increases the speed of computation and reduces resource requirements. For example, various embodiments are suitable for implementation on hardware devices such as on an FPGA or an ASIC.

Abstract: Techniques are generally described for generating an identification number for an integrated circuit (IC). In some examples, methods for generating an identification of an IC may comprise selecting circuit elements of the IC, evaluating measurements of an attribute of the IC for the selected circuit elements, wherein individual measurements are associated with corresponding input vectors previously applied to the IC, solving a plurality of equations formulated based at least in part on the measurements taken of the attribute of the IC for the selected circuit elements to determine scaling factors for the selected circuit elements, and transforming the determined scaling factors for the selected circuit elements to generate an identification number of the IC. Additional variants and embodiments may also be disclosed.

Abstract: A novel and useful apparatus for and method of local oscillator (LO) generation with non-integer multiplication ratio between the local oscillator and RF frequencies. The LO generation schemes presented are operative to generate I and Q square waves at a designated frequency while avoiding the well known issue of harmonic pulling. An input baseband signal is interpolated and upconverted in the digital domain to an IF. The LO operates at a frequency which is a n/m division of the target RF frequency fRF. The IF frequency is configured to ½ of the LO frequency. The upconverted IF signal is then converted to the analog domain via digital power amplifiers followed by voltage combiners. The output of the combiners is band pass filtered to extract the desired replica.

Abstract: A novel and useful apparatus for and method of local oscillator (LO) generation with non-integer multiplication ratio between the local oscillator and RF frequencies. The LO generation schemes presented are operative to generate I and Q square waves at a designated frequency while avoiding the well known issue of harmonic pulling. The signal is input to a synthesizer timed to a rational multiplier of the RF frequency fRF. The signal is then divided to generate a plurality of phases of the divided signal. A plurality of combination signals are generated which are then multiplied by a set of weights and summed to cancel out some undersired products. The result is filtered to generate the LO output signal.

Abstract: 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.

Abstract: A digital pre-distortion system which can provide the flexibility to model the highly non-linear distortion associated with High Efficiency RF Power Amplifiers while through a novel implementation of a least squares estimation process allows an implementation well suited for an FPGA application where limited resources and in particular memory resources are available.

Abstract: A novel and useful apparatus for and method of local oscillator (LO) generation with non-integer multiplication ratio between the local oscillator and RF frequencies. The LO generation schemes presented are operative to generate I and Q square waves at a designated frequency while avoiding the well known issue of harmonic pulling. The use of analog mixers of the prior art is avoided and replaced with an XOR gate configured to generate the correct average frequency. The edges are dynamically adjusted by ±T/12 or zero based on the state of the controlled oscillator down-divided clock.

Abstract: 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.

Abstract: A look-up table which is required during looking up table for data transferring and a method for looking up table are provided. The method reduces the size of the look-up table used in the method for looking up table by simplifying the calculations. A reasonable error range is obtained for the required look-up table by adjusting appropriate modifiers. The method can be applied in the method for looking up table similar to the Q ? ( x ) = x B A calculation in the digital signal coder/decoder (CODEC), where both A and B are integers, and the calculation is more efficient if B/A is close to 1 or smaller than 1.

Abstract: 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.

Abstract: 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 ? 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 ?oII.

Abstract: 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.

Abstract: A method and apparatus for providing a processor based nested form polynomial engine are disclosed. A concise instruction format is provided to significantly decrease memory required and allow for instruction pipelining without branch penalty using a nested form polynomial engine. The instruction causing a processor to set coefficient and data address pointers for evaluating a polynomial, to load loading a coefficient and data operand into a coefficient register and a data register, respectively, to multiply the contents of the coefficient register and data register to produce a product, to add a next coefficient operand to the product to produce a sum, to provide the sum to an accumulator and to repeat the loading, multiplying, adding and providing until evaluation of the polynomial is complete.

Abstract: A method and apparatus for efficiently generating complex sinusoids of a desired frequency by multiplying a phasor by a predetermined value once every sampling interval, and using the highest order bits within the phasor to identify if the phasor is at an integer multiple 45 degrees and substituting components in the phasor if it is determined that the phasor is an integer multiple of 45 degrees. If the phasor is not identified as being an integer multiple of 45 degrees then an error factor for both the real and imaginary components is determined and the real and imaginary components are corrected by removing the error factor.

Abstract: An arithmetic process of a quadratic formula that is contained in an exponent of a CAZAC sequence-defining expression is converted to an arithmetic process of a recursion formula to find the above-described exponent, the above-described exponent that was found is used to generate a CAZAC sequence, and the above-described CAZAC sequence that was generated is taken as the reference signal for transmitting and receiving or as a random access preamble signal.

Abstract: A waveform generator for generating a smooth version of an original waveform which contains abrupt transitions, includes a phase accumulator incremented at successive sampling times to produce an output representative of the phase of the original waveform, a phase scaler arranged to convert the residual contents of the accumulator following a transition from phase to time, computing means responsive to the time to calculate a number of samples along a smooth transition, each offset by that time from the sampling times, and a sequencer to replace the otherwise abrupt transition with the sequence of samples from the computed smooth transition.

Abstract: An apparatus employing control words to present a synthesized output signal having an output frequency and a delay with respect to an input signal includes: (a) A multiplexer receiving the input signal and having an output and an address input. (b) An output unit generates the output signal in response to a drive signal from the multiplexer. (c) A first register coupled with the multiplexer output. (d) A second register coupled with the multiplexer and the first register. The first register responds to a multiplexer output signal to provide a first control signal to the second register based upon the control words. The second register responds to the multiplexer output signal to provide a second control signal to the address input based upon the first control signal and the control words. The multiplexer presents the drive signal in response to the second control signal.

Abstract: A parameter controlling apparatus calculates similarity variation distribution of different data and that of identical data. The parameter controlling apparatus creates a collation break-off rate function and an error probability function based on the similarity variation distribution of the different data and that of the identical data, respectively, and creates a total collation time function and a total error probability function based on the collation break-off rate function and the error probability function. The parameter controlling apparatus creates a constraint equation based on the total collation time function, the total error probability function, total collation time constraint parameters, and total error probability constraint parameters.

Abstract: Systems and methods for determining characteristic transition values such as elbow values in sigmoid or growth-type curves, such as the cycle threshold (Ct) value in PCR amplification curves. A double sigmoid function with parameters determined by a Levenberg-Marquardt (LM) regression process is used to find an approximation to a curve that fits a PCR dataset. Once the parameters have been determined, the curve can be normalized using one or more of the determined parameters. Normalization is advantageous for determining the Ct value if one chooses the arbitrary fluorescence level (AFL) approach to calculating Ct values for amplification curves. After normalization, the normalized curve is processed by applying a root-finding algorithm to determine the root of the function representing the normalized curve, which root corresponds to the Ct value. The Ct value is then returned and may be displayed or otherwise used for further processing.

Abstract: A power function is approximated over an applicable data interval with polynomials determined by means of a Chebyshev minimax approximation technique. In some cases, multiple polynomials may be used to approximate the function over respective ranges of the desirable interval, in a piecewise manner. The appropriate polynomial that approximates the power function over the range of interest is derived and stored. When the power function is to be applied to a particular data value, the data value is first evaluated to determine where it lies within the applicable interval. The constants for the polynomial associated with that range of the interval are then retrieved and used to calculate the power of that data value.

Abstract: Discovering mixtures of models includes: initiating learning algorithms, determining, data sets including a cluster of points in a first region of a domain and a set of points distributed near a first line extending across the domain; inferencing parameters from the cluster and the set of points; creating a description of the cluster of points in the first region of the domain and computing approximations of a first learned mixture model and a second learned mixture model; determining a first and second probability, generating a confidence rating that each point of the cluster of points in the first region of the domain corresponds to the first learned mixture model and generating a confidence rating that each point of the set of points distributed near the first line correspond to the second learned mixture model, thus causing determinations of behavior of a system described by the learned mixture models.

Abstract: A system and method of generating a one-way function and thereby producing a random-value stream. Steps include: providing a plurality of memory cells addressed according to a domain value wherein any given domain value maps to all possible range values; generating a random domain value associated with one of the memory cells; reading a data value associated with the generated random domain value; generating dynamically enhanced data by providing an additional quantity of data; removing suspected non-random portions thereby creating source data; validating the source data according to a minimum randomness requirement, thereby creating a validated source data; and integrating the validated source data with the memory cell locations using a random edit process that is a masking, a displacement-in-time, a chaos engine, an XOR, an overwrite, an expand, a remove, a control plane, or an address plane module. The expand module inserts a noise chunk.

Abstract: An apparatus and method for generation of an M-length permutation sequence in a broadband wireless communication system are provided. Operations of a generator include splitting an L2-length seed value into a first part and a second part, determining coefficients of a generator polynomial using values of the first part and the second part, and calculating the permutation sequence using the generator polynomial.

Abstract: A method of learning discriminant function for predicting label information by using computer includes: receiving training data including attribute data and label information, to create an initial prediction model based on the attribute data and the label information; calculating, based on the initial prediction model used as a discriminant function, a gradient of a loss function, which is differentiable with respect to the discriminant function and satisfies a monotonous convex function, from the discriminant function and the label information; creating a prediction model from the attribute data and the gradient while assuming that the gradient is label information of each sample of the training data; and updating the discriminant function based on the created prediction model.

Abstract: A cyclic equation setting unit transforms and sets a Taylor series equation for calculating a sine function into a single cyclic equation common to terms of the Taylor series equation, the single cyclic equation having a new known number Q that is defined by multiplying a known number Q and the square of a variable X, shifting the result by a shift number S and then adding a constant K thereto. An adjustment unit adjusts and prepares the shift number S such that within a variation range of the variable X the variable X has a maximum value 1 with the constant K being not greater than 1. A cyclic equation executing unit inputs and converts angle information i to the variable X, and executing the cyclic equation in sequence from higher order term to lower order term for the number of terms of the Taylor series equation to derive a sine function of the angle information i.

Abstract: A signal processing method includes a first step of calculating a value indicating a value obtained by multiplying a ratio of the number of times of inputting the input signal having any one of values from p to m, where m is a maximum value of values of input signal which are subject to said signal processing and p is a value smaller than m and not a minimum value of the input signal, within a predetermined period to the number of times of inputting the input signal within the predetermined period, by the variable range of the converted value; and a second step of subtracting the calculated value from a maximum value within the variable range of the converted value or a value near the maximum value, wherein the input signal is converted according to the conversion characteristic specified based on a value obtained by subtraction.

Abstract: 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.

Abstract: One embodiment of the present invention provides a system that uses a computer to evaluate a function within a domain using an interval computing technique. During operation, the system receives the function and the domain over which the function is to be evaluated. Next, the system creates a set of sampling subdomains within the domain by generating a set of boxes of different sizes which are located at different positions across the domain. The system then performs evaluations on the set of sampling subdomains to generate evaluation results. Next, the system sorts the evaluation results based on box size. The system then selects a box size from the different box sizes by identifying a largest box size which achieves tight bounds on the evaluation results. The system next discretizes the domain into subdomains of the selected box size.

Abstract: Methods, apparatus, and articles of manufacture for performing calculations using reduced-width data are disclosed. In particular, an example method determines reduced-width data values associated with generating and evaluating functions. Some of the reduced-width data values are stored within instructions in an instruction memory during a compile phase and retrieved from instruction memory during a runtime phase.

Abstract: A breathing assistance system configured to determine pressure drop may include a gas delivery system configured to deliver gas toward a patient, one or more sensors configured to measure one or more parameters of gas delivered by the gas delivery system, a calibration module, and a pressure drop calculation module. The calibration module may be configured to perform one or more pressure drop calibration tests, each pressure drop calibration test measuring a pressure drop in gas flowing through a breathing assistance system apparatus at a particular flow rate; and based at least on the results of the one or more pressure drop calibration tests, generating a non-linear equation relating (a) pressure drop in gas flowing through the breathing assistance system apparatus with (b) flow rate of gas flowing through the breathing assistance system apparatus.

Abstract: A co-processor system is provided that includes an array of configurable logic blocks (CLBs). Each CLB including a plurality of look-up tables and a plurality of adders. Each CLB may be dynamically reconfigurable to perform a plurality of logical functions.

Abstract: 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.

Abstract: 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.

Abstract: Methods, apparatus, and articles of manufacture for generating a delay time using a counter are disclosed. In particular, the methods, apparatus, and articles of manufacture determine a number of loops value associated with the delay time and at least one characteristic value associated with a counter. A remaining count value is then determined based on the number of loops value. The delay time is generated with the counter based on the number of loops value and the remaining count value.

Abstract: Embodiments relate to genomic technologies using adaptive spline analysis that predict responses of cancer cells. For example, responses of cancer cells to specific medications and/or treatments may be predicted based on adaptive linear spline analyses.

Abstract: Methods, apparatus, and articles of manufacture for performing calculations using reduced-width data are disclosed. In particular, an example method determines reduced-width data values associated with generating and evaluating functions. Some of the reduced-width data values are stored within instructions in an instruction memory during a compile phase and retrieved from instruction memory during a runtime phase.