Abstract: Padding or adding data to a data signal can increase the speed with which a signal processor can process the data. Methods are provided herein that can accurately predict the optimal pad size of a two dimensional array of data, which can be used to increase the processing speed of a signal processor by optimizing run-time for a two-dimensional (2-D) fast Fourier transform (FFT) operation.

Abstract: The ability to examine the frequency content of a signal is critical in a variety of fields, and many techniques have been proposed to fill this need, including the Fourier and wavelet family of transforms. One of these, the S-transform, is a Fourier based transform that provides simultaneous time and frequency information similar to the wavelet transform but uses sinusoidal basis functions to produce true frequency and globally referenced phase measurements. It has been shown to be useful in several medical imaging applications but its use is limited due to high computational requirements of the original, continuous form. The described embodiments include a general framework for describing linear time-frequency transforms, using the Fourier, wavelet and S-transforms as examples. As an illustration of the utility of this formalism, a fast discrete S-transform algorithm is developed that has the same computational complexity as the fast Fourier transform.

Abstract: To generate at least one hash value for a feature vector that represents a data object, a discrete orthogonal transform is applied on a second vector produced from the feature vector. Applying the discrete orthogonal transform on the second vector produces a third vector. At least one value is selected from the third vector to produce the hash value. The at least one hash value is used to perform an action.

Abstract: A method separates multivariate data points in lower dimensional space, where each data point has been classified into one of a plurality of data clusters including at least a first data cluster and a second data cluster. The method includes the step of acquiring an ND-to-3D transformation matrix for transforming the plurality of multivariate data points to a plurality of three-dimensional data points. The method preferably includes the sub-step of performing a center of mass (COM) separation of the clusters to acquire a COM transformation matrix, where the COM transformation matrix is the ND-to-3D transformation matrix. The method also includes the step of performing a receiver-operator characteristic curve (ROC) separation to acquire an ROC transformation matrix for transforming the plurality of three-dimensional data points to a plurality of data points in a dimension lower than 3D and preferably a re-optimized COM transformation matrix.

Abstract: This disclosure provides implementations of dither-aware image coding processes, devices, apparatus, and systems. In one aspect, a portion of received image data is selected. First spatial domain values in the selected portion of the image data are transformed to first transform domain coefficients. Second spatial domain values in a designated dither matrix are transformed to second transform domain coefficients. A ratio of each of the first transform domain coefficients to a respective second transform domain coefficient is determined. The first transform domain coefficients are selectively coded in accordance with the determined ratios to define coded first transform domain coefficients. A reverse transformation is performed to transform the coded first transform domain coefficients to third spatial domain values defining a coded portion of the image data. By way of example, transformations such as discreet cosine transforms or discreet wavelet transforms can be used.

Abstract: Methods and apparatus for relative pitch tracking of multiple arbitrary sounds. A probabilistic method for pitch tracking may be implemented as or in a pitch tracking module. A constant-Q transform of an input signal may be decomposed to estimate one or more kernel distributions and one or more impulse distributions. Each kernel distribution represents a spectrum of a particular source, and each impulse distribution represents a relative pitch track for a particular source. The decomposition of the constant-Q transform may be performed according to shift-invariant probabilistic latent component analysis, and may include applying an expectation maximization algorithm to estimate the kernel distributions and the impulse distributions. When decomposing, a prior, e.g. a sliding-Gaussian Dirichlet prior or an entropic prior, and/or a temporal continuity constraint may be imposed on each impulse distribution.

Abstract: The present disclosure is directed to techniques for efficient streaming SVD computation. In an embodiment, streaming SVD can be applied for streamed data and/or for streamed processing of data. In another embodiment, the streamed data can include time series data, data in motion, and data at rest, wherein the data at rest can include data from a database or a file and read in an ordered manner. More particularly, the disclosure is directed to an efficient and faster method of computation of streaming SVD for data sets such that errors including reconstruction error and loss of orthogonality are error bounded. The method avoids SVD re-computation of already computed data sets and ensures updates to the SVD model by incorporating only the changes introduced by the new entrant data sets.

Abstract: The present invention relates to a efficient implementation of integer and fractional 8-length or 4-length, or 8×8 or 4×4 DCT in a SIMD processor as part of MPEG and other video compression standards.

Abstract: In a data processing system, a method and system employing high fidelity inverse discrete cosine transform (IDCT) and discrete cosine transform (DCT) algorithms are provided. The values of the coefficients in a two-dimensional (2D) transform utilized in the IDCT and DCT algorithms may approximate the ideal integer output with sufficient visual quality. The transform coefficients may match a portion of the most significant bits (MSBs) or properly rounded bits of the coefficients of a reference transform matrix within an upper bound. The IDCT and DCT algorithms may specify constraints based on separating the 2D transform operation into two 1D transform operations in order to determine a minimum-bit width for each of the transform coefficients. The minimum-bit width may also be based on integer-bit precision of the data to be processed by the IDCT and DCT algorithms.

Abstract: A CORDIC processor has a plurality of stages, each of the stages having a X input, Y input, a sign input, a sign output, an X output, a Y output, a mode control input having a ROTATE or VECTOR value, and a stage number k input, each CORDIC stage having a first shift generating an output by shifting the Y input k times, a second shift generating an output by shifting X input k times, a multiplexer having an output coupled to the sign input when the mode control input is ROTATE and to the sign of the Y input when the mode input is VECTOR, a first multiplier forming the product of the first shift output and the multiplexer output, a second multiplier forming the product of the second shift output and an inverted the multiplexer output, a first adder forming the X output from the sum of the first multiplier output and the X input, and a second adder forming the Y output from the sum of the second multiplier output and the Y input.

Abstract: A discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) circuit includes a microcode memory, a processor, and a butterfly operation circuit. The microcode memory stores multiple microcode groups corresponding to DCT/IDCT operations and each of the microcode groups includes a series of microcodes. The processor obtains one of the microcode groups corresponding to one of the DCT/IDCT operations to be performed and retrieves microcodes in the obtained microcode group in sequence. The butterfly operation circuit performs butterfly operations according to the retrieved microcodes to execute one of the DCT/IDCT operations.

Abstract: Some embodiments of the invention provide a method of performing a Discrete Cosine Transform (“DCT”) encoding or decoding coefficients of a data array by (1) multiplying the coefficients by a scalar value before the encoding or decoding, and then (2) dividing the encoded or decoded coefficients by the scalar value. When used in conjunction with fixed-point arithmetic, this method increases the precision of the encoded and decoded results. In addition, some embodiments provide a method of performing a two-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). This method splits a pre-multiplication operation of the iDCT into two or more separate stages. When used in conjunction with fixed-point arithmetic, this splitting increases the precision of the decoded results of the iDCT.

Abstract: Apparatus, systems and techniques based on an integer transform for encoding and decoding video or image signals, including apparatus, systems and techniques for deriving an order-16 integer transform from an order-8 integer transform in image and video coding. In some implementations, eight additions and eight subtractions are used to assign the data elements to be transformed to an intermediate matrix; and then two fast algorithms for the computation of the order-8 transform may be applied to the first 8 vectors of the intermediate matrix, and the last 8 vectors of the intermediate matrix, respectively. The derived order-16 integer transform tends to produce small magnitude and high frequency transformed coefficients, and thus achieve high compressibility.

Abstract: Methods of generating Hilbert space-filling indexes using simple bit-wise transformation are described herein. One method is based on a linear-based transformation uses bit-wise AND and XOR operations on a simple input index counter. In another method, the regular structure of the transform matrix was then used to obtain a Gray-based transform at a reduced complexity. Due to the simple and regular structure of the transformation, an efficient hardware implementation of generating indexes (addresses) along the Hilbert curve results.

Abstract: An integrated transformation apparatus is provided. The apparatus includes a first multiplexer, a second multiplexer, and a transformation unit. The first multiplexer retrieves point data from columns or rows of a multi-dimensional matrix and input data. The second multiplexer retrieves transformation coefficients corresponding to the point data. The transformation unit transforms data blocks of the multi-dimensional matrix to a plurality of sub data blocks according to the input data, the point data, and the transformation coefficients.

Abstract: Signal processing devices and methods estimate transforms between signals using a least squares technique. From a seed set of transform candidates, a direct least squares method applies a seed transform candidate to a reference signal and then measures correlation between the transformed reference signal and a suspect signal. For each candidate, update coordinates of reference signal features are identified in the suspect signal and provided as input to a least squares method to compute an update to the transform candidate. The method iterates so long as the update of the transform provides a better correlation. At the end of the process, the method identifies a transform or set of top transforms based on a further analysis of correlation, as well as other results.

Abstract: The present in invention is directed to a method, system and program storage device for efficiently implementing a multidimensional Fast Fourier Transform (FFT) of a multidimensional array comprising a plurality of elements initially distributed in a multi-node computer system comprising a plurality of nodes in communication over a network, comprising: distributing the plurality of elements of the array in a first dimension across the plurality of nodes of the computer system over the network to facilitate a first one-dimensional FFT; performing the first one-dimensional FFT on the elements of the array distributed at each node in the first dimension; re-distributing the one-dimensional FFT-transformed elements at each node in a second dimension via “all-to-all” distribution in random order across other nodes of the computer system over the network; and performing a second one-dimensional FFT on elements of the array re-distributed at each node in the second dimension, wherein the random order facilitates eff

Abstract: A block transform-based digital media codec achieves faster performance by re-mapping components of the digital media data into vectors or parallel units on which many operations of the transforms can be performed on a parallel or single-instruction, multiple data (SIMD) basis. In the case of a one-dimensional lapped biorthogonal transform, the digital media data components are re-mapped into vectors on which butterfly stages of both overlap pre-/post-filter and block transform portions of the lapped transform can be performed on a SIMD basis. In the case of a two-dimensional lapped biorthogonal transform, the digital media data components are re-mapped into vectors on which a Hadamard operator of both overlap pre-/post-filter and block transform can be performed on a SIMD basis.

Abstract: The present invention provides an apparatus and method for providing a programmable inverse discrete cosine transform, wherein the transform coefficients are loaded into a memory area of a core transform device and a variety of coding standards can thereby be handled by the same programmable core device. The core device is configured to process a certain sized data block, and the incoming source blocks are converted to conform to this size. After transformation, the proper sized result can be extracted from the transform device output. A switchable speed-up mode provides for 4-point transforms, rather than 8-point transforms. Alternatively, the invention also provides for dedicated transform hardware to be switchably used in conjunction with programmable transform hardware, depending upon the type of coding being used, and the speed of inverse transform desired.

Abstract: A method and system for transposing a multi-dimensional array for a multi-processor system having a main memory for storing the multi-dimensional array and a local memory is provided. One implementation involves partitioning the multi-dimensional array into a number of equally sized portions in the local memory, in each processor performing a transpose function including a logical transpose on one of said portions and then a physical transpose of said portion, and combining the transposed portions and storing back in their original place in the main memory.

Abstract: Embodiments of the invention disclose a system and a method for reducing a dimensionality of a spectrogram matrix. The method constructs an intermediate time basis matrix and an intermediate frequency basis matrix and applies iteratively a non-negative matrix factorization (NMF) to the intermediate time basis matrix and the intermediate frequency basis matrix until a termination condition is reached, wherein the NMF is subject to a constraint on a an independence regularization term, wherein the constraint is in a form of a gradient of the term.

Abstract: Padding or adding data to a data signal can increase the speed with which a signal processor can process the data. Methods are provided herein that can accurately predict the optimal pad size of a two dimensional array of data, which can be used to increase the processing speed of a signal processor by optimizing run-time for a two-dimensional (2-D) fast Fourier transform (FFT) operation.

Abstract: Classes of web graph algorithms are extended to run directly on virtual node-type compressed web graphs where a reduction in runtime of the extended algorithms is realized which is approximately proportional to the compression ratio applied to the original (i.e., uncompressed) graph. In the virtual node compression technique, a succinct representation of a web graph is constructed by replacing dense subgraphs by sparse ones so that the resulting compressed graph has significantly fewer edges and a relatively small number of additional nodes.

Abstract: Encoding data includes: computing a first set of coefficients based on a plurality of transforms each computed over a different portion of an array of data, and a second set of coefficients based on a transform computed over the array of data; choosing a set of coefficients to represent the array of data from a group of multiple sets of coefficients, the group including the first set of coefficients and the second set of coefficients; and encoding the chosen coefficients and one or more parameters related to the chosen coefficients.

Abstract: Systems and methods that facilitate dimensional transformations of data points are disclosed. In particular, the subject invention provides for a system and methodology that simplifies dimensional transformations while mitigating variations of a distance property between pairs of points. A set of n data points in d dimensional space is represented as an n×d input matrix, where d also corresponds to the number of attributes per data point. A transformed matrix represents the n data points in a lower dimensionality k after being mapped. The transformed matrix is an n×k matrix, where k is the number of attributes per data point and is less than d. The transformed matrix is obtained by multiplying the input matrix by a suitable projection matrix. The projection matrix is generated by randomly populating the entries of the matrix with binary or ternary values according to a probability distribution.

Abstract: In an approximation computation apparatus, a location monitor designates, each time the number of data of a received data sequence exceeds an integer l, a starting location of the received data for calculating reduced received-data; a dimensionality reducer dimensionally reduces each data sequence including the received data after the corresponding designated starting location by random projection to generate the reduced received-data; an object selecting controller controls an object in response to a result of monitoring from the location monitor of the number of the received data reaching another integer n, deletes currently-stored object data, selects the reduced received-data after the oldest reduced received-data in the reduced received-data, and substitutes and updates an object data sequence to the selected reduced received-data; and a coefficient approximator calculates an approximate value of a wavelet coefficient on the basis of the object data and a wavelet matrix.

Abstract: A method, information processing system and computer readable medium for performing a transform of a multidimensional matrix in a distributed memory network. The method includes storing a multidimensional matrix of side N in a distributed memory network comprising a plurality of nodes and distributing work associated with a calculation of a transform of the matrix among N.sup.2 of the plurality of nodes. The method further includes receiving results of the calculation of the transform of the matrix by the nodes.

Abstract: A method separates multivariate data points in lower dimensional space, where each data point has been classified into one of a plurality of data clusters including at least a first data cluster and a second data cluster. The method includes the step of acquiring an ND-to-3D transformation matrix for transforming the plurality of multivariate data points to a plurality of three-dimensional data points. The method preferably includes the sub-step of performing a center of mass (COM) separation of the clusters to acquire a COM transformation matrix, where the COM transformation matrix is the ND-to-3D transformation matrix. The method also includes the step of performing a receiver-operator characteristic curve (ROC) separation to acquire an ROC transformation matrix for transforming the plurality of three-dimensional data points to a plurality of data points in a dimension lower than 3D and preferably a re-optimized COM transformation matrix.

Abstract: A device and method for evaluating multidimensional discrete Fourier transforms (DFT) by eliminating transpose operations by transforming every dimension concurrently. At least one computing node is enabled to evaluate a DFT of one of a multidimensional input data set and a subgroup of the input data set, wherein the subgroup comprises groupings of elements taken from a plurality of selected dimensions of the input data set for subsequent multidimensional DFT operations.

Abstract: A symmetric encryption/decryption method includes the steps of selecting a diffused mechanism, and the diffused mechanism includes at least one selected from a shift point, a block and a frame; obtaining a plurality of bits required for a cipher by the diffused mechanism and the element number of each dimension of a plaintext; carrying out at least one diffused operation for the plaintext; repeating the foregoing steps to achieve the effect of encrypting the plaintext. Since the sum of the encryption diffused times and the decryption diffused times equals to the diffused cycle, the cipher can be read and at least one dimensional diffused operation of the ciphertext can be carried out, and thus achieving the effect of decrypting the ciphertext.

Abstract: A multiplier and a method multiply, using an array of adders, two binary numbers X and Y defining a matrix [Eni=xn?i·yi], wherein the initial matrix [Eni=xn?i·yi] is transformed into a matrix [Eni=(xn?i?yi)·(yi?1?yi)=(xn?i?y1)·Yi] with Yi=yi?1?yi or [Eni=eni·Yi] with eni=xn?i?yi. A first approximation Un0 and Rn?1i?1 is formed of the sum and carry of the first two rows y0 and y1 of this matrix, and this is used as an input for the following estimation step which is repeated for all the following rows, successively carrying out the addition of the following Yi+1 rows up to the last non-zero row, according to a first given series of propagation equations, and then the propagation of the carries Rni?1 is carried out over the zero Yi+1 rows according to a second given series of propagation equations, in order to obtain the final result of the product P.

Abstract: A system and method for vector memory array transposition. The system includes a vector memory, a block transposition accelerator, and an address controller. The vector memory stores a vector memory array. The block transposition accelerator reads a vector of a block of data within the vector memory array. The block transposition accelerator also writes a transposition of the vector of the block of data to the vector memory. The address controller determines a vector access order, and the block transposition accelerator accesses the vector of the block of data within the vector memory array according to the vector access order.

Abstract: An apparatus, system, and method to perform QR decomposition of an input complex matrix are described. The apparatus may include a triangular systolic array to load the input complex matrix and an identity matrix, to perform a unitary complex matrix transformation requiring three rotation angles, and to produce a complex unitary matrix and an upper triangular matrix. The upper triangular matrix may include real diagonal elements. Other embodiments are described and claimed.

Abstract: Apparatus, systems and techniques based on an integer transform for encoding and decoding video or image signals, including transform of encoding and decoding of image and video signals and generation of an order-2N transform W from an order-N transform T in the field of image and video coding. For example, a retrieving unit is configured to retrieve an order-N transform T, where N is an integer; a deriving unit is configured to derive an order-2N transform W from the retrieved order-N transform T, and a transforming unit configured to generate an order-2N data Z using the derived transform W.

Abstract: Methods of generating Hilbert space-filling indexes using simple bit-wise transformation are described herein. One method is based on a linear-based transformation uses bit-wise AND and XOR operations on a simple input index counter. In another method, the regular structure of the transform matrix was then used to obtain a Gray-based transform at a reduced complexity. Due to the simple and regular structure of the transformation, an efficient hardware implementation of generating indexes (addresses) along the Hilbert curve results.

Abstract: In a 3-dimensional fast Fourier transformation implemented by using a parallel-processing computer, an overhead caused by transfers of data between processors employed in the computer is reduced for the purpose of increasing the efficiency of processing parallelism. In order to reduce the overhead, data is divided into data elements each having an even X coordinate and data elements each having an odd X coordinate. In processing 34, the date elements each having an even coordinate are subjected to the transformation in the Y direction while the date elements each having an odd X coordinate are being subjected to a process of permutation among the processors at the same time. In processing 35, on the other hand, the data elements each having an odd X coordinate are subjected to the transformation in the X direction while the data elements each having even coordinate are being subjected to the process of permutation among the processors at the same time.

Abstract: The invention is used in video coding. Systems, apparatuses and methods for processing an order-16 integer transform from an order-8 transform are provided. The order-16 transform method involves expanding an order-8 transform by generating an order-16 integer matrix and a scaling matrix.

Abstract: Systems and techniques, including machine-readable instructions, for modeling of nonlinear systems. In one aspect, an apparatus includes a collection of two or more inputs configured and arranged to receive input signals, a collection of two or more outputs configured and arranged to output output signals, a processing unit configured to transform the input signals into the output signals, wherein the transformation is non-linear and treats the non-linear system as a collection of multiple input, single output non-linear systems, and a data storage that stores characteristics of the transformation.

Abstract: A method and a system for designing a learning system (30) based on a cascade of weak learners. Every implementation of a cascade of weak learners is composed of a base block (60) and a cascade of identity blocks (80). The output (70, 90) of each of the learning subsystems (60, 80) is fed into the following one. The external output (10) is fed to cach of the learning subsystems to avoid ambiguities. The identity blocks (80) are designed to include the identity function within the class of functions that they can implement. The weak learners are added incrementally and each of them trained separately while the parameters of the others are kept frozen.

Abstract: In an elliptic curve cryptographic system, point coordinates in a first coordinate system are transformed into a second coordinate system. The transformed coordinates are processed by field operations, which have been modified for operating on the transformed point coordinates. In some implementations, the point coordinates are transformed using a linear transformation matrix having coefficients. The coefficients can be fixed, variable or random. In some implementations, the transformation matrix is invertible.

Abstract: The invention relates to a method (100) of adapting a geometric model to an image data comprising determining a first partial transformation for mapping a first part of the geometric model into the image data and a second partial transformation for mapping a second part of the geometric model into the image data. By determining the first partial transformation of the first part of the geometric model and the second partial transformation of the second part of the geometric model, the geometric model can assume more shapes and therefore can be more accurately adapted to an object comprised in the image data.

Abstract: Methods, systems, and articles of manufacture consistent with the present invention compute a multidimensional fast Fourier transform of an original matrix having rows and columns of data. The original matrix is divided into a number of blocks of data, each block including at least one datum, the number of rows of data in each block being less than a total number of rows of data in the original matrix. A one-dimensional partial fast Fourier transform of each block in a row of blocks is computed. A result of the computations is stored in a resultant matrix having rows and columns. The resultant matrix is transposed to a transposed matrix having rows and columns. While transposing the resultant matrix, one-dimensional partial fast Fourier transforms of each block of subsequent rows of blocks are simultaneously computed, one row of blocks at a time, until one-dimensional partial fast Fourier transforms are computed for each block.

Abstract: A new machine learning technique is herein disclosed which generalizes the support vector machine framework. A separating hyperplane in a separating space is optimized in accordance with generalized constraints which dependent upon the clustering of the input vectors in the dataset.

Abstract: A method for establishing a relationship between a physical structure of reflectance spectra as defined in a Euclidean color space and a perceptual space of color appearance defined in terms of human perception of colors is performed by obtaining a cube root spectrum of the physical reflectance spectrum in a selected spectral range, reconstructing the cube root of the physical reflectance spectrum by a weighted linear combination of three basis functions, the weights of the linear combination of the basis functions constituting the coordinates in a three-dimensional Euclidean color space with respect to which similarities and differences among reflectance spectra in metric terms and a color characterized in a perceptual space of color appearance can be analyzed, and making an analytic comparison between a physical system in the three-dimensional Euclidean color space and the perceptual system by means of a linear transformation therebetween.

Abstract: Computer-implemented methods and media bearing instructions for matching movements of objects are described. In one example, the method can include determining a position of a first point in a first coordinate system, converting the position of the first point from the first coordinate system to a second coordinate system, performing a transformation on a second point in the second coordinate system, wherein the second point is initialized to a starting position in the second coordinate system, determining an ending position of the second point in the second coordinate system based on the transformation, converting the ending position of the second point in the second coordinate system to the first coordinate system, and associating the ending position of the second point in the first coordinate system to the first point in the first coordinate system, wherein the associating causes a transformation of the first point to match the transformation performed on the second point.

Abstract: Some embodiments of the invention provide a method of performing a Discrete Cosine Transform (“DCT”) encoding or decoding coefficients of a data array by (1) multiplying the coefficients by a scalar value before the encoding or decoding, and then (2) dividing the encoded or decoded coefficients by the scalar value. When used in conjunction with fixed-point arithmetic, this method increases the precision of the encoded and decoded results. In addition, some embodiments provide a method of performing a two-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). This method splits a pre-multiplication operation of the iDCT into two or more separate stages. When used in conjunction with fixed-point arithmetic, this splitting increases the precision of the decoded results of the iDCT.

Abstract: A motion estimator 50 for image processing finds a motion vector from a search area in a reference picture to a source macroblock in a source picture by finding a maximum of a 2-dimensional normalised cross-correlation surface between the source macroblock and a portion of the reference search area using a transform domain.

Abstract: Some embodiments of the invention provide a method of performing a Discrete Cosine Transform (“DCT”) encoding or decoding coefficients of a data array by (1) multiplying the coefficients by a scalar value before the encoding or decoding, and then (2) dividing the encoded or decoded coefficients by the scalar value. When used in conjunction with fixed-point arithmetic, this method increases the precision of the encoded and decoded results. In addition, some embodiments provide a method of performing a two-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). This method splits a pre-multiplication operation of the iDCT into two or more separate stages. When used in conjunction with fixed-point arithmetic, this splitting increases the precision of the decoded results of the iDCT.

Abstract: A two-dimensional data memory (1) comprising memory elements which are arranged in rows and columns, which are designed to store in each case one data word, which in the row direction and in the column direction are coupled locally to their respectively adjacent memory elements such that with each control pulse of a row control signal the data words of the memory elements of all rows are shifted in a shift direction into the memory elements of the respectively adjacent row, with the data words of the last row being shifted into the first row, and such that with each control pulse of a column control signal the data words of the memory elements of all columns are shifted in a shift direction into the memory elements of the respectively adjacent column, with the data words of the last column being shifted into the first column, and which are designed such that an external write access is possible only in respect of at least one predefined row and at least one predefined column and such that an external read acc

Abstract: A method and system of monitoring multivariate process data in a process plant, where the multivariate process data comprises a plurality of process variables each having a plurality of observations, includes defining each process variable as a process variable vector comprising a set of observation components, where the set of observation components comprises time dependent process data corresponding to the observations of the process variable, calculation, a multivariable transformation as a function of a plurality of process variable vector transformation each corresponding to one of the process variables, where each process variable vector transformation is a function of a univariate variable unifying the process variables, and representing the operation of the process based on the multivariable transformation, where the representation of the operation of the process designates a multivariate projection of the process data by the univariate variable for each of the process variables.