Abstract: An apparatus for simulating a signal composed of a plurality of individual signals from respective signal locations at a simulation location, having a provider for providing the plurality of individual signals in the time domain, a transformer for transforming the individual signals to the frequency domain, a processor for processing the individual signals transformed to the frequency domain each depending on a signal channel existing between the simulation location and the respective signal location, a combiner for combining the processed individual signals transformed to the frequency domain to a combined signal, and a transformer for transforming the combined signal to the time domain for generating the simulated combined signal at the simulation location.

Abstract: A finite impulse response (FIR) filter having a differential output and capable of having negative coefficients, and a method of designing the filter, is disclosed. In contrast to the prior art, in which two output signals requires the use of two identical sets of impedance devices corresponding to the Fourier coefficients that create the desired response of the filter, the described method and system uses only a single set of impedance devices, and thus approximately one-half of the number of impedance devices used in the prior art. This is accomplished by appropriately selecting which resistors contribute to which output, so that a differential output may be obtained that is substantially the same as if impedance devices corresponding to all of the coefficients were used for each signal.

Abstract: Passive signal combiners are employed to transform at least one signal from one domain to another. In some aspects the transformation comprises an FFT, an IFFT, a DFT, or an IDFT. In some implementations the passive signal combiners comprise a set of planar waveguides (e.g., which may be referred to as beamformers or Rotman lenses) that have multiple inputs and outputs and are configured to provide orthogonal output signals. In some implementations an electrical signal (e.g., received via an antenna element) is coupled to passive beamformers that transform the electrical signal from one domain to another domain. Here, a transformation of the electrical signal by a given passive beamformer may have a first resolution, and outputs from the passive beamformers may correspond to orthogonal groups. A combiner circuit may be used to combine the outputs from the passive beamformers and produce a combined output having a second resolution and an associated error.

Abstract: There is provided a method for generating a table for reordering the output of a Fourier transform, the Fourier transform being performed on a predefined number of input samples, the method comprising performing one or more decomposition stages on a sequence corresponding in number to the predefined number of input samples to form a representation of the output of the Fourier transform; wherein at least one of the decomposition stages comprises a composite operation that is equivalent to two or more operations; and rearranging the representation of the output of the Fourier transform to generate a reordering table.

Abstract: Techniques are disclosed for converting data into a format tailored for efficient multidimensional fast Fourier transforms (FFTS) on single instruction, multiple data (SIMD) multi-core processor architectures. The technique includes converting data from a multidimensional array stored in a conventional row-major order into SIMD format. Converted data in SIMD format consists of a sequence of blocks, where each block interleaves s rows such that SIMD vector processors may operate on s rows simultaneously. As a result, the converted data in SIMD format enables smaller-sized 1D FFTs to be optimized in SIMD multi-core processor architectures.

Abstract: A method for providing an adiabatic RF pulse that is an inversion or refocusing pulse for a RF pulse sequence is provided. A linear phase frequency profile (Flp(?)) is determined for the adiabatic RF pulse. A quadratic phase is applied to the linear phase frequency profile for the adiabatic RF pulse to obtain F(?), wherein the applying the quadratic phase comprises setting F(?)=Flp(?)eik?2. A polynomial ? is set to equal a Fourier Transform (F(?)). A corresponding minimum phase ? polynomial is determined for the ? polynomial. (?,?) are set as inputs to an inverse Shinnar Le-Roux transform to generate an adiabatic RF waveform. The adiabatic RF waveform is truncated to produce the adiabatic RF pulse, wherein k>0.03?/(?5??p)/(N+1) and k<kmax, where kmax is a value at which the adiabatic RF pulse is truncated at 25% of a maximum RF amplitude.

Abstract: Described embodiments provide an apparatus for calculating an N-point discrete Fourier transform of an input signal having multiple sample values. The apparatus includes at least one input configured to receive the sample values and a counter to count sample periods. Also included are at least two parallel multipliers to multiply each sample value, with each of the multipliers having a corresponding multiplication factor. There is at least one multiplexer to select one of the at least two parallel multipliers. An adder sums the scaled sample values and an accumulator accumulates the summed sample values. N is an integer and the at least two parallel multipliers are selectable based upon the value of N and the value of the sample period count.

Abstract: In a data processing system, having a twiddle factor unit, a method for performing a mixed-radix discrete Fourier transform (DFT) having a block size, N, and a maximum block size, Nmax, wherein the maximum block size includes a radix that is not a power of 2 is provided. The method includes receiving a delta value at an input of the twiddle factor unit, the delta value representing a ratio of a modified maximum bock size to the block size, wherein the modified maximum block size is a power of 2. The method further includes using the delta value to obtain a step size for generating indices of a look-up table stored within the twiddle factor unit, wherein the look-up table stores real and imaginary components of twiddle factors corresponding to a set of block sizes of the DFT.

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: Provided are a high-speed Discrete Fourier Transform (DFT) apparatus and a method thereof. The high-speed DFT apparatus includes a zero padding unit, a Fast Fourier Transform (FFT) unit, and a preamble index decision unit. The zero padding unit receives a first input signal having a length of a prime number and changes the first input signal into a second input signal having a length of an exponentiation of 2. The FFT unit performs a FFT on the second input signal outputted from the zero padding unit. The preamble index decision unit detects a preamble index from an output signal from the FFT unit.

Abstract: A two-dimensional transmission cross coefficient is obtained based on a function representing a light intensity distribution formed by an illumination apparatus on a pupil plane of the projection optical system and a pupil function of the projection optical system. Based on the two-dimensional transmission cross coefficient and data of a pattern on an object plane of the projection optical system, an approximate aerial image is calculated by using at least one of plural components of an aerial image on an image plane of the projection optical system. Data of a pattern of an original is produced based on the approximate aerial image.

Abstract: A method for generating a transmit sequence in a single carrier frequency division multiple access (SC-FDMA) transmitter is disclosed. In one embodiment, the method includes generating a first time domain sequence, transforming the first time domain sequence to a first frequency domain sequence according to a first transform, distributing the first frequency domain sequence among a subset of subcarriers among a plurality of subcarriers in a second frequency domain sequence, transforming the second frequency domain sequence to a second time domain sequence, and adding a cyclic prefix to the second time domain sequence to form a transmit sequence. In one exemplary embodiment, the first time domain sequence is a plurality of pilot symbols that have known properties e.g., a constant amplitude, and zero autocorrelation (CAZAC).

Abstract: An orthogonal frequency division multiplexing (OFDM) receiving apparatus, including a receiving unit, a subcarrier demodulation unit and a signal output processing unit, is provided. The receiving unit is for receiving an RF signal to generate a set of discrete signals. The subcarrier demodulation unit is coupled to the receiving unit, and used for demodulating a set of discrete signals to obtain a complex signal. The signal output processing unit is coupled to the subcarrier demodulation unit, and used for capturing and outputting real parts of the complex signal.

Abstract: An apparatus and method for area and speed efficient fast Fourier transform (FFT) processing comprising mapping a one-dimensional DFT to a multi-dimensional representation; re-indexing the multi-dimensional representation as a radix 23 decimation architecture; simplifying the radix 23 decimation architecture to obtain a nested butterfly architecture; acquiring N samples of a finite duration time-sampled signal; and inputting the acquired N samples into the nested butterfly architecture to obtain a N-point fast Fourier transform (FFT) output.

Abstract: A method for calculating coefficients of a filter and a method for filtering are provided. The invention directly factorizes a specific function in a cepstrum domain by spectral factorization and cepstrum technique to obtain coefficients of denominator function from the filter. In other words, the invention adopts a non-iterative algorithm to reduce computational complexity and avoid convergence due to calculating coefficients. Besides, the specific function of the invention includes a compensation function, so that a Fourier transform with greatly reduced size can be utilized in the spectral factorization to greatly save the computations and keep good system performance at a receiver.

Abstract: Language-integrated query (LINQ) operators can be extended to a set of vectors associated with a digital signal processing (DSP) environment. A language-integrated query (LINQ) operator can be created to execute a change of basis for a set of vectors. LINQ operators can be further be utilized with specifically generated parameters to perform a change of basis for the set of vectors. Additionally, the standard LINQ operators can be extended to enable querying with LINQ against the set of vectors.

Abstract: An analyzing method for deriving phase information by analyzing a periodic pattern of moiré comprises steps of: subjecting at least a part of the periodic pattern of moiré to a windowed Fourier transform by a window function; calculating analytically, based on the moiré subjected to the windowed Fourier transform, information of a first spectrum carrying the phase information, and information of a second spectrum superimposed on the information of the first spectrum; and separating the information of the first spectrum from the information of the second spectrum, to derive the phase information.

Abstract: A method for receiving a pilot symbol in a receiver is disclosed. In one embodiment, the method includes removing a cyclic prefix from a received sequence to produce a modified sequence, transforming the modified sequence to a first frequency domain sequence according to a first transform, demapping a plurality of distributed subcarriers in the transformed modified sequence to extract a plurality of received symbols, deriving an intermediate channel estimate for each of the plurality of received symbols, and interpolating a final channel estimate based on the plurality of derived intermediate channel estimates. In one exemplary embodiment, the received symbols have one or more predefined characteristics such as a constant amplitude, and zero autocorrelation (CAZAC sequence).

Abstract: Disclosed herein are systems, methods, and non-transitory computer-readable storage media for simulating propagation of an electromagnetic field, performing phase retrieval, or sampling a band-limited function. A system practicing the method generates transformed data using a discrete Fourier transform which samples a band-limited function f(x) without interpolating or modifying received data associated with the function f(x), wherein an interval between repeated copies in a periodic extension of the function f(x) obtained from the discrete Fourier transform is associated with a sampling ratio Q, defined as a ratio of a sampling frequency to a band-limited frequency, and wherein Q is assigned a value between 1 and 2 such that substantially no aliasing occurs in the transformed data, and retrieves a phase in the received data based on the transformed data, wherein the phase is used as feedback to an optical system.

Abstract: Methods and apparatuses for 3D tomographic imaging of objects such as soft-tissues in humans are disclosed. They are similar to the Magnetic Resonance Imaging (MRI) methods and apparatuses but they are based on the new Field Paradigm founded on the principle that the field intensity distribution in a 3D volume space uniquely determines the 3D density distribution of the field emission source and vice versa. The object to be imaged is first magnetized by a polarizing magnetic field pulse. The magnetization of the object is specified by a 3D spatial Magnetic Density Image (MDI) that needs to be determined. The magnetic field due to the magnetized object is measured in a 3D volume space that extends in all directions and in particular substantially along the radial direction from the center of the object being imaged. Further, magnetic field intensity may be measured along multiple directions at each point.

Abstract: The present invention relates to a complex multiplier and a twiddle factor generator.

Abstract: The present invention discloses a signal processing method and a data processing method and apparatus. A time-domain to frequency-domain signal processing method includes: pre-processing time-domain data; pre-rotating the pre-processed data by using a rotation factor a·WNn+0.5; performing a discrete Fourier transform (DFT) of N/4 points on the pre-rotated data; and post-rotating the data transformed by the DFT by using a rotation factor b·WNk+0.5 to obtain frequency-domain data. A frequency-domain to time-domain signal processing method includes: twiddling frequency-domain data; pre-rotating the twiddled data by using a rotation factor c·WNk+0.5; performing a DFT of N/4 points on the pre-rotated data; and post-rotating the data transformed by the DFT by using a rotation factor d·WNn+0.5; and post-processing the post-rotated data to obtain time-domain data. The present invention increases the efficiency of signal processing.

Abstract: A system, method, and computer program for determining a descriptor, comprising calculating a maximum distance for a plurality of points in a sector between each of said plurality of points and an origin; calculating a minimal distance from one of said plurality of points and a target line, wherein said maximum distance is an initial value; computing a plurality of Fourier coefficients from said minimal distances; and defining an invariant descriptor from said Fourier coefficients, and appropriate means and computer-readable instructions.

Abstract: A processor (110) is disclosed for processing a plurality of Fourier-transformed instances of a symbol, each instance being comprised in one of a plurality of frequency-divided multiplexed subcarriers, said processor being arranged to estimate, for each instance, the channel gain and the inter-carrier interference contribution to said symbol from neighboring subcarriers due to a time-varying channel response of the received signal, and combine the instances into a single representation of said symbol based on the estimated channel gain and the inter-carrier interference contributions. A receiver comprising such a processor and a method for processing such signals are also disclosed.

Abstract: The present invention relates to a method for converting a signal, including the steps of: providing a first representation of the signal in a first domain; converting the first representation of the signal into a second representation of the signal in a second domain, by applying a transform involving a Haar transform and a Hadamard transform, such that a basis of the second domain is maximally incoherent to a Haar basis. The signal is converted to a domain whose basis is maximally incoherent to a Haar basis. Yet, it is not required to convert the input vector representing the signal to a Haar basis first. This allows reducing the number of steps which increases conversion efficiency. Accordingly, obtaining the structure of the signal requires fewer samples.

Abstract: The present invention provides apparatus, methods, and computer program products that can decrease the latency with which the coefficients of a function representative of signal are determined Specifically, the apparatus, methods, and computer program products of the present invention, taking advantage of the independence of samples, updates each of the coefficients of the function as each sample is received. As such, when the final sample is received, the apparatus, methods, and computer program products of the present invention need only update each coefficient with the contribution of the last sample prior to outputting the coefficients. As such, the latency from the time the last sample is received and the availability of the coefficients is decreased. To further decrease the latency, in one embodiment, the apparatus, methods, and computer program products of the present invention prestore either all or a portion of the possible values of the contribution of a sample to each coefficient.

Abstract: A spread spectrum signal demodulating method whereby spread-code synchronous acquisition and carrier synchronous acquisition are performed using FFT at high speed, wherein a received signal, of which the carrier wave is modulated with a signal obtained by spectrum-spreading data with a spread code, is subjected to the FFT and the result of the FFT is stored in a first memory. The FFT result of the received signal stored in the first memory and the result of FFT of the spread code stored in a second memory are read out and multiplied to detect the correlation between the received signal and the spread code. A readout address of either the FFT result of the received signal or the FFT result of the spread code is shifted by an amount corresponding to a carrier frequency of the received signal.

Abstract: Methods (500, 800) and corresponding systems (100, 200, 300, 400, 900) for generating a pilot symbol (330) include providing an M-point parallel transform sequence that is a discrete Fourier transform of a CAZAC sequence (312, 504-508). The M-point parallel transform sequence (312) is distributed (316, 510) to a set of M subcarriers among N subcarriers to form an N-point frequency-domain sequence (318) wherein the M subcarriers are evenly spaced apart. An N-point inverse fast Fourier transform (320, 512) is performed to convert the N-point frequency-domain sequence to an N-point time-domain sequence (322). The N-point time-domain sequence is converted (324, 514) to a serial sequence (326), and a cyclic prefix is added (328, 516) to the serial sequence to form a pilot symbol (330).

Abstract: A spread spectrum signal demodulating method whereby spread-code synchronous acquisition and carrier synchronous acquisition are performed using FFT at high speed, wherein a received signal, of which the carrier wave is modulated with a signal obtained by spectrum- spreading data with a spread code, is subjected to the FFT and the result of the FFT is stored in a first memory. The FFT result of the received signal stored in the first memory and the result of FFT of the spread code stored in a second memory are read out and multiplied to detect the correlation between the received signal and the spread code. A readout address of either the FFT result of the received signal or the FFT result of the spread code is shifted by an amount corresponding to a carrier frequency of the received signal.

Abstract: A system for via structure measurement is disclosed. The system comprises a reflectometer, a simulation unit and a comparing unit. The reflectometer is configured to collect a measured diffraction spectrum of at least a via. The simulation unit is configured to provide simulated diffraction spectrums of the at least a via. The comparing unit is configured to determine at least a depth and at least a bottom profile of the at least a via by comparing the collected diffraction spectrum and the simulated diffraction spectrums.

Abstract: A method for determining the position of impacts on an object comprising two acoustic sensors, and N active areas of said object, comprises the steps of: (a) receiving two acoustic signals S1(t) and S2(t); (b) calculating a sample signature function SIGS(?)=S1(?)?S2(?)*, where S1(?) and S2(?) are the respective Fourier transforms of S1(t) and S2(t), (c) comparing SIGS(?) with N predetermined reference signature functions SIGR,(?) corresponding to the predetermined area j for j from 1 to N; (d) determining the active area in which the impact occurred, on the basis of the comparison of step (c).

Abstract: A parallel computing system that performs simulation of a sphere by using a spherical harmonic function, and comprises a plurality of computing nodes interconnected with each other via a communication path, wherein each of the computing nodes includes: a storage unit that stores spectral data obtained by dividing spectral space data into a plurality of data elements on the basis of longitudinal wavenumber; a computation unit that performs inverse Legendre transformation for a computation region divided in a latitudinal direction on the sphere and thereby transforms each of the spectral data elements to Fourier coefficient data; and a communication unit that transmits the Fourier coefficient data, obtained through the transformation performed by the computation unit, to another computing node via the communication path after the inverse Legendre transformation for the next computation region divided in the latitudinal direction on the sphere has been started by the computation unit.

Abstract: Passive signal combiners are employed to transform at least one signal from one domain to another. In some aspects the transformation comprises an NFL an IFFT, a DFT, or an IDFT. In some implementations the passive signal combiners comprise a set of planar waveguides (e.g., which may be referred to as beamformers or Rotman lenses) that have multiple inputs and outputs and are configured to provide orthogonal output signals. In some implementations an electrical signal (e.g., received via an antenna element) is coupled to passive beamformers that transform the electrical signal from one domain to another domain. Here, a transformation of the electrical signal by a given passive beamformer may have a first resolution, and outputs from the passive beamformers may correspond to orthogonal groups. A combiner circuit may be used to combine the outputs from the passive beamformers and produce a combined output having a second resolution and an associated error.

Abstract: A digital signal processing apparatus includes a frame generator configured to generate a plurality of frames from a row of sample data of a time-domain, a part of each frame overlapping with adjoining frames, a Fourier transform unit configured to transform at least one of the generated frames into a frequency domain by Fourier transformation, an addition unit configured to add predetermined frequency characteristic to the transformed frame, and an inverse Fourier transform unit configured to transform the added frame into the time-domain by inverse Fourier transformation and to delete the overlap of the frame of the time-domain transformed.

Abstract: A method for providing an adiabatic RF pulse that is an inversion or refocusing pulse for a RF pulse sequence is provided. A linear phase frequency profile (Flp(?)) is determined for the adiabatic RF pulse. A quadratic phase is applied to the linear phase frequency profile for the adiabatic RF pulse to obtain F(?), wherein the applying the quadratic phase comprises setting F(?)=Flp(?)eik?2. A polynomial ? us set ti equal a Fourier Transform (F(?)). A corresponding minimum phase ? polynomial is determined for the ? polynomial. (?,?) are set as inputs to an inverse Shinnar Le-Roux transform to generate an adiabatic RF waveform. The adiabatic RF waveform is truncated to produce the adiabatic RF pulse, wherein k>0.03?/(?5??p)/(N+1) and k<kmax, where kmax is a value at which the adiabatic RF pulse is truncated at 25% of a maximum RF amplitude.

Abstract: An orthogonal frequency division multiplexing (OFDM) transmitting apparatus including a signal processing unit, a subcarrier orthogonalization processing unit, and a transmitting unit is provided. The signal processing unit divides a received signal into several real parts and several corresponding imaginary parts. The subcarrier orthogonalization processing unit is coupled to the signal processing unit for receiving the real and the imaginary parts of the signal, and for making the real and the imaginary parts respectively carried by a plurality of different and orthogonal subcarriers. The transmitting unit is coupled to the subcarrier orthogonalization processing unit to transmit the subcarriers.

Abstract: A system (100) and method (400) for peak limiting suitable for use in a communication system is provided. The method can include modulating (402) a symbol vector to produce a modulated waveform (500), wherein the symbol vector contains at least one symbol in at least one subcarrier (130), computing (404) at least one symbol adjustment that is based on at least one peak overshoot (512) of the modulated waveform, and applying (406) the at least one symbol adjustment to the symbol vector in accordance with an assigned weighting for reducing a peak power of the modulated waveform. The method limits an energy in the at least one subcarrier to a prespecified level of distortion.

Abstract: Methods (500, 800) and corresponding systems (100, 200, 300, 400, 900) for generating a pilot symbol (330) include providing an M-point parallel transform sequence that is a discrete Fourier transform of a CAZAC sequence (312, 504-508). The M-point parallel transform sequence (312) is distributed (316, 510) to a set of M subcarriers among N subcarriers to form an N-point frequency-domain sequence (318) wherein the M subcarriers are evenly spaced apart. An N-point inverse fast Fourier transform (320, 512) is performed to convert the N-point frequency-domain sequence to an N-point time-domain sequence (322). The N-point time-domain sequence is converted (324, 514) to a serial sequence (326), and a cyclic prefix is added (328, 516) to the serial sequence to form a pilot symbol (330).

Abstract: Detection of one or more abnormal situations is performed using various statistical measures, such as a mean, a median, a standard deviation, etc. of one or more process parameters or variable measurements made by statistical process monitoring blocks within a plant. This detection is enhanced in various cases by using specialized data filters and data processing techniques, which are designed to be computationally simple and therefore are able to be applied to data collected at a high sampling rate in a field device having limited processing power. The enhanced data or measurements may be used to provided better or more accurate statistical measures of the data, may be used to trim the data to remove outliers from this data, may be used to fit this data to non-linear functions, or may be use to quickly detect the occurrence of various abnormal situations within specific plant equipment, such as distillation columns and fluid catalytic crackers.

Abstract: Methods, circuits, and an apparatus for filtering high-speed serial data is disclosed. In one embodiment, a Programmable Logic Device (PLD) is configured with a filter circuit for filtering serial data at a first clock rate. The filter circuit converts an N number of serial data streams into an N number of M-bit words based on a deserialization factor. The M-bit words are converted to an M number of N-bit data words. The N-Bit data words are filtered at a second clock rate, reformatted, serialized, and outputted as individual serial data streams at the first clock rate. In one embodiment, the N-bit data words are digitally filtered by a Finite Impulse Response (FIR) filter operating at the second clock rate. The data output of the FIR filter is then serialized into an N number of serial data output streams operating at the first clock rate.

Abstract: A subscriber station for use in a wireless network capable of communicating according to a multi-carrier protocol, such as OFDM or OFDMA. The subscriber station comprises a size M Fourier Transform (FFT or DFT) block for receiving input symbols and generating M FT pre-coded outputs and a size N inverse Fourier Transform (IFFT or IDFT) block capable of receiving N inputs, where the N inputs include the M FT pre-coded outputs from the size M FT block. The size N IFT block generates N outputs to be transmitted to a base station of the wireless network. The input symbols comprise user data traffic to be transmitted to the base station. The size N IFT block also receives signaling and control information on at least some of N-M inputs. The FT pre-coding generates a time-domain signal that has a relatively lower peak-to-average power ratio (PAPR).

Abstract: The object is to aim at the reduction in the influence of noises in an output of an AE sensor in a working machine. In a working system comprising a working device for working a work W by causing a tool 14 to come into contact work W, an AE sensor 21, and an AE signal processing section 22 for processing an AE signal output from the AE sensor, AE signal processing section 22 comprises an A/D converter 33 for converting an AE signal into a digital signal, a frequency analysis section 34 for calculating the frequency characteristics of a digital AE signal, storage sections 35, 37 for storing the frequency characteristics when the tool is not in contact with the work or tool dresser as non-contact frequency characteristics, and a difference calculation section 35 for calculating a difference between the frequency characteristics of the detected digital AE signal and the non-contact frequency characteristics.

Abstract: A method and apparatus for detecting a signal using a cyclo-stationary characteristic value is provided. A method of detecting a signal using a cyclo-stationary characteristic value includes: calculating cyclo-stationary characteristic values with respect to a cyclic frequency domain of an input signal; multiplying the calculated cyclo-stationary characteristic values with each other; and detecting the signal from the input signal based on the result of the multiplication.

Abstract: Among other things, a combination comprises interaction with a system that has a perturbation. In such perturbed system, a non-directional input is applied to a first variable of the system. Based on an asymmetry of the perturbed system, a directional effect is achieved in a second variable of the system, the first and second variables comprising a conjugate pair of variables. At least one of the following pertains: the interaction occurs other than by an apparatus and other than in a way that actually achieves the directional effect, or the conjugate pair is other than position and momentum, or the input or the asymmetry are in a dimension other than spatial coordinates, or the directional effect is other than translational motion and other than rotary motion.

Abstract: The present invention is two-iteration Fourier transform processor for performing Fourier transform of N data inputs into N data outputs. The processor comprises a plurality of two-iteration radix-r modules and a combination phase element. Each radix-r module comprises r radix-r butterflies, a feedback network and a plurality of switches. Each radix-r butterfly comprises r inputs and outputs and a butterfly processing element. The butterfly processing element includes a plurality of multipliers for multiplying the input data and corresponding coefficients and an adder for summing the multiplication outputs from the multipliers. The feedback network feeds outputs of the radix-r butterflies to the corresponding inputs of the radix-r butterfly and the switches selectively pass the input data or the feedback, alternately, to the corresponding radix-r butterfly. The combination phase element includes at least one stage of butterfly computing elements for combining the outputs from the r radix-r butterfly.

Abstract: A memory-based Fast Fourier Transform device is provided, which adopts single-port random access memory (RAM), rather than dual-port RAM, as a storage, and the circuit area of the FFT device is therefore reduced. In order to enhance the access efficiency of the memory and the use efficiency of a processor, the transformer adopts a modified in-place conflict-free addressing to achieve similar performance of a traditional Fast Fourier Transform device.

Abstract: The present invention provides for a method of receiving a signal spread over a frequency range, and in particular a direct sequence spread spectrum signals including the step of employing a Fast Fourier Transform (FFT) in the Doppler search. In particular, the invention relates to the receipt of spread spectrum signals such as those transmitted as part of a GPS system.

Abstract: Disclosed is an apparatus that generates automatically a characteristic pattern in time series data by clustering a plurality of time series subsequences generated from the time series data. The apparatus includes a time series subsequence generation unit that generates a plurality of time series subsequences from the time series data, a phase alignment unit that aligns a phase of the generated time series subsequence, a clustering unit that performs clustering of a plurality of the time series subsequences, each having a phase aligned, a storage apparatus that stores the pattern obtained by the clustering, and an output apparatus that outputs the stored pattern.

Abstract: A segmented radial spatial light modulator has an active optic area comprising a plurality of radially extending active optic modulators disposed at various angular orientations with respect to a central axis. The segmented radial spatial light modulator is used in separating and isolating portions of Fourier transform optic patterns from images for characterization of images by shape for recording, storing, retrieving, searching, and comparison to other images for matches and near matches. The images can be ghosted to increase optical power in the Fourier transform optic pattern without adding new shape content and for grading comparisons to other image shape characteristics for identifying near matches in addition to matches.

Abstract: A subscriber station for use in a wireless network capable of communicating according to a multi-carrier protocol, such as OFDM or OFDMA. The subscriber station comprises a size M Fourier Transform (FFT or DFT) block for receiving input symbols and generating M FT pre-coded outputs and a size N inverse Fourier Transform (IFFT or IDFT) block capable of receiving N inputs, where the N inputs include the M FT pre-coded outputs from the size M FT block. The size N IFT block generates N outputs to be transmitted to a base station of the wireless network. The input symbols comprise user data traffic to be transmitted to the base station. The size N IFT block also receives signaling and control information on at least some of N-M inputs. The FT pre-coding generates a time-domain signal that has a relatively lower peak-to-average power ratio (PAPR).