3093 results about "Fourier transform on finite groups" patented technology

An alignment system uses a self-referencing interferometer that produces two overlapping and relatively rotated images of an alignment markers. Detectors detect intensities in a pupil plane where Fourier transforms of the images are caused to interfere. The positional information is derived from the phase difference between diffraction orders of the two images which manifests as intensity variations in the interfered orders. Asymmetry can also be measured by measuring intensities at two positions either side of a diffraction order.

The present invention involves method and apparatus for analyzing two measured signals that are modeled as containing primary and secondary portions. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, the present invention involves utilizing a transformation which evaluates a plurality of possible signal coefficients find appropriate coefficients. Alternatively, the present invention involves using statistical functions or Fourier transform and windowing techniques to determine the coefficients relating to two measured signals. Use of this invention is described in particular detail with respect to blood oximetry measurements.

A mass spectrometer is configured with individual multipole ion guides, configured in an assembly in alignment along a common centerline wherein at least a portion of at least one multipole ion guide mounted in the assembly resides in a vacuum region with higher background pressure, and the other portion resides in a vacuum region with lower background pressure. Said multipole ion guides are operated in mass to charge selection and ion fragmentation modes, in either a high or low pressure region, said region being selected according to the optimum pressure or pressure gradient for the function performed. The diameter, lengths and applied frequencies and phases on these contiguous ion guides may be the same or may differ. A variety of MS and MS/MSⁿ analysis functions can be achieved using a series of contiguous multipole ion guides operating in either higher background vacuum pressures, or along pressure gradients in the region where the pressure drops from high to low pressure, or in low pressure regions. Individual sets of RF, +/−DC and resonant frequency waveform voltage supplies provide potentials to the rods of each multipole ion guide allowing the operation of ion transmission, ion trapping, mass to charge selection and ion fragmentation functions independently in each ion guide. The presence of background pressure maintained sufficiently high to cause ion to neutral gas collisions along a portion of each multiple ion guide linear assembly allows the conducting of Collisional Induced Dissociation (CID) fragmentation of ions by axially accelerating ions from one multipole ion guide into an adjacent ion guide. Alternatively ions can be fragmented in one or more multipole ion guides using resonant frequency excitation CID. A multiple multipole ion guide assembly can be configured as the primary mass analyzer in single or triple quadrupole mass analyzers with or without mass selective axial ejection. Alternatively, the multiple multipole ion guide linear assembly can be configured as part of a hybrid Time-Of-Flight, Magnetic Sector, Ion Trap or Fourier Transform mass analyzer.

The present invention involves method and apparatus for analyzing two measured signals that are modeled as containing primary and secondary portions. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, the present invention involves utilizing a transformation which evaluates a plurality of possible signal coefficients in order to find appropriate coefficients. Alternatively, the present invention involves using statistical functions or Fourier transform and windowing techniques to determine the coefficients relating to two measured signals. Use of this invention is described in particular detail with respect to blood oximetry measurements.

Disclosed is a MIMO-OFDM system, wherein the transmitter comprises a serial/parallel converter for converting continuously inputted symbols of the number of subcarriers to K parallel signals; a signal reproducer for reproducing K parallel signals by the number of transmit antennas L an eigenmode generator for generating eigenbeam of the reproduced signals outputted from the signal reproducer at each subcarrier, on the basis of Nf eigenbeam forming vectors which are fed back long-term and information of a best eigenbeam forming vector at each subcarrier which is fed back short-term, through the feedback device; and a plurality of inverse Fourier converters for receiving the signals outputted from the eigenmode generator and generating an OFDM symbol.

Signal construction, detection and estimation techniques for use in uplink timing synchronization and access control in an orthogonal frequency division multiplexed (OFDM) wireless system or other type of wireless communication system. In accordance with an illustrative embodiment of the invention, timing and access signals to be transmitted in designated timing and access intervals are constructed from orthogonal multitone signals. The multitone signals may be similar to multitone signals used in OFDM data transmission, except that a cyclic prefix associated with reception of the signals in a base station is extended to cover the timing errors of mobile stations not yet synchronized. The invention also provides design techniques which optimize the time resolvability and peak-to-average ratio of the multitone signals, an efficient fast Fourier transform (FFT) based technique for maximum likelihood timing estimation, and a robust linear filtering technique for averaging timing estimates from different synchronizations.

A method and apparatus for processing an audio sound source to create four-dimensional spatialized sound. A virtual sound source may be moved along a path in three-dimensional space over a specified time period to achieve four-dimensional sound localization. A binaural filter for a desired spatial point is applied to the audio waveform to yield a spatialized waveform that, when the spatialized waveform is played from a pair of speakers, the sound appears to emanate from the chosen spatial point instead of the speakers. A binaural filter for a spatial point is simulated by interpolating nearest neighbor binaural filters chosen from a plurality of pre-defined binaural filters. The audio waveform may be processed digitally in overlapping blocks of data using a Short-Time Fourier transform. The localized sound may be further processed for Doppler shift and room simulation.

Techniques for calculating the system characteristic of the adaptive filtering used for equalization and echo-suppression in a digital communications receiver, such as one used for receiving over-the-air broadcast digital television signal, are described. In these techniques, the system characteristic of the adaptive filtering is calculated from the discrete Fourier transform of successive portions of the input signal supplied to the adaptive filtering and from the discrete Fourier transform of corresponding portions of the transmitted signal, as estimated in the receiver. Receivers for implementing these techniques in various ways are also disclosed.

A signal processing system for processing satellite positioning signals is described. The system comprises at least one processor and a signal processor operating under a number of operational modes. The signal processor includes at last one of a signal processing subsystem, a fast Fourier transform (FFT) subsystem, and a memory subsystem that are each dynamically and independently configurable in response to the operational modes. Further, the system includes a controller that couples to control transfer of data among the signal processing subsystem and the FFT subsystem via the memory subsystem. Configurability of the memory subsystem includes configuring the memory subsystem into regions according to the operational modes where each region is accessible in one of a number of manners according to the operational modes.

A transmitter for minimizing a PAPR in OFDM communication system. The transmitter includes: a precoder for coding input symbols so that a signal rotation is generated, and generating a complex vector including the coded symbols; an encoder for performing a frequency-space mapping for the symbols generated as the complex vector according to a predetermined scheme; a random mapper for randomly mapping the symbols for which the frequency-space mapping has been performed on a frequency plane through at least one transmit antenna; an Inverse Fast Fourier Transform (IFFT) unit for performing an IFFT for the symbols for which the frequency-space mapping has been performed; and a gradient algorithm unit for receiving IFFTed signals from the IFFT unit and reducing the PAPR.

A method and apparatus for pilot-symbol aided channel estimation in a wireless digital communication system which transmits packets of N OFDM data blocks, each data block comprising a set of K orthogonal carrier frequencies. At the transmitter, pilot symbols are inserted into each data packet at known positions so as to occupy predetermined positions in the time-frequency space. At the receiver, the received signal is subject to a two-dimensional inverse Fourier transform, two-dimensional filtering and a two-dimensional Fourier transform to recover the pilot symbols so as to estimate the channel response.

A dental optical coherence tomography apparatus for measuring tissue in a stomatognathic region of a living body or an artificial composition in the stomatognathic region as a measured object includes: a variable wavelength light source (15); a light splitting portion (19) that splits light-source light emitted from the variable wavelength light source (15) into reference light (29) and measuring light (28); an interference portion (19) that causes the measuring light (28) and the reference light (29) to interfere with each other, thereby generating interference light; a photodetection portion (41) that measures the interference light; and an arithmetic portion (27b) that generates an image of a measured object (22) by Fourier transforming or inverse Fourier transforming the intensity of the interference light, whose wavelength changes with time, that has been detected by the photodetection portion for each of the wavelengths. Accordingly, an optical coherence tomography apparatus applicable to dental measurement can be provided.

A disk drive is disclosed comprising a disk having a plurality of servo bursts written using perpendicular magnetic recording, wherein each servo burst is written at a servo burst frequency. A fill pattern is written between the servo bursts using perpendicular magnetic recording at a frequency substantially equal to an even harmonic of the servo burst frequency, and a phase shift occurs at the transition between the servo burst and the fill pattern. A head is actuated over the disk, and a sampling device samples a read signal emanating from the head to generate a sequence of read signal sample values. Control circuitry demodulates the servo bursts from the sequence of read signal sample values by computing a single-point Discrete Fourier Transform (DFT) at the servo burst frequency.

Method and apparatus for radiance processing by demultiplexing in the frequency domain. A frequency domain demultiplexing module obtains a radiance image captured with a lens-based radiance camera. The image includes optically mixed spatial and angular frequency components of light from a scene. The module performs frequency domain demultiplexing on the radiance image to generate multiple parallax views of the scene. The method may extract multiple slices at different angular frequencies from a Fourier transform of the radiance image, apply a Fourier transform to each of the multiple slices to generate intermediate images, stack the intermediate images to form a 3- or 4-dimensional image, apply an inverse Fourier transform along angular dimension(s) of the 3- or 4-dimensional image, and unstack the transformed 3- or 4-dimensional image to obtain the multiple parallax views. During the method, phase correction may be performed to determine the centers of the intermediate images.

A method of calculating a Head Media Separation (HMS) from a preamble of embedded servo sectors in a disk drive may include steps of reading the preamble, the read preamble being amplified by a variable gain amplifier (VGA) set at a predetermined gain; transforming samples of the read preamble into a first and a second frequency using a discrete time-to-frequency domain transform such as a Discrete Fourier Transform (DFT); calculating the ratio of the magnitude of the discrete time-to-frequency domain transform of the first frequency to the magnitude of the discrete time-to-frequency domain transform of the second frequency; determining the HMS from the calculated ratio, and enabling the predetermined gain to be updated in synchronism with the transforming step.

A radio communication system is provided. An uplink transmission method of a user equipment in a radio communication system includes performing Fourier transform on one or more data sequences to generate one or more first frequency-domain sequences, applying precoding for multi-antenna transmission to the one or more first frequency-domain sequences to generate one or more second frequency-domain sequences; performing inverse Fourier transform on the one or more second frequency-domain sequences to generate one or more transmission symbols, and transmitting the one or more transmission symbols via multiple antennas.

In projection exposure of isolated pattern such as a contact hole, in order to increase the depth of focus a coherence reducing member is disposed on a Fourier transform plane in an image-forming optical path between a mask and a sensitized base, so that coherence is reduced between image-forming beams respectively passing through a plurality of different, concentric regions around the optical axis of the projection optical system on the Fourier transform plane. The coherence reducing member may be a polarization state control member for making a difference in polarization state, a member for making a difference in optical path length, or space filters with different shapes.

The present invention relates to a method of measuring motion of an object such as a heart by magnetic resonance imaging. A pulse sequence is applied to spatially modulate a region of interest of the object and at least one first spectral peak is acquired from the Fourier domain of the spatially modulated object. The inverse Fourier transform information of the acquired first spectral-peaks is computed and a computed first harmonic phase image is determined from each spectral peak. The process is repeated to create a second harmonic phase image from each second spectral peak and the strain is determined from the first and second harmonic phase images. In a preferred embodiment, the method is employed to determine strain within the myocardium and to determine change in position of a point at two different times which may result in an increased distance or reduced distance. The method may be employed to determine the path of motion of a point through a sequence of tag images depicting movement of the heart. The method may be employed to determine circumferential strain and radial strain.

A system for efficiently filtering interfering signals in a front end of a GPS receiver is disclosed. Such interfering signals can emanate from friendly, as well as unfriendly, sources. One embodiment includes a GPS receiver with a space-time adaptive processing (STAP) filter. At least a portion of the interfering signals are removed by applying weights to the inputs. One embodiment adaptively calculates and applies the weights by Fourier Transform convolution and Fourier Transform correlation. The Fourier Transform can be computed via a Fast Fourier Transform (FFT). This approach advantageously reduces computational complexity to practical levels. Another embodiment utilizes redundancy in the covariance matrix to further reduce computational complexity. In another embodiment, an improved FFT and an improved Inverse FFT further reduce computational complexity and improve speed. Advantageously, embodiments can efficiently null a relatively large number of jammers at a relatively low cost and with relatively low operating power.

A method and system for processing radar data obtained from a platform which is subjected to non-uniform movement, the distance the platform travels during the formation of an image comprising an aperture; the system comprising software programming for performing a subroutine for building up an average pulse representing a single point on the aperture; the subroutine comprising the steps of inputting radar data from a radar antenna; passing the radar signal through low noise amplifier to reduce impact of electronic noise from the radar system; down converting the signal with a mixer to obtain a lower frequency; filtering out harmonics from the higher frequency range; sampling the radar data using an analog to digital converter at least at Nyquist down range frequency; based upon the IF of the radar; determining a scene center (center of SAR imagery) for the purpose of motion compensation; performing a two stage averaging scheme of the received signals with a variable window function; determining a window function based upon the velocity and acceleration of the platform and scene center; the window function comprising a first stage window; coherently averaging N pulses together to create an average pulse; performing an inverse Fourier transform; compensating to the scene center by multiplying by a complex exponential based upon both the GPS and inertial navigational system; summing the average pulses using low pass filter; the software programming operating to repeat the step of building up an average pulse a first predetermined number of times for a time period that is less than the Nyquist sample time interval; the software programming operating to repeat the step of building an average pulse for a predetermined number of times to generate a second predetermined number of average pulses; the software programming operating to perform a two dimensional inverse Fourier transform to obtain SAR image; outputting the SAR image on a display screen; and a display for displaying the outputted SAR image.

A transmitting apparatus, receiving apparatus, communication system, and a signal processing method for each apply a suitable modulation method and transmission path estimation method in accordance with the characteristics of the transmission information and capable of improving the transmission efficiency. At the transmission side, the method of estimation of the transmission path and the modulation method are selected in accordance with an attribute of the data to be transmitted, for example, the size of a packet to be transmitted, the transmission data is mapped by the selected modulation method, the signal is processed in accordance with the transmission path estimation method, and a transmission signal is created by increase fast Fourier transform processing and transmitted. At the reception side, the received signal is fast Fourier transformed, the transmission path is estimated by the transmission path estimation method selected at the transmission side, the received signal is corrected in accordance with the result, and the received data is reproduced in accordance with the modulation method. Therefore, it is possible to always adopt the optimum transmission method in accordance with the attribute of the transmission data etc. and possible to realize an improvement of a transmission efficiency and an enhancement of the quality of communication.