Showing papers on "Discrete Fourier transform published in 2002"

Locally adaptive dimensionality reduction for indexing large time series databases

Abstract: Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data. The most promising solutions involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and the Discrete Wavelet Transform (DWT). In this article, we introduce a new dimensionality reduction technique, which we call Adaptive Piecewise Constant Approximation (APCA). While previous techniques (e.g., SVD, DFT and DWT) choose a common representation for all the items in the database that minimizes the global reconstruction error, APCA approximates each time series by a set of constant value segments of varying lengths such that their individual reconstruction errors are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean distance approximation, and a non-lower-bounding, but very tight, Euclidean distance approximation, and show how they can support fast exact searching and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques and demonstrate its superiority.

StatStream: statistical monitoring of thousands of data streams in real time

Abstract: Consider the problem of monitoring tens of thousands of time series data streams in an online fashion and making decisions based on them. In addition to single stream statistics such as average and standard deviation, we also want to find high correlations among all pairs of streams. A stock market trader might use such a tool to spot arbitrage opportunities. This paper proposes efficient methods for solving this problem based on Discrete Fourier Transforms and a three level time interval hierarchy. Extensive experiments on synthetic data and real world financial trading data show that our algorithm beats the direct computation approach by several orders of magnitude. It also improves on previous Fourier Transform approaches by allowing the efficient computation of time-delayed correlation over any size sliding window and any time delay. Correlation also lends itself to an efficient grid-based data structure. The result is the first algorithm that we know of to compute correlations over thousands of data streams in real time. The algorithm is incremental, has fixed response time, and can monitor the pairwise correlations of 10,000 streams on a single PC. The algorithm is embarrassingly parallelizable.

Digital Signal Processing: A Practical Guide for Engineers and Scientists

Abstract: The Breadth and Depth of DSP Statistics, Probability and Noise ADC and DAC DSP Software Linear Systems Convolution Properties of Convolution The Discrete Fourier Transform Applications of the DFT Fourier Transform Properties Fourier Transform Pairs The Fast Fourier Transform Continuous Signal Processing Introduction to Digital Filters Moving Average Filters Windowed-Sinc Filters Custom Filters FFT Convolution Recursive Filters Chebyshev Filters Filter Comparison Audio Processing Image Formation and Display Linear Image Processing Special Imaging Techniques Neural Networks (and more!) Data Compression Digital Signal Processors Getting Started with DSPs Complex Numbers The Complex Fourier Transform The Laplace Transform The z-Transform Index

Exact Local Whittle Estimation of Fractional Integration

Abstract: An exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter (d) that applies throughout the stationary and nonstationary regions of d and which does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N(0,1/4) limit distribution for all values of d.

Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new at-top windows

Abstract: This report tries to give a practical overview about the estimation of power spectra/power spectral densities using the DFT/FFT. One point that is emphasized is the relationship between estimates of power spectra and power spectral densities which is given by the effective noise bandwidth (ENBW). Included is a detailed list of common and useful window functions, among them the often neglected flat-top windows. Special highlights are a procedure to test new programs, a table of comprehensive graphs for each window and the introduction of a whole family of new flat-top windows that feature sidelobe suppression levels of up to −248dB, as compared with −90dB of the best flat-top windows available until now.

Weighted multipoint interpolated DFT to improve amplitude estimation of multifrequency signal

Abstract: This paper describes the error reduction of frequency and amplitude estimates of the periodic signals with multipoint interpolated discrete Fourier transform (DFT). The bias removal and noise sensitivity properties of the interpolation algorithms are studied for rectangular and Hanning windows. The correction improves with increasing the number of the interpolation points of the DFT. The use of a suitable interpolation algorithm depends on the effective bits of the A/D conversion, on the position of the frequency component of the signal and on the mutual component interspacing along the frequency axis. Using different algorithms, we change adaptively the apparent window shape for the particular component.

Generalized Morse wavelets

Abstract: This paper examines the class of generalized Morse wavelets, which are eigenfunction wavelets suitable for use in time-varying spectrum estimation via averaging of time-scale eigenscalograms. Generalized Morse wavelets of order k (the corresponding eigenvalue order) depend on a doublet of parameters (/spl beta/, /spl gamma/); we extend results derived for the special case /spl beta/ = /spl gamma/ = 1 and include a proof of "the resolution of identity." The wavelets are easy to compute using the discrete Fourier transform (DFT) and, for (/spl beta/, /spl gamma/) = (2m, 2), can be computed exactly. A correction of a previously published eigenvalue formula is given. This shows that for /spl gamma/ > 1, generalized Morse wavelets can outperform the Hermites in energy concentration, contrary to a conclusion based on the /spl gamma/ = 1 case. For complex signals, scalogram analyses must be carried out using both the analytic and anti-analytic complex wavelets or odd and even real wavelets, whereas for real signals, the analytic complex wavelet is sufficient.

Block iterative DFE for single carrier modulation

Abstract: An iterative block decision feedback equaliser (IB-DFE) for single carrier modulation is proposed. Filtering operations are implemented by discrete Fourier transforms (DFTs) which yield a reduced computational complexity, for both filter design and signal processing, when compared to existing DFEs. Moreover, the new IB-DFE operates on blocks of the receive signal, thus allowing the use of error correction codes on the feedback data signal.

Digital Computation of Fractional Fourier Transform

Abstract: Based on the concept of the fractional fourier transform, its digital computation is given through computer simulation. In terms of linear frequency modulation (LFM) signal, the relation between fractional order and modulation slope is analyzed and the performance comparison with matched filter is given. Moreover, the separation of LFM signal and noise is realized in low signal-to-noise ratio through simulation. Simulation results indicate that the energy of LFM signal will be collected effectively when the fractional order is matching with its modulation slope. In weak signals detection of underwater acoustic domain, we can get high anti-Doppler performance using the Fractional fourier transform algorithm.

Compression of digital holograms for three-dimensional object reconstruction and recognition

Abstract: We present the results of applying lossless and lossy data compression to a three-dimensional object reconstruction and recognition technique based on phase-shift digital holography. We find that the best lossless (Lempel-Ziv, Lempel-Ziv-Welch, Huffman, Burrows-Wheeler) compression rates can be expected when the digital hologram is stored in an intermediate coding of separate data streams for real and imaginary components. The lossy techniques are based on subsampling, quantization, and discrete Fourier transformation. For various degrees of speckle reduction, we quantify the number of Fourier coefficients that can be removed from the hologram domain, and the lowest level of quantization achievable, without incurring significant loss in correlation performance or significant error in the reconstructed object domain.

Speech enhancement using MMSE short time spectral estimation with gamma distributed speech priors

Abstract: In this paper we consider optimal estimators for speech enhancement in the Discrete Fourier Transform (DFT) domain. We present an analytical solution for estimating complex DFT coefficients in the MMSE sense when the clean speech DFT coefficients are Gamma distributed and the DFT coefficients of the noise are Gaussian or Laplace distributed. Compared to the state-of-the-art Wiener or MMSE short time amplitude estimators the new estimators deliver improved signal-to-noise ratios. When the noise model is a Laplacian density the enhanced speech shows less annoying random fluctuations in the residual noise than for a Gaussian density.

Integer fast Fourier transform

Abstract: A concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures where the dynamic range of the lifting coefficients can be controlled by proper choices of lifting factorizations. Split-radix FFT is used to illustrate the approach for the case of 2/sup N/-point FFT, in which case, an upper bound of the minimal dynamic range of the internal nodes, which is required by the reversibility of the transform, is presented and confirmed by a simulation. The transform can be implemented by using only bit shifts and additions but no multiplication. A method for minimizing the number of additions required is presented. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts. Finally, they are applied to noise reduction applications, where the IntFFT provides significantly improvement over the FxpFFT at low power and maintains similar results at high power.

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform.

Abstract: Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack–Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector–matrix-multiply reconstructors. The boundary problem that prevented the accurate reconstruction of phase in circular apertures by means of square-grid Fourier transforms (FTs) is identified and solved. The methods are adapted for use on the Fried geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented with the use of both theory and simulation.

Fourier coefficients of modular forms on G2

Abstract: We develop a theory of Fourier coefficients for modular forms on the split exceptional group G2 over ℚ.

Apodization functions for 2-D hexagonally sampled synthetic aperture imaging radiometers

Abstract: It is now well established that synthetic aperture imaging radiometers promise to be powerful sensors for high-resolution observations of the Earth at low microwave frequencies. Within this context, the European Space Agency is currently developing the Soil Moisture and Ocean Salinity (SMOS) mission. The Y-shaped array selected for SMOS is fitted with equally spaced antennae and leads to a natural hexagonal sampling of the Fourier plane. This paper deals with the choice of the apodization function to be applied to the complex visibilities. The aim of this function is to reduce the Gibbs phenomenon produced by the finite extent of the star-shaped frequency coverage and the resulting sharp frequency cut-off. A large number of windows are introduced. A comparison of these in terms of their spatial domain properties is given, according to criteria relevant for remote sensing of the Earth's surface. This paper also describes how discrete Fourier transform calculations over hexagonal grids can be performed using a simple algorithm. Actually, standard fast Fourier transform algorithms designed for Cartesian grids and which have a long track record of optimization can be reused. Finally, an interpolation formula is given for resampling data from hexagonal grids without introducing any aliasing artifacts in the resampled data.

A simple adjustable window algorithm to improve FFT measurements

Abstract: The Fourier spectrum of a periodic signal may be obtained by fast Fourier transform algorithms, but, as is well known, special care must be taken to avoid severe distortions introduced by the sampling process. The main problem is the leakage generated by the truncation required to obtain a finite length sampled data. The usual procedure to reduce leakage is to multiply the sampled signal by a weighting window. Several kinds of windows have been proposed in the literature, and today they are also included in many commercial instruments. A simple alternative procedure is proposed in this paper. It is implemented with a PC compatible data acquisition board (DAQ) and consists of an algorithm that uses decimation and interpolation techniques. This algorithm is equivalent to the use of an adjustable sampling frequency and correspondingly an adjustable window size. Results obtained by this method on both harmonic and polyharmonic signals are empirically analyzed and compared with those given by an instrument with built-in FFT capabilities.

Improved Fourier transform methods for solving the parabolic wave equation

Abstract: [1] A standard method for modeling electromagnetic propagation in the troposphere is the Fourier split-step algorithm for solving the parabolic wave equation. An important advance in this technique was the introduction of the mixed Fourier transform, which permitted the extension of the method from propagation over only smooth perfectly conducting surfaces to quite general surfaces with impedance boundary conditions. This paper describes improvements in the implementation of the mixed Fourier transform, which make the method more robust and efficient and avoid potential numerical instabilities, which occasionally caused problems in the previous implementation. Some examples are also presented.

A comparative study of harmonic detection algorithms for active filters and hybrid active filters

Abstract: In this paper, the performance of three harmonic detection methods is evaluated in term of precision, speed of convergence and calculation complexity. The algorithms are respectively based on the recursive discrete Fourier transform (RDFT), Kalman filtering approach and the instantaneous reactive power theory. Results obtained by simulations with Matlab-Simulink and their real-time validation with dSPACE are presented to compare the detection methods. The effectiveness of the algorithms is demonstrated in their application to the control of a hybrid active filter dedicated to harmonic resonance damping in industrial power systems.

Linear Dynamic Systems and Signals

Abstract: Preface. 1. Introduction to Linear Systems. 1.1 Continuous and Discrete Linear Systems and Signals. 1.2 System Linearity and Time Invariance. 1.3 Mathematical Modeling of Systems. 1.4 System Classification. 1.5 MATLAB System Computer Analysis and Design. 1.6 Book Organization. 1.7 Chapter One Summary. 1.8 References. 1.9 Problems. 2. Introduction to Signals. 2.1 Common Signals in Linear Systems. 2.2 Signal Operations. 2.3 Signal Classification. 2.4 MATLAB Laboratory Experiment on Signals. 2.5 Chapter Two Summary. 2.6 References. 2.7 Problems. I. FREQUENCY DOMAIN TECHNIQUES. 3. Fourier Series and Fourier Transform. 3.1 Fourier Series. 3.2 Fourier Transform and Its Properties. 3.3 Fourier Transform in System Analysis. 3.4 Fourier Series in Systems Analysis. 3.5 From Fourier Transform to Laplace Transform. 3.6 Fourier Analysis MATLAB Laboratory Experiment. 3.7 Chapter Three Summary. 3.8 References. 3.9 Problems. 4. Laplace Transform. 4.1 Laplace Transform and Its Properties. 4.2 Inverse Laplace Transform. 4.3 Laplace Transform in Linear System Analysis. 4.4 Block Diagrams. 4.5 From Laplace to the z-Transform. 4.6 MATLAB Laboratory Experiment. 4.7 Chapter Four Summary. 4.8 References. 4.9 Problems. 5. The z Transform. 5.1 The z Transform and Its Properties. 5.2 Inverse of the z Transform. 5.3 The z Transform in Linear System Analysis. 5.4 Block Diagram. 5.5 Discrete-Time Frequency Spectra. 5.6 MATLAB Laboratory Experiment. 5.7 Chapter Five Summary. 5.8 References. 5.9 Problems. II. TIME DOMAIN TECHNIQUES. 6. Convolution. 6.1 Convolution of Continuous-Time Signals. 6.2 Convolution for Linear Continuous-Time Systems. 6.3 Convolution of Discrete-Time Signals. 6.4 Convolution for Linear Discrete-Time Systems. 6.5 Numerical Convolution Using MATLAB. 6.6 MATLAB Laboratory Experiments on Convolution. 6.7 Chapter Six Summary. 6.8 References. 6.9 Problems. 7. System Response in Time Domain. 7.1 Solving Linear Differential Equations. 7.2 Solving Linear Difference Equations. 7.3 Discrete-Time System Impulse Response. 7.4 Continuous-Time System Impulse Response. 7.5 Complete Continuous-Time System Response. 7.6 Complete Discrete-Time System Response. 7.7 Stability of Continuous-Time Linear Systems. 7.8 Stability of Discrete-Time Linear Systems. 7.9 MATLAB Experiment on Continuous-Time Systems. 7.10 MATLAB Experiment on Discrete-Time Systems. 7.11 Chapter Seven Summary. 7.12 References. 7.13 Problems. 8. State Space Approach. 8.1 State Space Models. 8.2 Time Response from the State Equation. 8.3 Discrete-Time Models. 8.4 System Characteristic Equation and Eigenvalues. 8.5 Cayley-Hamilton Theorem. 8.6 Linearization of Nonlinear System. 8.7 State Space MATLAB Laboratory Experiments. 8.8 Chapter Eight Summary. 8.9 References. 8.10 Problems. III. SYSTEMS IN ELECTRICAL ENGINEERING. 9. Signals in Digital Signal Processing. 9.1 Sampling Theorem. 9.2 Discrete-Time Fourier Transform (DFDT). 9.3 Double Sided z-Transform. 9.4 Discrete Fourier Transform. 9.5 Discrete-Time Fourier Series. 9.6 Correlation of Discrete-Time Signals. 9.7 FIR and IIR Filters. 9.8 Laboratory Experiment on Digital Signal Processing. 9.9 Chapter Nine Summary. 9.10 References. 9.11 Problems. 10. Signals in Communication Systems. 10.1 Signal Transmission in Communications. 10.2 Signal Correlation, Energy and Power Spectra. 10.3 Hilbert Transform. 10.4 Ideal Filter. 10.5 Modulation and Demodulation. 10.6 Digital Communication System. 10.7 Communication Systems Laboratory Experiment. 10.8 Chapter Ten Summary. 10.9 References. 10.10 Problems. 11. Linear Electric Circuits. 11.1 Basic Relations. 11.2 First-Order Linear Electrical Circuits. 11.3 Second-Order Linear Electrical Circuits. 11.4 Higher-Order Linear Electrical Circuits. 11.5 Chapter Eleven Summary. 11.6 References. 11.7 MATLAB Laboratory Experiment. 11.8 Problems. 12. Linear Controls Systems. 12.1 The Essence of Feedback. 12.2 Transient Response of Second-Order Systems. 12.3 Feedback System Steady State Errors. 12.4 Feedback System Frequency Characteristics. 12.5 Bode Diagrams. 12.6 Common Dynamic Controllers: PD, PI, PID. 12.7 Laboratory Experiment on Control Systems. 12.8 Chapter Twelve Summary. 12.9 References. 12.10 Problems. Appendices. A. Linear Algebra. B. Some Results from Calculus. C. Introduction to MATLAB. D. Introduction to SIMULINK. Index.

Robust frequency offset estimation for pilot symbol assisted packet CDMA with MIMO antenna systems

Abstract: We propose frequency offset estimation and combining techniques for pilot symbol assisted (PSA) packet downlink code-division multiple access (CDMA) with multiple-input and multiple-output (MIMO) antenna systems. Orthogonal Walsh codes are used for dedicated pilot symbols at the transmit antennas. The discrete Fourier transform (DFT)-based frequency offset estimation is used for simple implementation. In addition, simple interpolation is also used for resolution improvement of the DFT. When identical frequency offset is assumed, the frequency offset estimates for each single-input single-output (SISO) sub-stream (i.e., transmit/receive antenna pair) can be combined at the receiver. Simulation results show that the estimation and combining techniques proposed deliver improvement in the frequency offset estimation performance.

A similarity search method of time series data with combination of Fourier and wavelet transforms

Abstract: Time-series data, such as stock exchange rates and weather data, has widely been used in many fields. Similarity search of time-series data is important because it is useful for predicting data changes and searching for common sources. In this paper, we propose a new similarity search method of time-series data using both a discrete Fourier transform (DFT) and wavelet transform (WT). A method of reducing time-series indexing size, using a correlation coefficient, is also presented.

Minimum BER block precoders for zero-forcing equalization

Abstract: In this paper we derive an analytic expression for the linear precoder which minimizes the bit error rate (BER) for block transmission systems with zero-forcing equalization and threshold detection. The design is developed for the two standard schemes for eliminating inter-block interference; viz, zero padding (ZP) and cyclic prefix (CP). The CP minimum BER precoder has a structure similar to that of the conventional water-filling discrete multitone (DMT) modulation scheme, but the diagonal water-filling power loading matrix is replaced by a full matrix consisting of a diagonal minimum mean square error (MMSE) power loading matrix post-multiplied by a Discrete Fourier Transform (DFT) matrix. The ZP minimum BER precoder has a corresponding structure. Performance evaluations indicate that the signal-to-noise ratio (SNR) gain of the ZP and CP minimum BER precoders over conventional water-filling DMT, MMSE, and orthogonal frequency division multiplexing (OFDM) schemes can be as much as several decibels.

Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform.

Abstract: We show that the fractional Fourier transform is a suitable mechanism with which to analyze the diffraction patterns produced by a one-dimensional object because its intensity distribution is partially described by a linear chirp function. The three-dimensional location and the diameter of a fiber can be determined, provided that the optimal fractional order is selected. The effect of compaction of the intensity distribution in the fractional Fourier domain is discussed. A few experimental results are presented.

A complex-valued neuron to transform gray level images to phase information

Abstract: A system to deal with gray level images applying complex-valued networks has already been proposed The proposed system combines complex-valued networks with a 2-dimensional discrete Fourier Transform, and is based on the idea of phase matrix image representation This paper is intended to build pre-processing and post-processing based on network architecture in the system and propose a novel complex-valued neuron to transform gray level images to the phase matrices in the pre-processing The phase and amplitude of an input for the complex-valued neuron determine its output phase by shifting the input phase by the quantity, which is proportional to the input amplitude Introducing such neurons enables us easily to deal with gray level images using complex-valued networks Simulation results on the image representation ability through the pre-processing are also presented

Recent progress and applications in group FFTs

Abstract: The Cooley-Tukey FFT can be interpreted as an algorithm for the efficient computation of the Fourier transform for the finite cyclic groups, a compact group, or the non-compact group of the real line. All of which are commutative instances of a "Group FFT". A brief survey of some recent progress made in the direction of noncommutative generalizations and applications is given.

Efficient quantum computing operations

Abstract: A method of performing a quantum Fourier transform in a quantum computing circuit is disclosed. The method includes forming a quantum computing circuit as a collection of two-qubit gates operating on a sequence of input qubits. Auxiliary qubits are then interacted with the original input qubits to place the auxiliary qubits in a state corresponding to an output of a discrete Fourier transform of a classical state of the input qubits. The original input qubits are then re-set to their ground state by physically interacting the input qubits with the auxiliary qubits. The auxiliary qubits are then transformed to a state representative of a quantum Fourier transform of the sequence of input qubits.

Multi-resolution image watermarking scheme in the spectrum domain

Abstract: Many spectrum domain watermarking schemes have been proposed in recent years, but they seldom deal with the problem of progressively detecting the embedded watermark, which is desirable in some situations. This paper addresses this problem by embedding the watermark in the DCT domain of an image in a multi-resolution way. The DCT coefficients are treated as wavelet transform coefficients, and each watermark bit is embedded repeatedly into a block of coefficients, layer by layer, using a wavelet watermarking scheme, so that the embedded watermark can be detected progressively. Furthermore, for the scheme to be robust against geometric transformations, a second spread spectrum circular watermark is embedded in the DFT domain. Experimental results show that this scheme is robust against common signal processing procedures such as compression, median filtering and additive noise, as well as geometric transformations such as rotation and translation.

Numerically controlled oscillators with hybrid function generators

Abstract: Numerically controlled oscillators (NCOs), with a hybrid scheme of both look-up tables (LUT) and coordinate transformation digital computer (CORDIC) algorithms for a hardware efficient, high performance sine/cosine function generation are investigated. This scheme combines fast access and power efficiency of reasonably sized LUTs, and arbitrary precision obtainable from a rigorous iteration algorithm. Systematic studies using hardware description language (HDL) models and synthesis lead to optimum LUT/CORDIC ratios, which minimize power consumption and silicon area for a given operating clock frequency. First order error models are presented as guidelines for choosing internal NCO parameters. The NCO accuracy is tested with HDL simulations for all algorithmic states to limit output errors to 1 least significant bit (LSB) and by spectra derived from discrete Fourier transform (DFT) for typical frequency inputs f, resulting in a signal to noise ratio (SNR) of better than 100 dB for an amplitude word length AW of 16 bit. Two benchmark designs were adopted for the two clock frequencies 200 MHz and 20 MHz, as "high" and "moderate" performance, respectively. The NCO models are synthesized in a 0.35 /spl mu/m CMOS standard cell target technology and optimized to actually achieve after layout maximum clock frequencies exceeding 310 MHz, i.e., signal frequencies of up to 100 MHz.