Showing papers on "Discrete Fourier transform published in 1993"

Efficient Similarity Search In Sequence Databases

Abstract: We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coefficients, we use R * -trees to index the sequences and efficiently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1–3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.

Harmonic wavelet analysis

Abstract: A new harmonic wavelet is suggested. Unlike wavelets generated by discrete dilation equations, whose shape cannot be expressed in functional form, harmonic wavelets have the simple structure w(x) = {exp(i4$\pi $x)-exp(i2$\pi $x)}/i2$\pi $x. This function w(x) is concentrated locally around x = 0, and is orthogonal to its own unit translations and octave dilations. Its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain (rather than in the x domain). An efficient implementation of a discrete transform using this wavelet is based on the fast Fourier transform (FFT). Fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the FFT. The same process works backwards for the inverse transform.

Recursive high-resolution reconstruction of blurred multiframe images

Abstract: An approach to obtaining high-resolution image reconstruction from low-resolution, blurred, and noisy multiple-input frames is presented. A recursive-least-squares approach with iterative regularization is developed in the discrete Fourier transform (DFT) domain. When the input frames are processed recursively, the reconstruction does not converge in general due to the measurement noise and ill-conditioned nature of the deblurring. Through the iterative update of the regularization function and the proper choice of the regularization parameter, good high-resolution reconstructions of low-resolution, blurred, and noisy input frames are obtained. The proposed algorithm minimizes the computational requirements and provides a parallel computation structure since the reconstruction is done independently for each DFT element. Computer simulations demonstrate the performance of the algorithm. >

The Fourier Integral Method: An efficient spectral method for simulation of random fields

Abstract: The Fourier Integral Method (FIM) of spectral simulation, adapted to generate realizations of a random function in one, two, or three dimensions, is shown to be an efficient technique of non-conditional geostatistical simulation. The main contribution is the use of the fast Fourier transform for both numerical calculus of the density spectral function and as generator of random finite multidimensional sequences with imposed covariance. Results obtained with the FIM are compared with those obtained by other classic methods: Shinozuka and Jan Method in 1D and Turning Bands Method in 2D and 3D, the points for and against different methodologies are discussed. Moreover, with the FIM the simulation of nested structures, one of which can be a nugget effect and the simulation of both zonal and geometric anisotropy is straightforward. All steps taken to implement the FIM methodology are discussed.

Television transmission system using spread spectrum and orthogonal frequency-division multiplex

Abstract: An apparatus for encoding a television production signal for transmission, the television production signal including a first input signal carrying a first class of data and a second input signal carrying a second class of data, the second class data requiring a higher-quality transmission the first class data. For each word of the first input signal, the first stage generates N serial samples of the first output sample stream, each of the N serial samples being formed by a different combination of a set of more than one of the N samples of the each word. The second stage includes an input stage combining the second input signal stream with the first output sample stream to generate an intermediate input sample stream; a serial-to-parallel converter receiving the intermediate input sample stream and producing a second stream of words therefrom, each of the words of which being a parallel grouping of M successive samples of the intermediate input sample stream; a Discrete Fourier Transform (DFT) module producing a parallel output stream of words that is the discrete Fourier transform of the second word stream; and a parallel-to-series converter generating the FDM output signal from the parallel output stream of the DFT module.

The use of DFT windows in signal-to-noise ratio and harmonic distortion computations

Abstract: The discrete Fourier transform (DFT) can be used to compute the signal-to-noise ratio (SNR) and harmonic distortion of a waveform recorder. When the data record contains a non-integer number of cycles of the sine wave, energy leaks from the sine wave and its harmonics to adjacent frequencies. A.L. Benetazzo et al. (1992) describe a windowed DFT method for computing the RMS value of a sine wave from the magnitude of the main lobe of its DFT and recommend the use of minimum energy windows. We present criteria for choosing the DFT window. A constraint for the window coefficients is derived to insure that quantization error does not influence the estimate of the amplitude of a sine wave from the main lobe of its DFT. >

What's that deal with the DCT?

Abstract: Discrete cosine transforms (DCTs) and discrete Fourier transforms (DFTs) are reviewed in order to determine why DCTs are more popular for image compression than the easier-to-compute DFTs. DCT-based image compression takes advantage of the fact that most images do not have much energy in the high-frequency coefficients. It is suggested that DCTs are more popular because fewer DCT coefficients than DFT coefficients are needed to get a good approximation to a typical signal, since the higher-frequency coefficients are small in magnitude and can be more crudely quantized than the low-frequency coefficients. >

Irregular sampling of wavelet and short-time Fourier transforms

Abstract: We obtain irregular sampling theorems for the wavelet transform and the short-time Fourier transform. These sampling theorems yield irregular weighted frames for wavelets and Gabor functions with explicit estimates for the frame bounds.

A simple algorithm for fitting measured data to Fourier‐series models

Abstract: An algorithm is described for fitting measured data to Fourier‐series models of any order without recourse to discrete Fourier transform or curve‐fitting routines. The implementation of this algorithm requires only simple basic mathematical operations and can be easily implemented in microcomputer‐ or microprocessor‐based real‐time systems.

A method and means for transmultiplexing signals between signal terminals and radio frequency channels

Abstract: A method and means are provided of transmultiplexing a plurality of signals between a plurality of signal terminals (17 or 29) and a plurality of selected radio frequency channels. The method includes the step of, and means for, frequency translating and filtering the plurality of signals between the plurality of selected channels and a polyphase discrete Fourier transform filter bank (16 or 21) within a comb filter (15 or 22). The method further includes the step of frequency division multiplexing the plurality of signals between the plurality of signal terminals and comb filter (15 or 22) within a polyphase discrete Fourier transform filter bank (16 or 21).

Cramer-Rao bound for Gaussian random processes and applications to radar processing of atmospheric signals

Abstract: Calculations of the exact Cramer-Rao bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRBs are derived using the discrete Fourier transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRBs are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate SNR and moderate spectral width. >

Frequency-multiplexed cellular telephone cell site base station and method of operating the same

Abstract: The present invention is directed to a cellular telephone cell site base station (10) having a single radio transmitter (40) and radio receiver (14) for transmitting and receiving, respectively, multiplexed frequency-modulated (FM) signals. A filter bank synthesizer (36), associated with the transmitter, multiplexes individual signals for transmission by the transmitter by exponentially modulating the signals to higher frequency bands followed by low-pass filtering and interpolation using discrete Fourier transform techniques. A filter bank analyzer (18), associated with the receiver, demultiplexes multiplexed FM signals received by the receiver by exponentially modulating each signal to its original spectral position followed by low-pass filtering and decimation, using discrete Fourier transform techniques.

Accurate spectral estimation based on measurements with a distorted-timebase digitizer

Abstract: The timebase distortion present in an equivalent-time sampling oscilloscope introduces errors in the estimation of the values of the spectral components of a microwave signal when a classical discrete Fourier transform is used. A method is developed here to avoid these errors. The method is tested both in practice and with simulations. Two parts can be distinguished. At first, the timebase distortion is measured. This is done by digitizing a sinusoidal signal applied at the oscilloscope's input, and by calculating the phase of the analytical signal of the digitized waveform. Other possible methods to measure the timebase distortion are discussed, and it is shown why the method used is the most appropriate for our specific application. The knowledge of the timebase distortion is then used to build a least squares error estimator for the values of the spectral components of a digitized microwave signal. An experimental verification is done, from which is concluded that the method effectively removes the spectral estimation errors due to a timebase distortion. >

Analysis of dampled sinusoidal signals via a frequency domain interpolation algorithm

Abstract: An algorithm for the estimation of the parameters that characterize a linear combination of damped sinusoids is presented. The procedure is based on an interpolation scheme applied to the discrete Fourier transform samples. At first, a single damped exponential signal is analyzed; then the results are extended to multiple damped sinewaves. Numerical simulations show the good accuracy obtained under various measurement conditions; both the effects of spectral interference and wideband noise are considered, proving the reliability of the proposed method in a number of engineering applications. >

Apparatus and robust method for detecting tones

Abstract: A robust tone detector (100) is realized by applying a single taper d(n), which provides a relatively narrow bandwidth filter, to a received signal x'(n) and, then, performing a Discrete Fourier Transform (109) of the tapered signal. The result of the Fourier transform is used to obtain an estimate of energy in the frequency domain of the expected tone. A prescribed selection algorithm based on the relationship of the received signal energy in the time domain (from 107) and the energy estimate in the frequency domain is used to determine whether a valid tone has been received. Robustness of the tone detector is improved by performing a plurality of Discrete Fourier Transforms (in 109) of the single tapered version of the received signal at a corresponding plurality of frequencies relative to the nominal frequency of an expected one or more tones. A further improvement in the tone detector is obtained by dynamically adjusting tone acceptance thresholds (108) based on a measure of channel impairments.

An efficient recursive algorithm for time-varying Fourier transform

Abstract: An efficient recursive algorithm for computing the time-varying Fourier transform (TVFT) or short-time Fourier transform (STFT) of a time sequence is presented. In this approach, instead of excluding the old samples, their importance is diminished by using all-pole moving windows. This recursive algorithm requires about one half of the computation and storage of the Amin's algorithm. The resulting TVFT does not possess any sidelobes. The performance of the algorithm is illustrated by two numerical examples. >

A VLSI architecture for the real time computation of discrete trigonometric transforms

Abstract: The Discrete Trigonometric Transforms are defined as a class of transforms. An algorithm for calculating the Discrete Fourier Transform is extended to cover all members of the defined class. A VLSI architecture which provides for real time calculation of these transforms is presented. This architecture provides simple interconnections, identical processing elements and minimal control complexity.

A single-phase delta-modulated inverter for UPS applications

Abstract: The performance characteristics of the rectangular wave delta modulation (RWDM) scheme for uninterruptible power supply (UPS) applications is investigated. Normalized characteristic curves that show the effect of various modulator parameters on the frequency spectrum of the inverter output voltage are obtained using discrete Fourier transform (DFT) and harmonic analysis techniques. The performance of a single-phase half-bridge inverter with an LC filter is discussed, and experimental results are provided to validate the predicted and simulated results. It is shown that the harmonic content of the inverter output waveform can be controlled through the control of the modulator parameters. >

Implementation of Efficient FFT Algorithms on Fused Multiply- Add Architectures

Abstract: The decimation-in-time radix-2, radix-4, split-ra- dix, and radix-8 algorithms, presented in a paper by Linzer and Feig (5), are described in detail. These algorithms compute discrete Fourier transforms (DFT's) on input sequences with lengths that are powers of 2 with fewer multiply-adds than tra- ditional Cooley-Tukey algorithms. The descriptions given pro- vide the needed details to implement these algorithms efficiently in a computer program that could compute DFT's on a length 2" sequence for general m. We describe and give timing results for a radix-4 version that we have implemented on the RS/6000 workstation. The timing results show that a substantial saving in execution time is obtained when the new radix-4 FFT is used instead of a standard Cooley-Tukey radix-4 FFT. Finally, we present a set of experiments that suggest that numerical behav- ior of the new algorithms is slightly better than the numerical behavior of Cooley-Tukey FFT's.

Obtaining Fourier series graphically from large amplitude oscillatory shear loops

Abstract: Large amplitude oscillatory shear (LAOS) flow has been used to characterize the nonlinear viscoelasticity of polymer melts and solutions. Results are frequently reported with shear stress versus strain loops, or with shear stress versus shear rate loops. A Fourier analysis of the stress response to LAOS is often desired for comparison with theory, or for quantitative comparison between resins. A method is presented which employs the discrete Fourier transform to obtain the Fourier series coefficients from LAOS loops.

Estimation of the ECG signal spectrum during ventricular fibrillation using the fast Fourier transform and maximum entropy methods

Abstract: The aim of this study was to compare two approaches for estimating the spectrum of the surface ECG during ventricular fibrillation (VF): the fast Fourier transform (FFT) and maximum entropy spectral analysis (MESA). The first 10 s of 10 recordings of clinical VF sampled at 250 Hz were separated into 1 s epochs for analysis by the FFT, zero padded FFT and Burg algorithm with 5, 10, 20 and 50 coefficients. The mean difference in dominant frequency between the FFT and Burg algorithm with 50 coefficients was 0.04 Hz (SD 0.56). The mean frequency of the dominant peak in the spectrum of VF can be measured accurately using either the FFT, zero padded FFT or MESA with a model order of more than 10. The overall accuracy of the standard FFT when compared to MESA is not limited by its poor resolution as long as results are averaged over large numbers of recordings. >

Spatial bandwidth testing for digital data-compressed video system

Abstract: Spatial bandwidth testing for digital data-compressed video systems is performed using a complex, or high entropy, test signal. A portion of the test signal is acquired as a control frame. This control frame is divided into a plurality of blocks. Each block is processed by a two-dimensional Discrete Fourier Transform (DFT). The test signal is input to a digital data-compressed video system (10) and a corresponding portion of the output of the video system, a test frame, is acquired (20) and processed (22) in the same manner as the control frame. The resulting coefficient arrays from the control and test frames are compared (28) to each other to obtain an output array of ratios for each block. The ratio of those coefficients corresponding to the predominant frequency of each block of the control frame are displayed (30) as a three-dimensional gain plot. The ratio of those coefficients corresponding to low frequencies of each block of the control frame are displayed as a three-dimensional noise plot. The resulting plots provide an objective, visual indication of the characteristics of the digital data-compressed video system.

Coherent signal power detector using higher-order statistics

Abstract: A signal detection system divides a data sampling run into blocks and perms a fast Fourier transform on each block, sorting results by frequency. Combinations of results of the fast Fourier transform corresponding to each frequency are processed to derive a test statistic which is unbiased by Gaussian noise while including such combinations of results of the fast Fourier transform which would be redundant over other combinations. Information concerning the frequency behavior of the signal derived in the course of detection, is accomplished with increased sensitivity.

Non-uniform PRI pulse-Doppler radar

Abstract: Nonuniform pulse repetition interval (PRI) pulse-Doppler waveforms are processed by replacing the fast Fourier transform algorithm in standard pulse-Doppler processors with a more general discrete Fourier transform. Clutter rejection is a problem because the well-understood techniques of amplitude windowing are not available. However, processing weights with controllable properties can be synthesized by other means. Several applications most amenable to the strengths and limitations of nonuniform PRI waveforms are described.

Hartley transforms over finite fields

Abstract: A general framework is presented for constructing transforms in the field of the input which have a convolution-like property. The construction is carried out over finite fields, but is shown to be valid over the real and complex fields as well. It is shown that these basefield transforms can be viewed as "projections" of the discrete Fourier transform (DFT) and that they exist for all lengths N for which the DFT is defined. The convolution property of the basefield transforms is derived and a condition for such transforms to have the self-inverse property is given. Also, fast algorithms for these basefield transforms are developed, showing gains when compared to computations using the FFT. Application of the methodology to Hartley transforms over R leads to a simple derivation of fast algorithms for computing real Hartley transforms. >

Recursive pruning of the 2D DFT with 3D signal processing applications

Abstract: A recursively pruned radix-(2*2) two-dimensional (2D) fast Fourier transform (FFT) algorithm is proposed to reduce the number of operations involved in the calculation of the 2D discrete Fourier transform (DFT) It is able to compute input and output data points having multiple and possibly irregularly shaped (nonsquare) regions of support The computational performance of the recursively pruned radix-(2*2) 2D FFT algorithm is compared with that of pruning algorithms based on the one-dimensional (1D) FFT The former is shown to yield significant computational savings when employed in the combined 2D DFT/1D linear difference equation filter method to enhance three-dimensional spatially planar image sequences, and when employed in the MixeD moving object detection and trajectory estimation algorithm >

Radar receiver with adaptive clutter threshold reference

Abstract: A method of detecting a target signal at a target signal level below the level of clutter in the return signals of a radar receiver. The receiver i.f. signals are correlated by multiplying delayed i.f. signals with undelayed i.f. signals. The correlated signals are filtered and then decomposed into their spectral component frequencies. The spectral components are compared, in turn, with individual thresholds. The individual thresholds are formed by summing the weighted values of selected ones of the spectral components, the selection being such that the spectral component being compared with a threshold is not used in forming that threshold. A target output signal is generated whenever any one of the spectral components exceeds the level of the threshold against which it is compared. In a second embodiment, in-phase and quadrature correlator signals are formed by the use of two correlators and two delay lines having different delay times that provide a 90 degree phase difference. The complex correlated signals are filtered, decomposed into spectral component frequencies and processed as in the first embodiment to generate a target output signal. In both embodiments, decomposition of the correlated signals may be carried out by means of a Discrete Fourier Transform.

Logarithmic pruning of FFT frequencies

Abstract: A standard fast Fourier transform (FFT) computes the transform at evenly spaced points on a linear scale. A simple modification of the FFT algorithm that results in an efficient method for calculating the transform only at evenly spaced frequencies on a logarithmic scale is proposed. The saving in the number of operations, compared with a standard FFT, is approximately 60% for typical values. >

Forward-looking SAR imaging using a linear array with transverse motion

Abstract: The authors present a novel high-resolution forward-looking two-dimensional synthetic aperture radar (SAR) imaging technique based on discrete Fourier transform (DFT) processing and sequential mode operation. The system utilizes a linear phased array in transverse motion with respect to the flight path and the radar line of sight. No range gating is required. Multitarget detection is achieved on the basis of angular (azimuth and elevation) coordinates. The technique uses an improved signal model based on a third-order three-dimensional Taylor series expansion of the round-trip delay about incremental time, azimuth, and elevation. Computer simulation and an example show the impulse invariance and demonstrate the system's performance. >