We present a general procedure for obtaining equations of motion for the Wigner distribution of functions that are governed by ordinary and partial differential equations. For the case of fields we show that in genera...
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ISBN:
(纸本)0819437611
We present a general procedure for obtaining equations of motion for the Wigner distribution of functions that are governed by ordinary and partial differential equations. For the case of fields we show that in general one must consider Wigner distributions of the four variables, position, momentum, time and frequency. We also show that in general one cannot write an equation of motion for position and momentum however it can be done in some cases, the Schrodinger equation being one such case. Our method leads to an equation of motion for the Schrodinger equation with time dependent potentials in contrast to the result obtained by Wigner and Moyal which was for time independent potentials.
A comprehensive theory for time-frequency based signal detection has been developed during the past decade. The time-frequency detectors proposed in literature are linear structures operating on the time-frequency rep...
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ISBN:
(纸本)0819450782
A comprehensive theory for time-frequency based signal detection has been developed during the past decade. The time-frequency detectors proposed in literature are linear structures operating on the time-frequency representation of the signals and are equivalent to quadratic receivers that are defined in the,time domain. In this paper, an information theoretic approach for signal detection on the time-frequency plane is introduced. In recent years, Renyi entropy has been proposed as an effective measure for quantifying signal complexity on the time-frequency plane and some important properties of this measure have been proven. In this paper, a new approach that uses the entropy functional as the test statistic for signal detection is developed. The minimum error detection algorithm is derived and the performance of this new signal detection method is demonstrated through examples.
We present a number of methods that use image and signed processing techniques for removal of noise from a signal. The basic idea is to first construct a time-frequency density of the noisy signal. The time-frequency ...
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ISBN:
(纸本)0819432938
We present a number of methods that use image and signed processing techniques for removal of noise from a signal. The basic idea is to first construct a time-frequency density of the noisy signal. The time-frequency density, which is a function of two variables, can then be treated as an "image", thereby enabling use of image processing methods to remove noise and enhance the image. Having obtained an enhanced time-frequency density, one then reconstructs the signal. Various time frequency-densities are used and also a number of image processing methods are investigated. Examples of human speech and whale sounds are given. In addition, new methods are presented for estimation of signal parameters from the time-frequency density.
This paper considers a class of blind beamforming problems in which the amount of prior information is very limited. The array sensors are placed in unknown locations within a geographical region, and have unknown fre...
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ISBN:
(纸本)0819422347
This paper considers a class of blind beamforming problems in which the amount of prior information is very limited. The array sensors are placed in unknown locations within a geographical region, and have unknown frequency/spatial response. The sensors communicate synchronously with a main processor unit. The array is illuminated by a source, which may be narrow- or broadband, in near or far field. Additional disturbances may be present, in the form of interferers, possibly correlated or coherent with the main signal, and additive noise. The goal is required to steer beam toward the desired signal. Four schemes are presented, each based on the type of prior available information.
Fine-grain pipelined adaptive decision-feedback equalizer (ADFE) architectures are developed using the relaxed look-ahead technique. This technique, which is an approximation to the conventional look-ahead computation...
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ISBN:
(纸本)0819412767
Fine-grain pipelined adaptive decision-feedback equalizer (ADFE) architectures are developed using the relaxed look-ahead technique. This technique, which is an approximation to the conventional look-ahead computation, maintains functionality of the algorithm rather than the input-output behavior. Thus, it results in substantial hardware savings as compared to either parallel processing or look-ahead techniques. The delay relaxation, delay transfer relaxation, and sum relaxation are introduced for purposes of pipelining. Both the conventional and the predictor form of ADFE have been pipelined. The performance of the pipelined algorithms for the equalization of a magnetic recording channel is studied. It is demonstrated via simulations that, for a byte error rate of 10-7 or less, speed-ups of up to 8 can be easily achieved with the conventional ADFE. The predictor form of ADFE allows much higher speed-ups (up to 32) for less than 1 dB of SNR degradation.
Time-frequency distributions (TFDs) have proven useful in a wide variety of nonstationary signalprocessing applications. While sophisticated optimal bilinear TFDs have been developed to extract the maximum possible t...
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ISBN:
(纸本)0819422347
Time-frequency distributions (TFDs) have proven useful in a wide variety of nonstationary signalprocessing applications. While sophisticated optimal bilinear TFDs have been developed to extract the maximum possible time- frequency information from signals, certain applications dictate simpler linear, running-FFT processing techniques. In this paper, we propose a signal-dependent short-time Fourier transform/spectrogram that enjoys many of the advantages of optimal bilinear TFDs yet retains the simplicity and efficiency of running-FFT processing. In addition, we extend the optimal kernel design problem to linear spaces of signals.
A deconvolution technique to estimate the Evolutionary Spectrum (ES) of nonstationary signals by deconvolving the blurring effects of the kernel function fi om bilinear time frequency distributions (TFD) is presented....
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ISBN:
(纸本)0819429163
A deconvolution technique to estimate the Evolutionary Spectrum (ES) of nonstationary signals by deconvolving the blurring effects of the kernel function fi om bilinear time frequency distributions (TFD) is presented. The resulting ES has desirable properties such as positivity, higher resolution, higher concentration in time-frequency. The proposed algorithm is computationally more efficient compared to the recently proposed entropy based deconvolution method. Unlike the entropy method the new algorithm can be adapted to deconvolve TFDs other than the spectrogram.
In time-frequency analysis, we extend functions of one variable to functions of two variables. The functions of two variables provide information about the signal that is not easily discernible from the functions of o...
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ISBN:
(纸本)0819425842
In time-frequency analysis, we extend functions of one variable to functions of two variables. The functions of two variables provide information about the signal that is not easily discernible from the functions of one variable. In this paper, we investigate a method for creating quartic functions of three variables and also a quartic function of all four variables. These quartic functions provide a meaningful representation of the signal that goes beyond the well known quadratic functions. The quartic functions are applied to the design of signal-adaptive kernels for Cohen's class and shown to provide improvements over previous methods.
In this paper, the coherent signal-subspace method (CSM) is extended for estimation of bearing, elevation and range of multiple, near-field, broad-band sources. Analytical results are also derived to justify the effec...
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ISBN:
(纸本)0819412767
In this paper, the coherent signal-subspace method (CSM) is extended for estimation of bearing, elevation and range of multiple, near-field, broad-band sources. Analytical results are also derived to justify the effectiveness of the near-field CSM. It is shown that the coherently averaged sample covariance matrix in the near-field CSM has complex Wishart distribution with number of degrees-of-freedom equaling the time-bandwidth product, provided that (1) the frequency components of the array output are statistically independent and Gaussian distributed, and (2) the errors between all the actual source locations and the preliminary estimate of the source cluster center are upperly bounded by a small constant. Some simulation results are provided to show the effectiveness of the near-field CSM.
Cohen's class of time-frequency distributions has been recognized to have significant potential for the analysis of complicated signals. The spectrogram, though it offers comparatively lower time-frequency resolut...
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ISBN:
(纸本)081940943X
Cohen's class of time-frequency distributions has been recognized to have significant potential for the analysis of complicated signals. The spectrogram, though it offers comparatively lower time-frequency resolution than other, more recently investigated members of Cohen's class, is still the most broadly used TFD today. Packages are available which perform SP evaluation and offer signal synthesis from the closely related short-time Fourier transform. These packages allow the SP to be the widely accessible signalprocessing tool that it is. In this paper, we introduce two decompositions of TFDs, the SP decomposition and the weighted reversal correlator decomposition. The decompositions are useful for TFD interpretation, fast implementations using SP building blocks and related high-resolution, linear signal synthesis method using STFT signal synthesis building blocks. It is hoped that these decompositions will facilitate the development of TFD signal analysis/synthesis packages (using existing SP analysis/synthesis packages), and that these packages will make TFDs other than the SP accessible to a broad audience.
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