A multidimensional isomorphic operator and its properties-aproposal of finite-extent multidimensional cepstrum

We propose a new multidimensional homomorphic operator that replaces the conventional complex cepstrum transformation. We treat multidimensional signals of finite support since any signal we can actually observe and deal with is of finite support. We first show that for any sequence of finite support there exists a coordinate transformation that transforms the support of a given sequence into the first quadrant in the multidimensional signal space. We then propose a new multidimensional homomorphic operator Ψ which transforms a sequence of finite support into another sequence of finite support in the first quadrant. It is proved that the operator Ψ is an isomorphism between two multidimensional signal spaces of finite support where finite convolution and usual addition, respectively, are defined as binomial operations. It is also shown that unlike the conventional complex cepstrum, the proposed operator Ψ is quite simple to compute and requires no complicated procedure like phase unwrapping, while it maintains the special features of the conventional complex cepstrum transformation that are useful in homomorphic signal processing. Moreover we clarify some algebraic structure of the multidimensional signal space with the finite convolution as a binomial operation. Finally it is shown by a numerical example that the deconvolution system using the proposed operator Ψ gives a much better result than the conventional complex cepstrum method     

Design of two-dimensional digital filters using singular-valuedecomposition and balanced approximation method

It is shown that the singular-value decomposition (SVD) of the sampled amplitude response of a two-dimensional (2-D) digital filter possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD can be applied along with 1-D finite impulse response (FIR) techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (ωΨω₂) plane. The balanced approximation method is applied to linear-phase 2-D FIR filters of the type that may be obtained by using the SVD method. The method leads to economical and computationally efficient filters, usually infinite impulse response filters, which have prescribed amplitude responses and whose phase responses are approximately linear     

Design and characterization of a mode-splitting Ψ-junction

It will he shown In this paper, that the mode conversion factor (MCF) as defined for Y-junctions, can be profitably applied for the design of three branch junctions for splitting the three lowest-order modes of a channel waveguide. Accordingly, these so-called mode-splitting Ψ-junctions were designed for implementation in PECVD SiON-technology. Propagation calculations point to crosstalk levels well below -20 dB at 10-20 mm junction length. The produced Ψ-junctions show crosstalk of less than -17 dB, mainly originating from the nonhomogeneity of the refractive indexes of the SiON layers     

To reject or not to reject: that is the question-an answer in caseof neural classifiers

A method defining a reject option that is applicable to a given 0-reject classifier is proposed. The reject option is based on an estimate of the classification reliability, measured by a reliability evaluator Ψ. Trivially, once a reject threshold σ has been fixed, a sample is rejected if the corresponding value of Ψ is below σ. Obviously, as σ represents the least tolerable classification reliability level, when its value varies the reject option becomes more or less severe. In order to adapt the behavior of the reject option to the requirements of the considered application domain, a function P characterizing the reject option's adequacy to the domain has been introduced. It is shown that P can be expressed as a function of σ and, consequently, the optimal value for σ is defined as the one which maximizes the function P. The method for determining the optimal threshold value is independent of the specific 0-reject classifier, while the definition of the reliability evaluators is related to the classifier's architecture. General criteria for defining appropriate reliability evaluators within a classification paradigm are illustrated in the paper and are based on the localization, in the feature space, of the samples that could be classified with a low reliability. The definition of the reliability evaluators for three popular architectures of neural networks (backpropagation, learning vector quantization and probabilistic network) is presented. Finally, the method has been tested with reference to a complex classification problem with data generated according to a distribution-of-distributions model     

Deterministic approach to full-wave analysis of discontinuities inMICs using the method of lines

Arbitrarily shaped one-port and in-line two-port discontinuities in any quasiplanar configuration can be analyzed by this one-step method. Using the hybrid homogeneous conditions, this approach simplifies the calculation, with Ψ^e and Ψ^h being discretized only in and near the discontinuity regions. Illustrative examples of S-parameter calculation are given. Computed results are compared with measured data and with the published results of other authors     

Wavelet packets feasibility study for the design of an ECG compressor

Most of the recent electrocardiogram (ECG) compression approaches developed with the wavelet transform are implemented using the discrete wavelet transform. Conversely, wavelet packets (WP) are not extensively used, although they are an adaptive decomposition for representing signals. In this paper, we present a thresholding-based method to encode ECG signals using WP. The design of the compressor has been carried out according to two main goals: (1) The scheme should be simple to allow real-time implementation; (2) quality, i.e., the reconstructed signal should be as similar as possible to the original signal. The proposed scheme is versatile as far as neither QRS detection nor a priori signal information is required. As such, it can thus be applied to any ECG. Results show that WP perform efficiently and can now be considered as an alternative in ECG compression applications.     

Synchronous sampling theorem for nonlinear systems

It is shown that the sampled output of a nonlinear system with sampled-data input is given by the discrete equivalent of a Volterra series in which the kernels are the sampled Volterra kernels of the system. This theorem is then extended to the common case in which the sampled-data input is applied to the nonlinear system through a zero-order hold.     

Adaptive recovery of a chirped sinusoid in noise. I. Performance ofthe RLS algorithm

The authors study the ability of the exponentially weighted recursive least square (RLS) algorithm to track a complex chirped exponential signal buried in additive white Gaussian noise (power P _n). The signal is a sinusoid whose frequency is drifting at a constant rate Ψ. lt is recovered using an M-tap adaptive predictor. Five principal aspects of the study are presented: the methodology of the analysis; proof of the quasi-deterministic nature of the data-covariance estimate R(k); a new analysis of RLS for an inverse system modeling problem; a new analysis of RLS for a deterministic time-varying model for the optimum filter; and an evaluation of the residual output mean-square error (MSE) resulting from the nonoptimality of the adaptive predictor (the misadjustment) in terms of the forgetting rate (β) of the RLS algorithm. It is shown that the misadjustment is dominated by a lag term of order β^-2 and a noise term of order β. Thus, a value β_opt exists which yields a minimum misadjustment. It is proved that β_opt={(M+1)ρΨ²} ^1/3, and the minimum misadjustment is equal to (3/4)P_n(M+1)β_opt, where ρ is the input signal-to-noise ratio (SNR)     

Maximum Likelihood Receiver for Multiple Channel Transmission Systems

A maximum likelihood (ML) estimator for digital sequences disturbed by Gaussian noise, intersymbol interference (ISI) and interchannel interference (ICI) is derived. It is shown that the sampled outputs of the multiple matched filter (MMF) form a set of sufficient statistics for estimating the input vector sequence. Two ML vector sequence estimation algorithms are presented. One makes use of the sampled output data of the multiple whitened matched filter and is called the vector Viterbi algorithm. The other one is a modification of the vector Viterbi algorithm and uses directly the sampled output of the MMF. It appears that, under a certain condition, the error performance is asymptotically as good as if both ISI and ICI were absent.     

The Gabor compression- expansion system using non-Gaussian windows and its application to television coding and decoding

The bandwidth compressor-expander developed by Gabor more than 25 years ago is reexamined. It is shown that the compressor or expander can be simulated by comb filtering followed by frequency translation of the tooth contents. With a proper choice of window function, the comb teeth do not overlap and no ambiguity is introduced by the coding process. When applied to television messages, with the line harmonics chosen as preferred frequencies, compression or expansion is best described as providing a line frequency standards conversion. The combined compression-expansion system gives a reduced transmission bandwidth at the expense of vertical resolution and provides a flexible technique for the two-dimensional smoothing of television pictures in which simultaneous control of vertical and horizontal resolution is possible. A sampled signal form of the compressor-expander can be realized in digital form by using shift registers as delay lines. The digital version permits simple control of the compression ratio and preferred frequencies.     

Microprocessor application for numerical ECG encoding and transmission

Over the past few years a number of hospitals have established computer facilities for routine ECG interpretation. The combined workload of several hospitals could be processed by a "regional ECG interpretation center," if ECG data could be conveniently and efficiently transmitted to this center. ECG transmission over the public telephone network is common practice today, using FM techniques. However, because of the limited bandwidth of the telephone network and of occasionally severe noise, the signal quality achieved is only marginally adequate for computer interpretation. Transmission of binary-coded ECG's could overcome this problem but the data rates required greatly exceed the available channel capacity of telephone lines. Digital transmission may still be possible if ECG are preprocessed in order to eliminate redundant information and thereby lower the data rate. In this paper the operational characteristics of digital ECG communication are discussed in the context of computer-aided interpretation. Encoding methods proposed by other authors are briefly reviewed, and finally, a prototype system based on an 8-bit microprocessor is described. This system provides real-time transmission of 3 encoded ECG leads, sampled at a rate of 300 per second per lead and digitized with a resolution of 8 bits, using a 2400-Bd synchronous MODEM on standard (unconditioned) telephone lines. Some preliminary results are shown.     

基于C8051单片机的无线心电监护系统设计

介绍一款低功耗无线心电监护系统,它由数据采集盒和PC监护终端两部分构成。数据采集盒在C8051F320单片机控制下实时采集心电数据．通过NRF24L01无线模块发送给PC监护终端。终端中的C8051F320通过NRF24L01模块接收心电数据．并由自带的USB接口将数据传送给PC机进行心电波形的显示和分析处理。该系统可实现多个病人心电信号的采集、存储和分析等功能,小巧便携、方便实用。     

Resampling of data between arbitrary grids using convolutioninterpolation

For certain medical applications resampling of data is required. In magnetic resonance tomography (MRT) or computer tomography (CT), e.g., data may be sampled on nonrectilinear grids in the Fourier domain. For the image reconstruction a convolution-interpolation algorithm, often called gridding, can be applied for resampling of the data onto a rectilinear grid. Resampling of data from a rectilinear onto a nonrectilinear grid are needed, e.g., if projections of a given rectilinear data set are to be obtained. In this paper we introduce the application of the convolution interpolation for resampling of data from one arbitrary grid onto another. The basic algorithm can be split into two steps. First, the data are resampled from the arbitrary input grid onto a rectilinear grid and second, the rectilinear data is resampled onto the arbitrary output grid. Furthermore, we like to introduce a new technique to derive the sampling density function needed for the first step of our algorithm. For fast, sampling-pattern-independent determination of the sampling density function the Voronoi diagram of the sample distribution is calculated. The volume of the Voronoi cell around each sample is used as a measure for the sampling density. It is shown that the introduced resampling technique allows fast resampling of data between arbitrary grids. Furthermore, it is shown that the suggested approach to derive the sampling density function is suitable even for arbitrary sampling patterns. Examples are given in which the proposed technique has been applied for the reconstruction of data acquired along spiral, radial, and arbitrary trajectories and for the fast calculation of projections of a given rectilinearly sampled image.     

A class of order statistic LMS algorithms

Conventional gradient-based adaptive filters, as typified by the well-known LMS algorithm, use an instantaneous estimate of the error-surface gradient to update the filter coefficients. Such a strategy leaves the algorithm extremely vulnerable to impulsive interference. A class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented. These algorithms, dubbed order statistic least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from Gaussian to highly impulsive. Three specific OSLMS filters are defined: the median LMS, the average LMS, and the trimmed-mean LMS. The properties of these algorithms are investigated and the potential for improvement demonstrated. Finally, a general adaptive OSLMS scheme in which the nature of the order-statistic operator is also adapted in response to the statistics of the input signal is presented. It is shown that this can facilitate performance gains over a wide range of input data types     

Sampling representations and the optimum reconstruction of signals

This paper treats the problem of the representation and reconstruction of signals from several sets of sampled values using a multiple-channel sampling and reconstruction scheme. Realizable and unrealizable solutions are presented for the optimum linear postfiltering and prefiltering operations. It is shown that the number of "independent" sets of samples which are necessary for the exact reconstruction of a signal is equal to the maximum number of overlappings of its sampled spectrum. This enables many different sampling expansions to be derived. The simultaneous optimization of the unrealizable linear prefilter and postfilter combination is carried out for the case where two sets of sampled values are taken. It is shown that with the optimum combination of filters, the angular frequency range of the input signal is limited by the prefilters to a total width of4pi rho, which is a natural extension of the single-channel result.     

AM-FM energy detection and separation in noise using multibandenergy operators

This paper develops a multiband or wavelet approach for capturing the AM-FM components of modulated signals immersed in noise. The technique utilizes the recently-popularized nonlinear energy operator Ψ(s)=(s˙)²-ss¨ to isolate the AM-FM energy, and an energy separation algorithm (ESA) to extract the instantaneous amplitudes and frequencies. It is demonstrated that the performance of the energy operator/ESA approach is vastly improved if the signal is first filtered through a bank of bandpass filters, and at each instant analyzed (via Ψ and the ESA) using the dominant local channel response. Moreover, it is found that uniform (worst-case) performance across the frequency spectrum is attained by using a constant-Q, or multiscale wavelet-like filter bank. The elementary stochastic properties of Ψ and of the ESA are developed first. The performance of Ψ and the ESA when applied to bandpass filtered versions of an AM-FM signal-plus-noise combination is then analyzed. The predicted performance is greatly improved by filtering, if the local signal frequencies occur in-band. These observations motivate the multiband energy operator and ESA approach, ensuring the in-band analysis of local AM-PM energy. In particular, the multi-bands must have the constant-Q or wavelet scaling property to ensure uniform performance across bands. The theoretical predictions and the simulation results indicate that improved practical strategies are feasible for tracking and identifying AM-FM components in signals possessing pattern coherencies manifested as local concentrations of frequencies     

Advanced Biometric Pen System for Recording and Analyzing Handwriting

Handwriting dynamics which reflect fine motor skills of writers can be recorded with pen based writing systems. They are generally equipped with a diversity of sensors, such as pen tip pressure and tilt-acceleration sensors mounted inside the pen or pen tip x-y position sensors integrated on a specific graphic tablet. Such writing systems are essentially applied for biometric personal identification or handwriting recognition. In this paper, an advanced biometric pen based system for capturing and analyzing handwriting dynamics of a person is presented. Features of the device as well as evaluation of its sensor data are discussed. The system actually comprises a standard WACOM graphic tablet where its input pen is equipped additionally with a sensor to measure the grip pressure of fingers holding the pen. By combining x-y position data of the tablet and grip pressure data of the pen an improvement of performance in handwriting and person recognition is achieved. The experimental results have shown that among the single sensors, the grip sensor data gives best recognition accuracy and improves the recognition rates of handwritten PINs or persons by about 1%, when fused with x-y position data. It shows excellent accuracy in handwriting recognition and depicts detailed information about fine motor skill which is primarily because of data sampled by the finger grip pressure sensor. The enhanced input device has great promise not only for biometrics but also for biomedical applications.     

Criteria for Optimal Averaging of Cardiac Signals

The averaging process is modeled as a linear system whose low-pass filter characteristics are determined by the degree in temporal misalignment of signals. Assuming the errors in temporal alignment of successive cardiac cycles are random, then the model transfer function is equivalent to the probability density function. The response of the model to a step input is equivalent to the probability distribution function, which can be readily quantified. To validate the model, a high resolution ECG amplifier and QRS recognition system was constructed that synchronizes a step input with a point on the QRS. Design criteria for optimal amplification, filtering, and triggering of the ECG are determined. Test of the model reveals a close correspondence between observed and predicted step responses. From the average step response, the recording fidelity of any average can be determined-rapidly while the alignment is adjusted for optimal precision. Using ECG signals from patients, our model system demonstrates that alignment errors can both add and subtract signal components. Methods for estimating the extent of signal distortion induced by averaging as well as criteria for minimizing it are presented.     

Heart instantaneous frequency (HIF): an alternative approach to extract heart rate variability

Our study focuses on a new method of estimating the heart rate variability (HRV) which does not require the use of electrocardiogram (ECG) R-wave detection. Contrary to the R-wave detection method which requires a sampling frequency higher than 100 Hz, the one proposed here can be used to calculate the HRV from an ECG signal sampled at a frequency of approximately 5 Hz with a relative mean error of 0.03. This new method is based on extracting the instantaneous fundamental frequency from the ECG. The method could be efficiently used to extract the HRV from an ECG measured for healthy subjects performing an exercise in which the HRV increases linearly with time, and for subjects with respiratory and cardiac problems. The overall error decreased as we low-pass filtered the HRV with lower cut-off frequencies. Moreover, it was shown that the method could be efficiently used to calculate the HRV from blood pressure measurements and to be robust to noise.     

Universal image compression using multiscale recurrent patterns with adaptive probability model.

In this work, we further develop the multidimensional multiscale parser (MMP) algorithm, a recently proposed universal lossy compression method which has been successfully applied to images as well as other types of data, as video and ECG signals. The MMP is based on approximate multiscale pattern matching, encoding blocks of an input signal using expanded and contracted versions of patterns stored in a dictionary. The dictionary is updated using expanded and contracted versions of concatenations of previously encoded blocks. This implies that MMP builds its own dictionary while the input data is being encoded, using segments of the input itself, which lends it a universal flavor. It presents a flexible structure, which allows for easily adding data-specific extensions to the base algorithm. Often, the signals to be encoded belong to a narrow class, as the one of smooth images. In these cases, one expects that some improvement can be achieved by introducing some knowledge about the source to be encoded. In this paper, we use the assumption about the smoothness of the source in order to create good context models for the probability of blocks in the dictionary. Such probability models are estimated by considering smoothness constraints around causal block boundaries. In addition, we refine the obtained probability models by also exploiting the existing knowledge about the original scale of the included blocks during the dictionary updating process. Simulation results have shown that these developments allow significant improvements over the original MMP for smooth images, while keeping its state-of-the-art performance for more complex, less smooth ones, thus improving MMP's universal character.