Some physical constraints on the use of "Carrier-free" waveforms in radio-wave transmission systems

Are there practical applications in radio-wave transmission of inherently broad-band "carrier-free" waveforms such as Walsh functions? We demonstrate in this paper that the band-limiting constraints of radiating systems limit mission of the low-frequency spectral components of such waveforms and severely restrict the radiation directivity that may be achieved in systems that employ them. We also find that dispersion in the propagating medium poses difficulties for the use of such waveforms, and we present an example that illustrates their impracticality in a case in which medium-related limits on coherence bandwidth are of concern. Considerations of capital cost, reliability, and maintenance militate against the use of these waveforms and in favor of conventional spread-spectrum modulation schemes where such service is required. Troublesome aspects of engineering analysis methods for systems employing such modulation schemes are also exposed, as are some practical and economic difficulties to be expected if they are to be introduced as co-users of the electromagnetic spectrum with conventional radio systems.     

Walsh Series Expansions of Probability Distributions

This paper discusses the representation of probability distribution functions by Walsh series expansions. Generally, such expansions may be employed for the representation of multivariate distributions. However, we confine attention here to univariate and bivariate distributions. The resulting expansions are consequently utilized in the derivation of useful expressions for the moments of corresponding probability distributions. Applications of Walsh expansions of probability distributions are further illustrated by computing output moments for some general classes of nonlinear systems.     

Expansion of Walsh Functions in Terms of Shifted Rademacher Functions and Its Applications to the Signal Processing and the Radiation of Electromagnetic Walsh Waves

The expressions for Walsh functions in terms of shifted Rademacher functions are applicable to the design of a directive and selective array antenna for Walsh waves which is capable of eliminating the interference caused by impulsive noises. They also are applicable to voice processing because of their shift-invariant property. The shifted Rademacher functions were previously introduced by shiftiAg horizontally the periodic Rademacher functions. It was shown that the Walsh functions could be expressed as a linear combination of a finite number of the shifted Rademacher functions. This paper develops the actual expansions of the Walsh functions in terms of the shifted Rademacher functions. The coefficients in this series take only the values of either + 1 or -1. The shifted Rademacher coefficients appearing in the expansion of a given function in tenns of shifted Rademacher functions have the advantage that the coefficients of a shifted function are available by shifting cyclically the original coefficients.     

Oblique generalizations of the Walsh basis

An approach to building generalized oblique discrete Walsh basis is suggested. Methods that allow forming transformation matrices based on oblique discrete Walsh functions are developed. Some properties of the suggested oblique discrete Walsh transformations and their applications to synthesizing algorithms of parametric estimation of polynomial trend models of digital signals are considered.     

A new Walsh domain technique of harmonic elimination and voltagecontrol in pulse-width modulated inverters

A method for selective harmonic elimination in pulse-width-modulated (PWM) inverter waveforms by the use of Walsh functions is presented. The Walsh operational matrix of PWM is introduced as a means of obtaining the Walsh spectral equations of PWM waveforms. The slope and intercept Fourier operational matrices of PWM are also introduced as a means of obtaining Fourier spectral equations of PWM waveforms. A noniterative algorithm that produces piecewise-linear, global solutions between angles and for the angles is proposed. The algorithm also produces the full range of variation of fundamental voltage for given harmonic elimination constraints. The set of systems of linear equations obtained replaces the system of nonlinear transcendental equations used in the Fourier series harmonic elimination approach. In general, the algorithm makes possible the synthesis of two-state PWM inverter waveforms with specified old harmonic content     

On the Application of Haar Functions

Recent interest in the application of Walsh functions suggests that Haar functions, close relatives of Walsh functions, may also be useful. In this primarily tutorial paper, Haar functions are reviewed briefly and the computational and memory requirements of the Haar transform are analyzed; applications are then discussed. It is concluded that, whereas Haar functions are unlikely to be useful in as many applications as Walsh functions may be, they seem especially well suited to data coding, edge detection, and, perhaps, multiplexing.     

Walsh analysis of power-law systems (Corresp.)

Walsh-type signals exciting memoryless power-law systems are considered. The input is assumed to consist of a sum of weighted Walsh functions. A method is given for finding the weights of the Walsh functions in the output when the input is a finite Walsh series. It is shown that the fast Walsh transform can be used to facilitate the necessary computation.     

A Simple Recursive Definition for Walsh Functions

This paper presents a simple recursive definition for Walsh functions, which overcomes the shortcomings of other recursive definitions. A rule of thumb for writing down the explicit representation for Walsh functions of any order is also devised. In addition, this recursive formula is used to generate discrete Walsh functions in matrix form.     

The zeros of entire functions: Theory and engineering applications

Functions that are analytic over a complex plane are called entire functions. They may be viewed as generalizations of polynomials because they admit power series expansions that converge everywhere. Entire functions are useful models for physical phenomena having finite "spectra," such as important classes of time-varying signals and spatially varying fields. Entire function models may be studied through the linear expansion techniques (e.g., Fourier series and integrals) familiar to most engineers, but product expansions akin to polynomial factorizations provide a less familiar alternative which is often more powerful when phenomena have a nonlinear character. This paper provides a tutorial introduction to relevant aspects of the theory of entire functions of a single complex variable, and also a discussion of exemplary applications. The paper deals specifically with a class of entire functions of exponential type, dubbed B-functions, which contain all functions that are band limited according to the variious extant definitions of bandlimitation. Product expansions are emphasized because they lead one to regard the real and complex zeros of a B-function as its information bearing attributes. This view leads naturally to the study of sampling, clipping, and similar applications, and to more general issues concerned with the sufficiency of zero-based representations and the recovery of a B-function's waveform from a zero-based representation.     

An improved design of chip waveforms for band-limited DS-CDMA systems

This paper introduces an efficient and improved design of chip waveforms to minimize the multiple-access interference in band-limited direct-sequence code-division multiple-access (DS-CDMA) systems. For ease of implementation, the DS-CDMA system employs a time-limited chip waveform, whereas its band limitation is ensured by the low-pass filters at both the transmitter and receiver ends. The design uses sinusoids to synthesize the time-limited chip waveform so that the portion of its spectrum across the specified bandwidth is as flat as possible. It is shown that by using a simple series expansion (with only a few terms) the synthesized chip waveforms significantly outperform the spreading/despreading waveforms previously proposed, particularly for large values of the chip duration-bandwidth product.     

基于非参数基函数的自适应信号分解算法

 提出了一种分解信号特征的自适应信号处理算法。算法的核心是将观察信号分解为一组最好匹配信号局部结构的特征波形的线性展开,这些特征波形是由非参数基函数特征波形估计方法计算所得。分解算法中模板信号的自适应调整使算法可以不再过多地需要信号的先验知识,在实际应用中具有更加良好的柔性和适应性。通过对算法自适应性和收敛性的测试,验证了算法的性能。仿真信号的提取结果与传统匹配追踪算法分解结果及EMD方法分解结果的比较,进一步表明了所提算法的可行性和有效性。     

The simulation of independent Rayleigh faders

Multiple independent Rayleigh fading waveforms are often required for the simulation of wireless communications channels. Jakes (1974) Rayleigh fading model and its derivatives based on the sum-of-sinusoids provide simple simulators, but they have major shortcomings in their simulated correlation functions. A novel sum-of-sinusoids fading model is proposed and verified, which generates Rayleigh fading processes satisfying the theoretical independence requirements and providing desired power spectral densities with ideal second-order moment. The effects of replacing sinusoids in the proposed model by their approximate waveforms are also analyzed and tested. Performance evaluation and comparison are provided, using the quality measures of the mean-square-error of autocorrelation function and the second-order moment of the power spectral density.     

Matching pursuit and atomic signal models based on recursive filterbanks

The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictionary of time-frequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signal adaptive. In this paper, we apply matching pursuit to the derivation of signal expansions based on damped sinusoids. It is shown that expansions in terms of complex damped sinusoids can be efficiently derived using simple recursive filter banks. We discuss a subspace extension of the pursuit algorithm that provides a framework for deriving real-valued expansions of real signals based on such complex atoms. Furthermore, we consider symmetric and asymmetric two-sided atoms constructed from underlying one-sided damped sinusoids. The primary concern is the application of this approach to the modeling of signals with transient behavior such as music; it is shown that time-frequency atoms based on damped sinusoids are more suitable for representing transients than symmetric Gabor atoms. The resulting atomic models are useful for signal coding and analysis modification synthesis     

Applications of Walsh functions in communications

Communication theory was founded on the system of sine-cosine functions. A more general theory has become known more recently; it replaces the sine-cosine functions by other systems of orthogonal functions, and the concept of frequency by that of sequency. Of these systems, the Walsh functions are of great practical interest since they lead to equipment that is easily implemented by semiconductor technology. Filters, multiplexing equipment, and a voice analyzer/synthesizer have been built successfully for Walsh functions. Some interesting applications of electromagnetic Walsh waves have been found theoretically.     

Orthonormal (Fourier and Walsh) models of time-varying evokedpotentials in neurological injury

The hypothesis that injury-related changes in evoked potential (EP) signals can be modeled by orthonormal basis functions is tested. Two models of time-varying EP signals are evaluated: the Fourier series model (FSM) and the Walsh function model (WFM). The Fourier and Walsh coefficients are estimated with the aid of an adaptive least-mean-squares (LMS) technique. Results from computer simulations illustrate how selection of model order and of the adaptation rate of the estimator affect the signal-to-noise ratio (SNR). The FSM results in a somewhat higher steady-state SNR than does the WFM; however, the WFM is less computationally complex than is the FSM. These two orthonormal functions are used to evaluate transient response to hypoxic hypoxia in anesthetized cats. Trends of the first five frequencies (Fourier) and sequencies (Walsh) show that the lower frequencies and sequencies may be sensitive indicators of hypoxic neurological injury     

On Representations of Walsh Functions

A new recursive formula for defining Walsh functions on the real line is presented. It leads, in a natural way, to an explicit representation of Walsh futctions. The explicit representation can be identified with. the representation of Walsh functions by the products of Rademacher functions. It can also lead to other representations of Walsh functions in a straight-forward manner. Using the new-formulation, one can prove many known properties of Walsh functions easily and systematically and gain new insight.     

Introduction to Bridge Functions

In this paper, a bridge function system is introduced, where bridge functions make up a three-valued function system, only taking the values +1, -1, and 0, and they are orthogonal. It is constructed with the concepts of sequence shift and sequence copying. The notation, waveforms, and recursive relation of the bridge functions are given. Walsh functions are a special case of the bridge functions. Block pulses are another special case. The bridge functions connect the Walsh functions and the block pulse functions. The bridge functions have the property of modulo 2 sum.     

Random and pseudorandom inputs for Volterra filter identification

This paper studies input signals for the identification of nonlinear discrete-time systems modeled via a truncated Volterra series representation. A Kronecker product representation of the truncated Volterra series is used to study the persistence of excitation (PE) conditions for this model. It is shown that i.i.d. sequences and deterministic pseudorandom multilevel sequences (PRMS's) are PE for a truncated Volterra series with nonlinearities of polynomial degree N if and only if the sequences take on N+1 or more distinct levels. It is well known that polynomial regression models, such as the Volterra series, suffer from severe ill-conditioning if the degree of the polynomial is large. The condition number of the data matrix corresponding to the truncated Volterra series, for both PRMS and i.i.d. inputs, is characterized in terms of the system memory length and order of nonlinearity. Hence, the trade-off between model complexity and ill-conditioning is described mathematically. A computationally efficient least squares identification algorithm based on PRMS or i.i.d. inputs is developed that avoids directly computing the inverse of the correlation-matrix. In many applications, short data records are used in which case it is demonstrated that Volterra filter identification is much more accurate using PRMS inputs rather than Gaussian white noise inputs     

Automated decomposition of intramuscular electromyographic signals

We present a novel method for extracting and classifying motor unit action potentials (MUAPs) from one-channel electromyographic recordings. The extraction of MUAP templates is carried out using a symbolic representation of waveforms, a common technique in signature verification applications. The assignment of MUAPs to their specific trains is achieved by means of repeated template matching passes using pseudocorrelation, a new matched-filter-based similarity measure. Identified MUAPs are peeled off and the residual signal is analyzed using shortened templates to facilitate the resolution of superimpositions. The program was tested with simulated data and with experimental signals obtained using fine-wire electrodes in the biceps brachii during isometric contractions ranging from 5% to 30% of the maximum voluntary contraction. Analyzed signals were made of up to 14 MUAP trains. Most templates were extracted automatically, but complex signals sometimes required the adjustment of 2 parameters to account for all the MUAP trains present. Classification accuracy rates for simulations ranged from an average of 96.3% +/- 0.9% (4 trains) to 75.6% +/- 11.0% (12 trains). The classification portion of the program never required user intervention. Decomposition of most 10-s-long signals required less than 10 s using a conventional desktop computer, thus showing capabilities for real-time applications.     

Nonparametric waveform estimation using filter banks

This paper presents a nonparametric method for estimating waveforms of event-related signals embedded in additive noise. The signals have transient character with varying shapes and arrival times. The estimation method is based on a series expansion of the signal by a set of basis functions. Using a template that contains a priori information, two sets of basis functions are designed by means of one uniform and one nonuniform bandpass filter bank. Then, signal-dependent basis functions are obtained. When no a priori information about the signal is available, signal-independent basis functions are constituted by the impulse responses of the subfilters. Delayed copies are created for each basis function with which time jitter in arrival time of the signal can be handled. The method gives a robust estimate of the waveform of transient signals having unknown waveforms and arrival times since no model assumptions are needed. One application is discussed through examples and compared with the estimate, which is obtained by the Karhunen-Loeve expansion