Real-valued Samples Research Articles

Design of Intelligent Channelizer for Extracting Signals of Arbitrary Centre Frequency and Bandwidth

There are two standard approaches to the problem of wideband signal channelization, namely those based upon the use of a digital down conversion (DDC) unit and those based upon the use of a polyphase discrete Fourier transform (DFT) or PDFT. There are clear advantages and disadvantages with both approaches, however, in that: a) with the DDC approach, optimal performance and flexibility is obtained but at the expense of a heavy computational load; whereas b) with the PDFT approach, a sub optimal and less flexible performance is obtained but at a greatly reduced computational cost through the exploitation of a suitably defined fast Fourier transform (FFT). An intelligent channelizer is described herein which possesses a flexible design able to exploit the merits of both approaches for the case where the input data comprises real-valued samples. The two key design features are: a) optimal setting of the PDFT parameters to ensure that for every signal of interest there is at least one channel completely containing it; and b) simultaneous computation of two real-data FFTs: the first as required by the PDFT and the second, a high-resolution FFT with high update rate, able to accurately direct the application of the low-rate DDC units to the relevant PDFT channel outputs.

Control Variates for Constrained Variables

Numerical Bayesian inference methods typified by Markov chain Monte Carlo generate a set of samples from a probability distribution. When using real-valued samples to approximate the expectation of a random variable, the variance of the resulting estimator, obtained by averaging over those samples, decreases as the number of samples increases. However, it is often useful to reduce the variance without increasing the number of samples. Using control variates is one method to achieve such variance reduction and is applicable in contexts where the random variable is unconstrained. To make it possible to use control variates with constrained variables, this paper proposes the use of a non-linear mapping from an unconstrained space to the constrained space. Results indicate that significant reductions in Monte-Carlo error is achieved with negligible additional computational cost.

A DCT/DST Based Fast OFDM Method in IM/DD Systems

Intensity modulation and direct detection (IM/DD) method is widely used in optical communications. IM/DD systems require the transmitted symbols to be real-valued. Fast orthogonal frequency division multiplexing (FOFDM) is a multi-carrier communication method which can transmit by all the subcarriers and produce real-valued samples at the output. Besides the advantages of FOFDM the single-tap equalizer is unfeasible to compensate for inter symbol interference because of linear convolution property cannot be fulfilled by the inverse discrete cosine and discrete cosine transform (IDCT/DCT) pair that extensively used in FOFDM systems. In this letter, a novel FOFDM method is proposed which uses inverse discrete sine and discrete sine transform (IDST/DST) and IDCT/DCT pairs together. The proposed method provides the use of single-tap equalizer with the advantage of lower peak to average power ratio (PAPR).

Clarifying and quantifying the geometric correlation for probability distributions of inter-sensor monitoring data: A functional data analytic methodology

In structural health monitoring (SHM), revealing the underlying correlations of monitoring data is of considerable significance, both theoretically and practically. In contrast to the traditional correlation analysis for numerical data, this study seeks to analyse the correlation of probability distributions of inter-sensor monitoring data. Due to induced by some commonly shared random excitations, many structural responses measured at different locations are usually correlated in distributions. Clarifying and quantifying such distributional correlations not only enables a more comprehensive understanding of the essential dependence properties of SHM data, but also has appealing application values; however, statistical methods pertinent to this topic are rare. To this end, this article proposes a novel approach using functional data analysis techniques. The monitoring data collected by each sensor are divided into time segments and later summarized by the corresponding probability density functions (PDFs). The geometric relations of the PDFs in terms of their shape mappings between sensors are first characterized by warping functions, and they are subsequently decomposed into finite functional principal components (FPCs); one FPC of the warping functions characterizes one deformation pattern in the transformation of the shapes of the PDFs from one sensor to another. Using this principle, the inter-sensor geometric correlation patterns of PDFs can be clarified by analysing the correlation of the FPC scores of warping functions to the PDFs from one sensor. To overcome the challenge of correlation quantification for real-valued samples (FPC scores) coupled with their functional counterparts (PDFs), a novel nonparametric functional regression (NFR)-based correlation coefficient is defined. Both simulation and real data studies are conducted to illustrate and validate the proposed method.

Schrödinger operators with dynamically defined potentials

In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schrödinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an introductory part explaining basic spectral concepts and fundamental results, we present the general theory of such operators, and then provide an overview of known results for specific classes of potentials. Here we focus primarily on the cases of random and almost periodic potentials.

Separated Design of Encoder and Controller for Networked Linear Quadratic Optimal Control

For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. The encoder outputs are quantized samples, but our results also apply to two other formats for encoder outputs: real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop syst...

Q인자 조절 가능 2차원 이산 웨이브렛 변환 필터의 설계와 성능분석

The general wavelet transform has profitable property in non-stationary signal analysis specially. The tunable Q-factor wavelet transform is a fully-discrete wavelet transform for which the Q-factor Q and the asymptotic redundancy r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented. The transform is based on a real valued scaling factor and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. The transform is parameterized by its Q-factor and its over-sampling rate, with modest over-sampling rates being sufficient for the analysis/synthesis functions to be well localized. This paper describes filter design of 2D discrete-time wavelet transform for which the Q-factor is easily specified. With the advantage of this transform, perfect reconstruction filter design and implementation for performance improvement are focused in this paper. Hence, the 2D transform can be tuned according to the oscillatory behavior of the image signal to which it is applied. Therefore, application for performance improvement in multimedia communication field was evaluated.

Pipelined Architectures for Real-Valued FFT and Hermitian-Symmetric IFFT With Real Datapaths

This brief presents novel parallel pipelined architectures for the computation of the fast Fourier transform (FFT) of real signals and inverse FFT of Hermitian-symmetric signals using only real datapaths. The real FFT structure is transformed by transferring twiddle factors to subsequent stages, such that each stage in the proposed flow graph contains one column of butterfly units and one column of twiddle factor blocks, and each column of the flow graph contains only N samples. This is a key requirement for the design of architectures that are based on only real datapaths. This structure is then mapped to pipelined architectures. The proposed architectures can be used with any FFT size or level of parallelism, which is a power of two. A systematic method to design architectures for FFTs with different levels of parallelism and radix values is presented. By modifying the FFT flow graph for real-valued samples, this methodology leads to architectures with fewer adders, delays, and interconnections.

Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We explore the extension of these ideas to signals with complex-valued samples, using a quaternion-valued equivalent of the analytic signal obtained from a one-sided quaternion Fourier transform which we refer to as the hypercomplex representation of the complex signal. We discuss its derivation and properties and show how to obtain a complex envelope and a real phase from it.A classical result in the case of real signals is that an amplitude modulated signal may be decomposed into its envelope and carrier using the analytic signal provided that the modulating signal has frequency content not overlapping with that of the carrier. We show that this idea extends to the complex case, provided that the complex signal modulates an orthonormal complex exponential. Examples are presented to demonstrate these concepts.

Compact Modeling of Interconnect Circuits over Wide Frequency Band by Adaptive Complex-Valued Sampling Method

In this article, we propose a new model order-reduction method for compact modeling of interconnect circuits over wide frequency band using a novel complex-valued adaptive sampling and error estimation scheme. We address the outstanding error control problems in the existing sampling-based reduction framework over a frequency band. Our new method, WBMOR , explicitly and efficiently computes the exact residual errors to guide the sampling process. We show by sampling along the imaginary axis and performing a new complex-valued reduction that the reduced model will match exactly with the original model at the sample points. Additionally, we show in theory that the proposed method can achieve the error bound over a given frequency range. In practice, the new algorithm can help designers choose the best order of the reduced model for the given frequency range and error bound via the adaptive sampling scheme. In addition, WBMOR can perform wideband accurate reductions of interconnect circuits for analog and RF applications where model accuracy needs to be maintained over a wide frequency range. We compare several sampling schemes such as Monte Carlo, logarithmic, recently proposed resampling, and ARMS methods. Experimental results on a number of RLC circuits show that WBMOR is much more efficient than all the other sampling methods, including the recently proposed resampling and ARMS schemes with the same reduction orders. Compared with the traditional real-valued sampling methods, the complex-valued sampling method is more accurate for the same computational cost.

Wavelet Transform With Tunable Q-Factor

This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of Z. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.

The theoretical foundations of statistical learning theory based on fuzzy random samples in Sugeno measure space

Statistical learning theory is regarded as an appropriate theory to deal with learning problems on small samples, and it has now become a novel research interest of the machine learning field. However, the theory is based on real-valued random samples and established on probability measure space; it rarely deals with learning problems based on fuzzy random samples and established on Sugeno measure space. It is well known that fuzzy random samples and Sugeno measure space are interesting and important extensions of real-valued random samples and probability measure space, respectively. Therefore, the statistical learning theory based on fuzzy random samples in Sugeno measure space is further discussed in this paper. Firstly, based on definitions of the distribution function and the expected value of fuzzy random variables in Sugeno measure space, the Hoeffding inequality of fuzzy random variables is proved. Secondly, for the sake of completeness of the paper, the key theorem of learning theory based on fuzzy random samples in Sugeno measure space is introduced. Finally, the bounds on the rate of uniform convergence of a learning process based on fuzzy random samples in Sugeno measure space are constructed.

The theoretical fundamentals of learning theory based on fuzzy complex random samples

Statistical learning theory based on real-valued random samples has been regarded as one of the influential developments for small samples statistical estimation and learning. The key theorem of learning theory and the bounds on the rate of convergence of learning process are the most important theoretical fundamentals of the statistical learning theory. In this paper, we discuss a statistical learning theory based on fuzzy complex random samples. Firstly, the definition of fuzzy complex numbers is introduced and the fuzzy complex random variables along with their numeric characteristic are investigated. Secondly, we carry out further research focused on a special type of fuzzy complex number, namely rectangular fuzzy complex number and establish some properties and develop important theorems. We also prove the strong law of large numbers based on fuzzy complex random variables. Thirdly, the definitions of the fuzzy complex expected risk functional, the fuzzy complex empirical risk functional, the fuzzy complex empirical risk minimization principle and the consistency are provided and discussed. Finally, the key theorem of learning theory and the bounds on the rate of convergence of learning process based on fuzzy complex random samples are discussed.

Schrödinger operators defined by interval-exchange transformations

We discuss discrete one-dimensional Schr\odinger operators whose potentials are generated by an invertible ergodic transformation of a compact metric space and a continuous real-valued sampling function. We pay particular attention to the case where the transformation is a minimal interval exchange transformation. Results about the spectrum and the spectral type of these operators are established. In particular, we provide the first examples of transformations for which the associated Schr\odinger operators have purely singular spectrum for every non-constant continuous sampling function.

The theoretical foundations of statistical learning theory based on fuzzy number samples

Statistical learning theory based on real-valued random samples has been regarded as a better theory on statistical learning with small sample. The key theorem of learning theory and bounds on the rate of convergence of learning processes are important theoretical foundations of statistical learning theory. In this paper, the theoretical foundations of the statistical learning theory based on fuzzy number samples are discussed. The concepts of fuzzy expected risk functional, fuzzy empirical risk functional and fuzzy empirical risk minimization principle are redefined. The key theorem of learning theory based on fuzzy number samples is proved. Furthermore, the bounds on the rate of convergence of learning processes based on fuzzy number samples are discussed.

Asymptotics for trimmed k-means and associated tolerance zones

Impartial trimming procedures with respect to general ‘penalty’ functions, Φ, have been recently introduced in Cuesta-Albertos et al. (1997. Ann. Statist. 25, 553–576) in the (generalized) k-means framework. Under regularity assumptions, for real-valued samples, we obtain the asymptotic normality both of the impartial trimmed k-mean estimator (Φ(x)=x2) and of the impartial trimmed k-median estimator (Φ(x)=x). In spite of the additional complexity coming from the several groups setting, the empirical quantile methodology used in Butler (1982. Ann. Statist. 10, 197–204) for the LTS estimator (and subsequently in Tableman (1994. Statist. Probab. Lett. 19, 387–398) for the LTAD estimator) also works in our framework. Besides their relevance for the robust estimation of quantizers, our results open the possibility of considering asymptotic distribution-free tolerance regions, constituted by unions of intervals, for predicting a future observation, generalizing the idea in Butler (1982).