Multitaper power spectrum estimation and thresholding: wavelet packets versus wavelets

It was suggested that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a wavelet packet tree to the log multitaper spectrum ordinates, thresholding the empirical wavelet packet coefficients, and then inverting the transform. For a small number of tapers, suitable transforms/partitions for the logarithm of the multitaper spectrum estimator are derived using a method matched to statistical thresholding properties. The partitions thus derived starting from different stationary time series are all similar and easily derived, and any differences between the wavelet packet and discrete wavelet transform (DWT) approaches are minimal. For a larger number of tapers, where the chosen parameters satisfy the conditions of a proven theorem, the simple DWT again emerges as appropriate. Hence, using our approach to thresholding and the method of partitioning, we conclude that the DWT approach is a very adequate wavelet-based approach and that the use of wavelet packets is unnecessary.     

Wavelet power spectrum smoothing for random vibration control

This paper compares the wavelet power spectrum smoothing method with the Welch method in the random vibration control algorithm of an electrodynamic shaker. Practical results show that the wavelet smoothing method improves the control algorithm performance significantly     

Wavelet thresholding for multiple noisy image copies

This correspondence addresses the recovery of an image from its multiple noisy copies. The standard method is to compute the weighted average of these copies. Since the wavelet thresholding technique has been shown to effectively denoise a single noisy copy, we consider in this paper combining the two operations of averaging and thresholding. Because thresholding is a nonlinear technique, averaging then thresholding or thresholding then averaging produce different estimators. By modeling the signal wavelet coefficients as Laplacian distributed and the noise as Gaussian, our investigation finds the optimal ordering to depend on the number of available copies and on the signal-to-noise ratio. We then propose thresholds that are nearly optimal under the assumed model for each ordering. With the optimal and near-optimal thresholds, the two methods yield similar performance, and both show considerable improvement over merely averaging.     

Adaptive thresholding for motion estimation prejudgement

The authors propose an adaptive method of detecting zero motion blocks for motion estimation prejudgement. By combining our method with motion estimation algorithms, much computational effort is saved while almost the same matching performance is achieved     

Wavelet thresholding of multivalued images

In this paper, a denoising technique for multivalued images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients. Specific functions of the wavelet coefficients are defined that exploit interscale and/or interband correlation of the signal. Three functions are studied: the square of the wavelet coefficients, products of coefficients at adjacent scales, and products of coefficients from different bands. For these functions, the signal and noise probability density functions (pdf) become more separated. The high signal correlation between bands is exploited by summing these products over all bands, in this way separating noise and signal pdfs even more. The noise pdf of the proposed quantities is derived analytically and from this, a wavelet threshold is derived. The technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images and on multimodal MRI images.     

随机噪声信号的功率谱估计的仿真

在通讯与电子信息工程行业及领域中,大部分问题的解决需要进行估计一个随机信号在频率域上的功率谱分布,诸如此类的问题有很多,比如：设计滤波器消除噪声信号,振动随机信号的回波抵消,随机信号的特征抽取与表示等等。功率谱估计的分类：一般分为两大类,一类是参数法功率谱估计,一类是非参数法功率谱估计。参数法功率谱估计通常对数据进行一种建模,比如把数据建模成滑动平均模型（Moving Average）,或者自回归（Autoregressive）模型,而非参数法功率谱估计。除了要求信号满足广义平稳之外,不需要其它的统计假设。与非参数法相比较,参数法的优点是在一个给定的数据集合上能够有较少的误差、偏差与方差。     

Iterative maximum entropy power spectrum estimation for multirate systems

In multirate systems, observations are generally insufficient to determine the power spectrum of the input signal. In this paper, we reformulate the problem using a novel matrix notation and the discrete entropy function. Then we present an iterative maximum entropy power spectrum estimation algorithm for the solution of this problem. Contrary to the existing solutions, the new algorithm is computationally efficient since it is based on fast Fourier transform (FFT) and simple matrix calculations. Furthermore, simulation results show that the new algorithm converges to the maximum entropy solution and can be successfully used in multirate statistical data estimation.     

Two-dimensional model-based power spectrum estimation for nonextendible correlation bisequences

The extendibility of estimated correlation bisequences from an available sampled data array is described in terms of the generating functions of associated block Toeplitz with Toeplitz block (BTTB) matrices. The periodogram-based correlation bisequences are shown to be extendible. It is shown that the method of resultants and subresultants is convenient for generating the nonlinear constraints in the optimization problem which is solved iteratively for power spectrum estimation. A nontrivial example illustrates the concepts developed.This paper is in memory of Sydney R. Parker.This work was partly supported by Korea Telecom and partly by HRB Systems.     

Using SAT-based techniques in power estimation

Recent algorithmic advances in Boolean satisfiability (SAT), along with highly efficient solver implementations, have enabled the successful deployment of SAT technology in a wide range of applications domains, and particularly in electronic design automation (EDA). SAT is increasingly being used as the underlying model for a number of applications in EDA. This paper describes how to formulate two problems in power estimation of CMOS combinational circuits as SAT problems or 0–1 integer linear programming (ILP). In these circuits, it was proven that maximizing dissipation is equivalent to maximizing gate output activity, appropriately weighted to account for differing load capacitances. The first problem in this work deals with identifying an input vector pair that maximizes the weighted circuit activity. In the second application we attempt to find an estimate for the maximum power-up current in circuits where power cut-off or gating techniques are used to reduce leakage current. Both problems were successfully formulated as SAT problems. SAT-Based and generic Integer Linear Programming (ILP) solvers are then used to find a solution. The experimental results obtained on a large number of benchmark circuits provide promising evidence that the proposed complete approach is both viable and useful and outperforms the random approach.     

Advanced spectrum estimation methods for signal analysis in power electronics

Modern frequency power converters generate a wide spectrum of harmonic components. Large converters systems can also generate noncharacteristic harmonics and interharmonics. Standard tools of harmonic analysis based on the Fourier transform assume that only harmonics are present and the periodicity intervals are fixed, while periodicity intervals in the presence of interharmonics are variable and very long. A novel approach to harmonic and interharmonic analysis, based on the "subspace" methods, is proposed. Min-norm harmonic retrieval method is an example of high-resolution eigenstructure-based methods. The Prony method as applied for signal analysis was also tested for this purpose. Both high-resolution methods do not show the disadvantages of the traditional tools and allow exact estimation of the interharmonics frequencies. To investigate the methods several experiments were performed using simulated signals, current waveforms at the output of a simulated frequency converter, and current waveforms at the output of an industrial frequency converter. For comparison, similar experiments were repeated using the fast Fourier transform (FFT). The comparison proved the superiority of the new methods. However, their computation is much more complex than FFT.     

Adaptive power techniques for blind channel estimation in CDMA systems

The problem of blind adaptive channel estimation in code-division multiple access (CDMA) systems is considered. Motivated by the iterative power method, which is used in numerical analysis for estimating singular values and singular vectors, we develop recursive least squares (RLS) and least mean squares (LMS) subspace-based adaptive algorithms in order to identify the impulse response of the multipath channel. The schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind. Both versions (RLS and LMS) exhibit rapid convergence combined with low computational complexity. With the help of simulations, we demonstrate the improved performance of our methods as compared with the already-existing techniques in the literature.     

High-order ar estimation method of ARMA power spectrum

In this paper, the high-order AR estimation method of ARMA power spectrum and the whitened-noise decision order criterion of AR order are presented. It is indicated that the quality of high-order AR estimation is related to the ill-condition problem and the algorithmic stability of numerical calculation in the paper. The latter can be solved well by using the recurrence algorithm of Householder transform in the solution of high-order AR parameter estimation.     

Statistical estimation of average power dissipation usingnonparametric techniques

In this paper, we present a new statistical technique for estimation of average power dissipation in digital circuits. The present parametric statistical technique estimates the average power based on the assumption that the power distribution can be characterized by a preassumed function. Large error can incur when the assumption is not met. On the other hand, the existing nonparametric technique, although accurate, is too conservative and requires a large sample size in order to achieve convergence. For a good tradeoff between simulation accuracy and computational efficiency, we propose a new nonparametric technique using the properties of the order statistics. It is generally applicable to any type of circuit irrespective of its power distribution function. Compared to the existing nonparametric technique, it is much more computationally efficient since it requires a much smaller sample size to achieve the same accuracy specification. This new technique is implemented in the distribution-independent power estimation tool (DIPE). DIPE is empirically demonstrated to be more robust and accurate than the parametric technique     

A digital power spectrum estimation method for the adaptation of high-speed equalizers

This work presents a method to estimate the power spectrum of digital signals, which is then used to generate an error signal to tune Gbps data rate equalizers for digital communications. The proposed power spectrum estimation method can be realized with standard digital circuits and has been fabricated and tested in 0.35-/spl mu/m CMOS technology for 1-Gbps data rate. Compared with the traditional bandpass filter followed by a rectifier implementation, this method has wider input signal range and is scalable to higher speed technologies beyond the gigahertz range, in addition to largely reduced power dissipation and die area. Also presented are system simulations on the bit-error rate performance and the error space analysis of the proposed method in comparison with the method of using a bandpass filter followed by a rectifier.     

Wavelet estimation

An important problem in seismic exploration is the estimation of and correction for the seismic wavelet. A seismic signal may be modeled as a convolutional model with the wavelet as one component. The wavelet propagated by the seismic energy source is complicated by transmission and recording filters. Some filters in the system can be deterministically defined while others are more conjectural. The estimation of the wavelet is useful in two major ways. Borehole measurements are used to model the surface seismograms. The wavelet used in the model needs to match that of the seismogram to correlate the two measurements. Conversely, the estimated wavelet can be used to design inverse filters which make the seismogram approach the borehole measures. Some well-known methods for estimation of the wavelet are based on assumptions about the wavelet or the earth reflectivity. Examples of the methods indicate success on some data even though each makes different assumptions. The methods serve to point out basic problems in reliably estimating the wavelet from the seismogram. Basic problems include noise, band-limiting, nonstationarity, uncertain theoretical models, assumption failure, and widely diverse geological sequences of the earth. Quality control or evaluation of the performance of an estimation algorithm is a nontrivial problem. The estimation of the wavelet from a seismic recording remains an area of challenging research and importance in exploration for hydrocarbons.     

A survey of power estimation techniques in VLSI circuits

With the advent of portable and high-density microelectronic devices, the power dissipation of very large scale integrated (VLSI) circuits is becoming a critical concern. Accurate and efficient power estimation during the design phase is required in order to meet the power specifications without a costly redesign process. In this paper, we present a review of the power estimation techniques that have recently been proposed     

Spectrum estimation by wavelet thresholding of multitaperestimators

Current methods for power spectrum estimation by wavelet thresholding use the empirical wavelet coefficients derived from the log periodogram. Unfortunately, the periodogram is a very poor estimate when the true spectrum has a high dynamic range and/or is rapidly varying. In addition, because the distribution of the log periodogram is markedly non-Gaussian, special wavelet-dependent thresholding schemes are needed. These difficulties can be bypassed by starting with a multitaper spectrum estimator. The logarithm of this estimator is close to Gaussian distributed if a moderate number (⩾5) of tapers are used. In contrast to the log periodogram, log multitaper estimates are not approximately pairwise uncorrelated at the Fourier frequencies, but the form of the correlation can be accurately and simply approximated. For scale-independent thresholding, the correlation acts in accordance with the wavelet shrinkage paradigm to suppress small-scale “noise spikes” while leaving informative coarse scale coefficients relatively unattenuated. This simple approach to spectrum estimation is demonstrated to work very well in practice. Additionally, the progression of the variance of wavelet coefficients with scale can be accurately calculated, allowing the use of scale-dependent thresholds. This more involved approach also works well in practice but is not uniformly preferable to the scale-independent approach