The autocorrelation function and the run structure are two basic notions for binary sequences, and they have been used as two independent criterions to characterize the randomness of binary sequences for more than 30 years. In this paper, we establish a run series expansion formula for autocorrelation function of the binary sequence and show that the autocorrelation function is in fact complete...

Issue of finding a wavelet matched to signal has been addressed by various researchers in past. This paper presents a new method of estimating wavelet that is matched to a given signal in the statistical sense. The key idea lies in the estimation of analysis wavelet filter from a given signal and is similar to a sharpening filter used in image enhancement. The output of analysis wavelet filter ...

The accurate estimation of covariance matrices is essential for many signal processing and machine learning algorithms. In high dimensional settings the sample covariance is known to perform poorly, hence regularization strategies such as analytic shrinkage of Ledoit/Wolf are applied. In the standard setting, i.i.d. data is assumed, however, in practice, time series typically exhibit strong aut...

The formula for the spectral moments is expanded in a series consisting of autocorrelation terms. By using the autocorrelation extrapolation inherent in the maximum entropy method (MEM) for spectral analysis, it is found that good estimates of the moments can be found from a very low order autoregressive model. The motivation for this investigation came from results obtained during spectral ana...

When the input to a quantizer is a sampled time series represented by x1, x2, x3, . . . , the quantization noise is a time series represented by ν1, ν2, ν3, . . . Suppose that the input time series is stationary and that its statistics satisfy the conditions for multivariable QT II (it would be sufficient that two-variable QT II conditions were satisfied for x1 and x2, x1 and x3, x1 and x4, and...

We study the sample autocovariance and autocorrelation function of the stationary AR(1) process with ARCH(1) errors. In contrast to ARCH and GARCH processes, AR(1) processes with ARCH(1) errors can not be transformed into solutions of linear stochastic recurrence equations. However, we show that they still belong to the class of stationary sequences with regular varying nite-dimensional distrib...

In this paper, we propose an easy method to generate standard normal random variables and this method is compared with the other existing methods. It is observed that the proposed method is quite competitive with most of the existing methods. Randomness of the generated sample is tested using the autocorrelation function and Ljung-Box test. Normality of the samples is checked with the help of r...

Based on measurement of the intensity autocorrelation function, a new method to determine the modulation depth of scattered laser light modulated by an ultrasonic wave in turbid media was applied to ultrasound-modulated optical tomography. Good signal-to-noise ratios and high sensitivities were demonstrated. Images of double optically absorbing objects buried in a highly optically scattering ge...

This paper proposes a new technique for improving the performance of linear prediction analysis by utilizing a refined version of the autocorrelation function. Problems in analyzing voiced speech using linear prediction occur often due to the harmonic structure of the excitation source, which causes the autocorrelation function to be an aliased version of that of the vocal tract impulse respons...