Related papers: Autocorrelation type functions for big and dirty d…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
The amount of randomness in a signal generated by physical or non-physical process can reveal important information about that process. For example, the presence of randomness in ECG signals may indicate a cardiac disease. On the hand, the…
Complexity measures are introduced, that quantify the change of the natural entropy fluctuations at different length scales in time-series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death…
A scheme is presented to extract detailed dynamical signatures from successive measurements of complex systems. Relative entropy based time series tools are used to quantify the gain in predictive power of increasing past knowledge. By…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
Correlations in music that exist within its waveform are studied. Monophonic wave files of random music are generated and the probability distribution function of time interval between large signal values is analyzed. A power law behavior…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
The correlation properties of the magnitudes of a time series (sometimes called volatility) are associated with nonlinear and multifractal properties and have been applied in a great variety of fields. Here, we have obtained analytically…
Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…
We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide…
Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…
An electrocardiogram (ECG) is a time-series signal that is represented by one-dimensional (1-D) data. Higher dimensional representation contains more information that is accessible for feature extraction. Hidden variables such as frequency…
Entanglement entropy, which is a measure of quantum correlations between separate parts of a many-body system, has emerged recently as a fundamental quantity in broad areas of theoretical physics, from cosmology and field theory to…
We present a new system for simultaneous estimation of keys, chords, and bass notes from music audio. It makes use of a novel chromagram representation of audio that takes perception of loudness into account. Furthermore, it is fully based…
Prior research has shown that autocorrelation and variance in voltage measurements tend to increase as power systems approach instability. This paper seeks to identify the conditions under which these statistical indicators provide reliable…
Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones,…
We derive relations between standard order parameter correlations and the noise correlations in time of flight images, which are valid for systems with long range order as well as low dimensional systems with algebraic decay of…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We live in a digital world that, in 2010, crossed the mark of one zettabyte data. This huge amount of data processed on computers extremely fast with optimized techniques allows one to find insights in new and emerging types of data and…