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The problem of information extraction from discrete stochastic time series, produced with some finite sampling frequency, using flicker-noise spectroscopy, a general framework for information extraction based on the analysis of the…

Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…

Traditional resolvent analysis is a powerful framework for identifying the most amplified input-output structures in fluid flows from a stationary base state. Extending this resolvent analysis to periodic base flows poses computational…

Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the…

The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We…

We consider the response of a finite string to white noise and obtain the exact time-dependent spectrum. The complete exact solution is obtained, that is, both the transient and steady-state solution. To define the time-varying spectrum we…

Cyclic spectral analysis is a signal processing technique designed to deal with stochastic signals whose statistics vary periodically with time. Pulsar radio emission is a textbook example of this signal class, known as cyclostationary…

Graph theory is emerging as a new source of tools for time series analysis. One promising method is to transform a signal into its visibility graph, a representation which captures many interesting aspects of the signal. Here we introduce…

The focus of this thesis is the construction and analysis of efficient representations in nonlinear signal processing, and the applications of these structures to inverse problems in a variety of fields. The work is composed of three major…

We present a second quantization description of frequency-based continuous variables quantum computation in the subspace of single photons. For this, we define frequency and time operators using the free field Hamiltonian and its Fourier…

Self-supervised pre-training models have been used successfully in several machine learning domains. However, only a tiny amount of work is related to music. In our work, we treat a spectrogram of music as a series of patches and design a…

Elucidating a connection with nonlinear Fourier analysis, we extend a well known algorithm in quantum signal processing to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous…

It is demonstrated experimentally that a spin-torque nano-oscillator (STNO) rapidly sweep-tuned by a bias voltage can be used for time-resolved spectrum analysis of frequency-manipulated microwave signals with complicated multi-tone…

Incoming sound is in cochlea and auditory nerve encoded into spike trains. At the third neuron of the auditory pathway, spike trains of the left and right sides are processed in brainstem nuclei to yield sound localization information. Two…

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…

The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a…

I develop the idea that time perception is the quantum counterpart to time measurement. Phase-locking and prime number theory were proposed as the unifying concepts for understanding the optimal synchronization of clocks and their 1/f…

While deep learning has reduced the prevalence of manual feature extraction, transformation of data via feature engineering remains essential for improving model performance, particularly for underwater acoustic signals. The methods by…

In this work, time series analysis techniques are used to analyze sequential, equispaced mass measurements of a Si density artifact, collected from an electromechanical transducer. Specifically, techniques such as Power Spectral Density,…

Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral…