Related papers: Intrinsic Frequency Analysis and Fast Algorithms
High-concentration time-frequency (TF) representation provides a valuable tool for characterizing multi-component non-stationary signals. In our previous work, we proposed using an instantaneous frequency (IF) equation to sharpen the TF…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
The intrinsic mode function (IMF) provides adaptive function bases for nonlinear and non-stationary time series data. A fast convergent iterative method is introduced in this paper to find the IMF components of the data, the method is…
This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the…
In this study we investigate the fast image filtering algorithm based on Intro sort algorithm and fast noise reduction of infrared images. Main feature of the proposed approach is that no prior knowledge of noise required. It is developed…
In this work, we implement a relatively new analytical technique, the Improved Amplitude-Frequency Formulation (IAFF) method, approach for solving accurate approximate analytical solutions for strong nonlinear oscillators, which may contain…
In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to…
The Fast Folding Algorithm (FFA) is a phase-coherent search technique for periodic signals. It has rarely been used in radio pulsar searches, having been historically supplanted by the less computationally expensive Fast Fourier Transform…
Independent Component Analysis (ICA) is a dimensionality reduction technique that can boost efficiency of machine learning models that deal with probability density functions, e.g. Bayesian neural networks. Algorithms that implement…
Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years,…
The FFT algorithm that implements the discrete Fourier transform is considered one of the top ten algorithms of the $20$th century. Its main strengths are the low computational cost of $\mathcal{O}(n \log n$) and its stability. It is one of…
In this study, the kinetic inviscid flux (KIF) is improved and an implicit strategy is coupled. The recently proposed KIF is a kind of inviscid flux, whose microscopic mechanism makes it good at solving shock waves, with advantages against…
We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of…
The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…
Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern distribution systems with high penetration of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC)…
The direct-forcing immersed boundary method (DF-IBM) algorithm previously developed by the authors is extended by coupling the Navier-Stokes equations with the Newton-Euler equations for rigid body dynamics within the DF-IBM framework. This…
We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete dynamical system in which each time step corresponds to the application of one of a finite collection of maps. The maps, which represent…
Interatomic-force measurements are regularly performed using frequency-modulation atomic force microscopy. This requires conversion of the observed shift in the resonant frequency of a force-sensing cantilever, to the actual force…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…