## What is/are Adaptive Fourier?

Adaptive Fourier - The Adaptive Fourier Analyzer has been developed for measuring the harmonic components of periodic signals with changing or unknown fundamental frequency.^{[1]}Thus, a joint rational basis function system (JRBFS) based on class adaptivity is here first built for an HSI by adaptive Fourier decomposition (AFD).

^{[2]}This paper proposes a novel feature representation approach for heartbeat classification using single-lead electrocardiogram (ECG) signals based on adaptive Fourier decomposition (AFD).

^{[3]}The numerical approach is a variant of the Angular Spectrum (AS) method, called Non Uniform ADaptive Angular Spectrum (NUADAS) method, which relies on the combination of non-uniform and adaptive Fourier transform algorithms to allow the computation of an arbitrary field distribution in a plane that is shifted and tilted with respect to the source.

^{[4]}In this paper, a trajectory tracking control algorithm based on adaptive Fourier decomposition is proposed for linear discrete systems by using the adaptive and fast convergence characteristics of adaptive Fourier decomposition.

^{[5]}In this article, we propose a nonlinear Proportional+Derivative (PD) tracking controller with adaptive Fourier series compensation.

^{[6]}In this work, an Adaptive Neural Networks PID controller structure, called Adaptive Fourier Series Neural Networks PID controller (AFSNNPID), is developed.

^{[7]}Adaptive Fourier decomposition (AFD) provides an expansion of an analytic function into a sum of basic signals, called mono-components.

^{[8]}In this study, a new type of sparse representation learning framework called statistical $n$ -best adaptive Fourier decomposition (SAFD) originated by Qian is adopted in ECG biometric identification.

^{[9]}This paper presents a novel signal compression algorithm based on the Blaschke unwinding adaptive Fourier decomposition (AFD).

^{[10]}In this paper, we introduce the adaptive Fourier decomposition (AFD) algorithm to deal with the system identification problem.

^{[11]}In this paper, we propose an innovative algorithm that combines with Core Adaptive Fourier Decomposition (Core-AFD) for text encryption.

^{[12]}This paper presents a new two-dimensional (2D) signal analysis method, namely partial unwinding adaptive Fourier decomposition.

^{[13]}This paper proposes a new type of supervised learning approach - statistical adaptive Fourier decomposition (SAFD).

^{[14]}Recently, several papers have considered a nonlinear analogue of Fourier series in signal analysis, referred to as either nonlinear phase unwinding or adaptive Fourier decomposition.

^{[15]}MSC Classification: 42A50; 32A30; 32A35; 46J15 This paper proposes a two-dimensional (2D) partial unwinding adaptive Fourier decomposition method to identify 2D system functions.

^{[16]}Adaptive Fourier decomposition (AFD) method was used in system identification in recent years.

^{[17]}The contribution of this paper is designing a robust controller using a novel adaptive Fourier series expansion.

^{[18]}In this paper, we study the convergence of adaptive Fourier sums for real-valued $$2\pi $$2π-periodic functions.

^{[19]}The proposed model combines adaptive Fourier decomposition method, a new signal preprocessing technology, for extracting useful element from the original electricity demand series through filtering the noise factors.

^{[20]}System spectral analysis of temporal variations in the electron density in the range of 30–180 min is based on windowed Fourier transform, adaptive Fourier transform, and wavelet transform.

^{[21]}Adaptive Fourier decomposition (AFD) provides an expansion of an analytic function into a sum of basic signals, called mono-components.

^{[22]}Furthermore, in order to overcome the effect of the tolerance of component size and internal electrode and unfixed weld line position resulted from lead frame process on foreign material detection result, the multiscale adaptive Fourier analysis (MAFA) is proposed in the concept of texture anomaly detection for foreign material defect detection.

^{[23]}Moreover, an adaptive Fourier spectrum segmentation scheme using iterative backward-forward search algorithm is developed to achieve adaptive empirical wavelet transform for fault-related mode extraction.

^{[24]}In this paper, we propose a dual-optimization technique using adaptive Fourier decomposition in conjunction with sparse spectral reconstruction (AFODSS) using a multiple measurement vectors (MMVs) model and a regularized bi-conjugate gradient focal underdetermined system solver (BCG-FOCUSS) algorithm.

^{[25]}By the terminology adaptive Fourier decomposition (AFD), we refer to approximations in the H2(T) space by using linear combinations of the analytic Szegö kernels.

^{[26]}The methodology of the approximation is a pre-orthogonal method, called Pre-Adaptive Fourier Decomposition.

^{[27]}

## Unwinding Adaptive Fourier

This paper presents a novel signal compression algorithm based on the Blaschke unwinding adaptive Fourier decomposition (AFD).^{[1]}This paper presents a new two-dimensional (2D) signal analysis method, namely partial unwinding adaptive Fourier decomposition.

^{[2]}MSC Classification: 42A50; 32A30; 32A35; 46J15 This paper proposes a two-dimensional (2D) partial unwinding adaptive Fourier decomposition method to identify 2D system functions.

^{[3]}

## adaptive fourier decomposition

Thus, a joint rational basis function system (JRBFS) based on class adaptivity is here first built for an HSI by adaptive Fourier decomposition (AFD).^{[1]}This paper proposes a novel feature representation approach for heartbeat classification using single-lead electrocardiogram (ECG) signals based on adaptive Fourier decomposition (AFD).

^{[2]}In this paper, a trajectory tracking control algorithm based on adaptive Fourier decomposition is proposed for linear discrete systems by using the adaptive and fast convergence characteristics of adaptive Fourier decomposition.

^{[3]}Adaptive Fourier decomposition (AFD) provides an expansion of an analytic function into a sum of basic signals, called mono-components.

^{[4]}In this study, a new type of sparse representation learning framework called statistical $n$ -best adaptive Fourier decomposition (SAFD) originated by Qian is adopted in ECG biometric identification.

^{[5]}This paper presents a novel signal compression algorithm based on the Blaschke unwinding adaptive Fourier decomposition (AFD).

^{[6]}In this paper, we introduce the adaptive Fourier decomposition (AFD) algorithm to deal with the system identification problem.

^{[7]}In this paper, we propose an innovative algorithm that combines with Core Adaptive Fourier Decomposition (Core-AFD) for text encryption.

^{[8]}This paper presents a new two-dimensional (2D) signal analysis method, namely partial unwinding adaptive Fourier decomposition.

^{[9]}This paper proposes a new type of supervised learning approach - statistical adaptive Fourier decomposition (SAFD).

^{[10]}Recently, several papers have considered a nonlinear analogue of Fourier series in signal analysis, referred to as either nonlinear phase unwinding or adaptive Fourier decomposition.

^{[11]}MSC Classification: 42A50; 32A30; 32A35; 46J15 This paper proposes a two-dimensional (2D) partial unwinding adaptive Fourier decomposition method to identify 2D system functions.

^{[12]}Adaptive Fourier decomposition (AFD) method was used in system identification in recent years.

^{[13]}The proposed model combines adaptive Fourier decomposition method, a new signal preprocessing technology, for extracting useful element from the original electricity demand series through filtering the noise factors.

^{[14]}Adaptive Fourier decomposition (AFD) provides an expansion of an analytic function into a sum of basic signals, called mono-components.

^{[15]}In this paper, we propose a dual-optimization technique using adaptive Fourier decomposition in conjunction with sparse spectral reconstruction (AFODSS) using a multiple measurement vectors (MMVs) model and a regularized bi-conjugate gradient focal underdetermined system solver (BCG-FOCUSS) algorithm.

^{[16]}By the terminology adaptive Fourier decomposition (AFD), we refer to approximations in the H2(T) space by using linear combinations of the analytic Szegö kernels.

^{[17]}The methodology of the approximation is a pre-orthogonal method, called Pre-Adaptive Fourier Decomposition.

^{[18]}

## adaptive fourier series

In this article, we propose a nonlinear Proportional+Derivative (PD) tracking controller with adaptive Fourier series compensation.^{[1]}In this work, an Adaptive Neural Networks PID controller structure, called Adaptive Fourier Series Neural Networks PID controller (AFSNNPID), is developed.

^{[2]}The contribution of this paper is designing a robust controller using a novel adaptive Fourier series expansion.

^{[3]}

## adaptive fourier transform

The numerical approach is a variant of the Angular Spectrum (AS) method, called Non Uniform ADaptive Angular Spectrum (NUADAS) method, which relies on the combination of non-uniform and adaptive Fourier transform algorithms to allow the computation of an arbitrary field distribution in a plane that is shifted and tilted with respect to the source.^{[1]}System spectral analysis of temporal variations in the electron density in the range of 30–180 min is based on windowed Fourier transform, adaptive Fourier transform, and wavelet transform.

^{[2]}