Novel Fourier quadrature transforms and analytic signal representations for nonlinear and non-stationary time-series analysis

@article{Singh2018NovelFQ,
  title={Novel Fourier quadrature transforms and analytic signal representations for nonlinear and non-stationary time-series analysis},
  author={Pushpendra Singh},
  journal={Royal Society Open Science},
  year={2018},
  volume={5}
}
  • Pushpendra Singh
  • Published 29 March 2018
  • Computer Science
  • Royal Society Open Science
The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well known and widely used mathematical formulations for modelling and analysis of signals in various applications. In this study, like the HT, to obtain quadrature component of a signal, we propose novel discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine quadrature transforms (FSQTs), designated as Fourier quadrature transforms (FQTs). Using these FQTs, we propose 16 Fourier… 
View on Royal Society
royalsocietypublishing.org
34 Citations
Background Citations
6
Methods Citations
8
Results Citations
1

34 Citations

Some Studies on Multidimensional Fourier Theory for Hilbert Transform, Analytic Signal and AM–FM Representation

The notion of Fourier frequency vector (FFV) which is inherently associated with the multidimensional (MD) Fourier representation (FR) of a signal is proposed which provides physical meaning to the so-called negative frequencies in the MD-FR that in turn yields MD spatial and MD space-time series analysis.

Some Studies on Multidimensional Fourier Theory for Hilbert Transform, Analytic Signal and AM–FM Representation

In this paper, we propose the notion of Fourier frequency vector (FFV) which is inherently associated with the multidimensional (MD) Fourier representation (FR) of a signal. The proposed FFV provides…

Studies on Generalized Fourier Representations and Phase Transforms

This study presents the generalized Fourier representation (GFR) that is completely based on the FR of a signal, and introduces the phase transform (PT) which is a special case of the GFR and a true generalization of the Hilbert transform.

The Generalized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and Z Transforms

The efficacy of GFT in solving the initial value problems (IVPs) and the generalization presented for FT is extended for other integral transforms with examples shown for wavelet transform and cosine transform.

Empirical Fourier decomposition: An accurate signal decomposition method for nonlinear and non-stationary time series analysis

Non-Uniform Sparse Fourier Transform and Its Applications

A novel estimation algorithm is constructed for NUDFT-II, which is the general form of the sparse Fourier transform (SFT), and the cyclic convolution in the non-uniform frequency domain is proposed and derive the product and convolution theorem.

General Parameterized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and $Z$ Transforms

The GP-FT is applicable to a much larger class of signals, some of which cannot be analyzed with FT and Laplace transform, and the exponential isomorphic mapping in GP- FT leads to a general parameterized version of Mellin transform, designated as Fourier scale transform (FST).

Time-Frequency Analysis of Gravitational Waves

In this paper, IF of gravitational waves is estimated by applying the energy preserving empirical mode decomposition and the Fourier decomposition method to demonstrate a superior performance in terms of better time-frequency resolution as compared to the widely used continuous wavelet transform.

Subbands and cumulative sum of subbands based nonlinear features enhance the performance of epileptic seizure detection

Classification of Epileptic Seizure in EEG Signal Using Support Vector Machine and EMD

An efficient method based on empirical mode decomposition (EMD) has been proposed to detect the epileptic activity and shows that the proposed scheme has attained better classification accuracy when compared to existing state-of-the-art methods.

References

SHOWING 1-10 OF 69 REFERENCES

Some studies on multidimensional Fourier theory for Hilbert transform, analytic signal and space-time series analysis

Some Studies on Multidimensional Fourier Theory for Hilbert Transform, Analytic Signal and AM–FM Representation

The notion of Fourier frequency vector (FFV) which is inherently associated with the multidimensional (MD) Fourier representation (FR) of a signal is proposed which provides physical meaning to the so-called negative frequencies in the MD-FR that in turn yields MD spatial and MD space-time series analysis.

The Fourier decomposition method for nonlinear and non-stationary time series analysis

A novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, is proposed, and its efficacy for the analysis of nonlinear and non-stationary time series is demonstrated.

Fourier-Bessel series expansion based empirical wavelet transform for analysis of non-stationary signals

Time-Frequency analysis via the Fourier Representation

This study presents time-frequency analysis by the Fourier transform which maps the time-domain signal into the frequency-domain and defines the concept of 'frequen-taneous time' which is frequency derivative of phase.

Interpretation of mechanical signals using an improved Hilbert-Huang transform

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

  • N. HuangZheng Shen Henry H. Liu
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the ‘empirical mode decomposition’ method with which any complicated data set can be…

On Instantaneous Frequency

This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF, and finds that the NHT and direct quadrature gave the best overall performance.

Theory of the Hilbert Spectrum

A multicomponent model of a signal that enables rigorous definition of instantaneous frequency on a per-component basis and has shifted all uncertainty of the latent signal to its quadrature.

Eigenvalue Decomposition of Hankel Matrix-Based Time-Frequency Representation for Complex Signals

An eigenvalue decomposition of Hankel matrix-based TFR method, which is a data-driven technique, has been extended for the analysis of complex-valued signals to perform better than compared methods.
...