# 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} }

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…

## 34 Citations

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

- MathematicsCircuits Syst. Signal Process.
- 2019

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

- MathematicsCircuits, Systems, and Signal Processing
- 2019

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

- Computer Science
- 2018

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

- Mathematics, Computer ScienceArXiv
- 2021

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

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### Non-Uniform Sparse Fourier Transform and Its Applications

- Computer ScienceIEEE Transactions on Signal Processing
- 2022

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

- Computer ScienceIEEE Transactions on Signal Processing
- 2022

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

- Engineering2018 International Conference on Signal Processing and Communications (SPCOM)
- 2018

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

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

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- 2020

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.

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