184 citations · 372 across the 9 of their papers we have counts for
9 papers
The Generalized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and Transforms
Pushpendra Singh, Anubha Gupta, Shiv Dutt Joshi
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observe…
Studies on Generalized Fourier Representations and Phase Transforms
Pushpendra Singh
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications.…
Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis
Pushpendra Singh
The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals i…
Breaking the Limits -- Redefining the Instantaneous Frequency
Pushpendra Singh
The Carson and Fry (1937) introduced the concept of variable frequency as a generalization of the constant frequency. The instantaneous frequency (IF) is the time derivative of the…
Time-Frequency analysis via the Fourier Representation
Pushpendra Singh
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the G…
LINOEP vectors, spiral of Theodorus, and nonlinear time-invariant system models of mode decomposition
Pushpendra Singh
In this paper, we propose a general method to obtain a set of Linearly Independent Non-Orthogonal yet Energy (square of the norm) Preserving (LINOEP) vectors using iterative filter…
Some studies on multidimensional Fourier theory for Hilbert transform, analytic signal and space-time series analysis
Pushpendra Singh, Shiv Dutt Joshi
In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical…
The Hilbert spectrum and the Energy Preserving Empirical Mode Decomposition
Pushpendra Singh, Shiv Dutt Joshi, Rakesh Kumar Patney +1
In this paper, we propose algorithms which preserve energy in empirical mode decomposition (EMD), generating finite number of band limited Intrinsic Mode Functions (IMFs). In t…
The Fourier Decomposition Method for nonlinear and nonstationary time series analysis
Pushpendra Singh, Shiv Dutt Joshi, Rakesh Kumar Patney +1
Since many decades, there is a general perception in literature that the Fourier methods are not suitable for the analysis of nonlinear and nonstationary data. In this paper, we pr…