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Novel generalized Fourier representations and phase transforms.

ABSTRACT: The Fourier representations (FRs) are indispensable mathematical formulations for modeling and analysis of physical phenomena and engineering systems. This study presents a new set of generalized Fourier representations (GFRs) and phase transforms (PTs). The PTs are special cases of the GFRs and true generalizations of the Hilbert transforms. In particular, the Fourier transform based kernel of the PT is derived and its various properties are discussed. The time derivative and integral, including fractional order, of a signal are obtained using the GFR. It is demonstrated that the general class of time-invariant and time-variant filtering operations, analog and digital modulations can be obtained from the proposed GFR. A narrowband Fourier representation for the time-frequency analysis of a signal is also presented using the GFR. A discrete cosine transform based implementation, to avoid end artifacts due to discontinuities present in the both ends of a signal, is proposed. A fractional-delay in a discrete-time signal using the FR is introduced. The fast Fourier transform implementation of all the proposed representations is developed. Moreover, using the analytic wavelet transform, a wavelet phase transform (WPT) is proposed to obtain a desired phase-shift in a signal under-analysis. A wavelet quadrature transform (WQT) is also presented which is a special case of the WPT with a phase-shift of ?/2 radians. Thus, a wavelet analytic signal representation is derived from the WQT. Theoretical analysis and numerical experiments are conducted to evaluate effectiveness of the proposed methods.

SUBMITTER: Singh P

PROVIDER: S-EPMC7416779 | biostudies-literature | 2020 Nov

REPOSITORIES: biostudies-literature

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Novel generalized Fourier representations and phase transforms.

Singh Pushpendra P

Digital signal processing 20200810

The Fourier representations (FRs) are indispensable mathematical formulations for modeling and analysis of physical phenomena and engineering systems. This study presents a new set of generalized Fourier representations (GFRs) and phase transforms (PTs). The PTs are special cases of the GFRs and true generalizations of the Hilbert transforms. In particular, the Fourier transform based kernel of the PT is derived and its various properties are discussed. The time derivative and integral, includin ...[more]

PMID: 32834705

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Project description:Fast Fourier transform (FFT)-based protein ligand docking together with parallel simulated annealing for both rigid and flexible receptor docking are implemented on graphical processing unit (GPU) accelerated platforms to significantly enhance the throughput of the CDOCKER and flexible CDOCKER - the docking algorithms in the CHARMM program for biomolecule modeling. The FFT-based approach for docking, first applied in protein-protein docking to efficiently search for the binding position and orientation of proteins, is adapted here to search ligand translational and rotational spaces given a ligand conformation in protein-ligand docking. Running on GPUs, our implementation of FFT docking in CDOCKER achieves a 15 000 fold speedup in the ligand translational and rotational space search in protein-ligand docking problems. With this significant speedup it becomes practical to exhaustively search ligand translational and rotational space when docking a rigid ligand into a protein receptor. We demonstrate in this paper that this provides an efficient way to calculate an upper bound for docking accuracy in the assessment of scoring functions for protein-ligand docking, which can be useful for improving scoring functions. The parallel molecular dynamics (MD) simulated annealing, also running on GPUs, aims to accelerate the search algorithm in CDOCKER by running MD simulated annealing in parallel on GPUs. When utilized as part of the general CDOCKER docking protocol, acceleration in excess of 20 times is achieved. With this acceleration, we demonstrate that the performance of CDOCKER for redocking is significantly improved compared with three other popular protein-ligand docking programs on two widely used protein ligand complex data sets: the Astex diverse set and the SB2012 test set. The flexible CDOCKER is similarly improved by the parallel MD simulated annealing on GPUs. Based on the results presented here, we suggest that the accelerated CDOCKER platform provides a highly competitive docking engine for both rigid-receptor and flexible-receptor docking studies and will further facilitate continued improvement in the physics-based scoring function employed in CDOCKER docking studies.

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Novel generalized Fourier representations and phase transforms.

Publications

Novel generalized Fourier representations and phase transforms.

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