Research on Sub-Nyquist Rate Sampling Method Based on Sparse Fourier Transform Theory

2021 ◽  
Author(s):  
Bo Xu ◽  
Tailin Han ◽  
Zhi Zhang ◽  
Xuan Liu ◽  
Mingchi Ju
Keyword(s):  
Fourier Transform ◽  
Sampling Method ◽  
Nyquist Rate

Irregular Sampling of GPS Signal for Real-Time Implementation of Pipelined PFFT

2014 ◽  
Vol 519-520 ◽  
pp. 969-974 ◽  
Author(s):  
Jian Hua Huang ◽  
Gao Yong Luo
Keyword(s):  
Fourier Transform ◽  
Computational Complexity ◽  
Real Time ◽  
High Speed ◽  
Sampling Method ◽  
Prime Factor ◽  
Irregular Sampling ◽  
Utilization Rate ◽  
Sampled Data ◽  
Simulation Results

We present a nonuniform method sampling to form the 1 105 points of GPS signal for real-time implementation of prime factor Fourier transform (PFFT) processor, which uses less resource with more utilization rate, and is more efficient and computationally faster than fast Fourier transform (FFT). The high-speed capturing method by irregular sampling for GPS quick positioning is developed to obtain the specified number of sampled data to suit the requirement of fast pipelined PFFT implementation. Simulation results show that the irregular sampling method is efficient in terms of computational complexity and achieves minimum operations of sampling for 1 105 samples based PFFT processing.

scholarly journals Frequency Interpolation of LOFAR Embedded Element Patterns Using Spherical Wave Expansion

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
M. J. Arts ◽  
D. S. Prinsloo ◽  
M. J. Bentum ◽  
A. B. Smolders
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Spline Interpolation ◽  
Spherical Wave ◽  
Linear Interpolation ◽  
Frequency Resolution ◽  
Wave Expansion ◽  
Penrose Pseudoinverse ◽  
Nyquist Rate ◽  
Spherical Wave Expansion

This paper describes the use of spherical wave expansion (SWE) to model the embedded element patterns of the LOFAR low-band array. The goal is to reduce the amount of data needed to store the embedded element patterns. The coefficients are calculated using the Moore–Penrose pseudoinverse. The Fast Fourier Transform (FFT) is used to interpolate the coefficients in the frequency domain. It turned out that the embedded element patterns can be described by only 41.8% of the data needed to describe them directly if sampled at the Nyquist rate. The presented results show that a frequency resolution of 1 MHz is needed for proper interpolation of the spherical wave coefficients over the 80 MHz operating frequency band of the LOFAR low-band array. It is also shown that the error due to interpolation using the FFT is less than the error due to linear interpolation or cubic spline interpolation.

scholarly journals Using A Particular Sampling Method for Impedance Measurement

2014 ◽  
Vol 21 (3) ◽  
pp. 497-508 ◽  
Author(s):  
Grzegorz Lentka
Keyword(s):  
Fourier Transform ◽  
Measurement Method ◽  
Sampling Method ◽  
Dft Calculation ◽  
Impedance Measurement ◽  
Measurement Instrument ◽  
System On Chip ◽  
Excitation Signal ◽  
Measured Impedance ◽  
On Chip

Abstract The paper presents an impedance measurement method using a particular sampling method which is an alternative to DFT calculation. The method uses a sine excitation signal and sampling response signals proportional to current flowing through and voltage across the measured impedance. The object impedance is calculated without using Fourier transform. The method was first evaluated in MATLAB by means of simulation. The method was then practically verified in a constructed simple impedance measurement instrument based on a PSoC (Programmable System on Chip). The obtained calculation simplification recommends the method for implementation in simple portable impedance analyzers destined for operation in the field or embedding in sensors.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

FR-IR Molecular Microanalysis System

1990 ◽  
Vol 48 (2) ◽  
pp. 270-271
Author(s):  
John A. Reffner ◽  
William T. Wihlborg
Keyword(s):  
Fourier Transform ◽  
Fourier Transform Infrared ◽  
Integrated System ◽  
Morphological Examination ◽  
Fully Integrated ◽  
Ir Microscopy ◽  
Normal Functions ◽  
Infrared Microspectroscopy ◽  
Infrared Spectral ◽  
Ft Ir

The IRμs™ is the first fully integrated system for Fourier transform infrared (FT-IR) microscopy. FT-IR microscopy combines light microscopy for morphological examination with infrared spectroscopy for chemical identification of microscopic samples or domains. Because the IRμs system is a new tool for molecular microanalysis, its optical, mechanical and system design are described to illustrate the state of development of molecular microanalysis. Applications of infrared microspectroscopy are reviewed by Messerschmidt and Harthcock.Infrared spectral analysis of microscopic samples is not a new idea, it dates back to 1949, with the first commercial instrument being offered by Perkin-Elmer Co. Inc. in 1953. These early efforts showed promise but failed the test of practically. It was not until the advances in computer science were applied did infrared microspectroscopy emerge as a useful technique. Microscopes designed as accessories for Fourier transform infrared spectrometers have been commercially available since 1983. These accessory microscopes provide the best means for analytical spectroscopists to analyze microscopic samples, while not interfering with the FT-IR spectrometer’s normal functions.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

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