Randomized nonuniform sampling and reconstruction in fractional Fourier domain

Xu, Liyun; Zhang, Feng; Tao, Ran

doi:10.1016/j.sigpro.2015.09.016

Cited by 27 publications

(18 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(In reality, uniform sampling cannot be achieved due to trigger uncertainties and jitter of the rotational speed. However, the resulting non-uniformly sampled signal can be interpolated to a uniformly sampled signal without loss of quality as long as the average sampling rate is the same [ 35 , 36 ].)

…”

Section: Theorymentioning

confidence: 99%

Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Lich

Wollmann

Filippatos

et al. 2021

Sensors

View full text Add to dashboard Cite

Due to their lightweight properties, fiber-reinforced composites are well suited for large and fast rotating structures, such as fan blades in turbomachines. To investigate rotor safety and performance, in situ measurements of the structural dynamic behaviour must be performed during rotating conditions. An approach to measuring spatially resolved vibration responses of a rotating structure with a non-contact, non-rotating sensor is investigated here. The resulting spectra can be assigned to specific locations on the structure and have similar properties to the spectra measured with co-rotating sensors, such as strain gauges. The sampling frequency is increased by performing consecutive measurements with a constant excitation function and varying time delays. The method allows for a paradigm shift to unambiguous identification of natural frequencies and mode shapes with arbitrary rotor shapes and excitation functions without the need for co-rotating sensors. Deflection measurements on a glass fiber-reinforced polymer disk were performed with a diffraction grating-based sensor system at 40 measurement points with an uncertainty below 15 μrad and a commercial triangulation sensor at 200 measurement points at surface speeds up to 300 m/s. A rotation-induced increase of two natural frequencies was measured, and their mode shapes were derived at the corresponding rotational speeds. A strain gauge was used for validation.

show abstract

…”

Section: Theorymentioning

confidence: 99%

Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Lich

Wollmann

Filippatos

et al. 2021

Sensors

View full text Add to dashboard Cite

show abstract

“…In this paper, we give another recovery approach instead. We begin with a nonuniform sampling model [31] as in Fig. 2, where {x(t n )} is the sampling sequence of a random signal x(t), and {t n } is the sequence of sampling points.…”

Section: Nonuniform Samplingmentioning

confidence: 99%

“…But, if the original random signal x(t) is not bandlimited in the Fourier domain, the approximate recovery approach might not work. Motivated by [14], Xu, Zhang, and Tao [31] considered the case when the random signal is bandlimited in the fractional Fourier domain. Since LCT is a more general transform, which includes Fourier transform and fractional Fourier transform as its special cases, it is possible that a signal which is non-bandlimited in the Fourier domain or the fractional Fourier domain, is bandlimited in the LCT domain.…”

Section: Approximate Recovery Approachmentioning

confidence: 99%

“…Due to the perfect recovery of bandlimited signals from their nonuniform samples with sinc interpolation, Maymon and Oppenheim [14] proposed a class of approximate recovery approaches for bandlimited signals from their nonuniform samples by utilizing sinc interpolation functions. Furthermore, Xu, Zhang and Tao [31] generalized the results mentioned in [14] from traditional Fourier domain to fractional Fourier transform domain. In order to learn more information on nonuniform sampling, we refer the readers to [1,3,6,9,13,23,25,33].…”

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Nonuniform sampling for random signals bandlimited in the linear canonical transform domain

Huo

Sun

2019

Multidim Syst Sign Process

View full text Add to dashboard Cite

In this paper, we mainly investigate the nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain. We show that the nonuniform sampling for a random signal bandlimited in the LCT domain is equal to the uniform sampling in the sense of second order statistic characters after a prefilter in the LCT domain. Moreover, we propose an approximate recovery approach for nonuniform sampling of random signals bandlimited in the LCT domain. Furthermore, we study the mean square error of the nonuniform sampling. Finally, we do some simulations to verify the correctness of our theoretical results.

show abstract

“…The fractional Fourier transform (FRFT) [1][2][3], which is a generalization of the Fourier transform (FT) [4], has been found as one of the most useful mathematical and optical tools for signal processing. In the past decade, FRFT has attracted much attentions in signal processing community, as the generalization of FT, the relevant theory for FRFT has been developed, including the convolution theorem [5][6][7][8][9][10][11], uncertainty principle [3,12,13], sampling theory [14][15][16][17][18], and so on.…”

Section: Introductionmentioning

confidence: 99%

Convolution theorem for fractional cosine‐sine transform and its application

Feng

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

Fractional cosine transform (FRCT) and fractional sine transform (FRST), which are closely related to the fractional Fourier transform (FRFT), are useful mathematical and optical tool for signal processing. Many properties for these transforms are well investigated, but the convolution theorems are still to be determined. In this paper, we derive convolution theorems for the fractional cosine transform (FRCT) and fractional sine transform (FRST) based on the four novel convolution operations. And then, a potential application for these two transforms on designing multiplicative filter is presented. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

Randomized nonuniform sampling and reconstruction in fractional Fourier domain

Cited by 27 publications

References 31 publications

Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Nonuniform sampling for random signals bandlimited in the linear canonical transform domain

Convolution theorem for fractional cosine‐sine transform and its application

Contact Info

Product

Resources

About