Fractional Power Spectrum and Fractional Correlation Estimations for Nonuniform Sampling

2020 ◽  
Vol 27 ◽  
pp. 930-934
Author(s):  
Jinming Ma ◽  
Ran Tao ◽  
Yongzhe Li ◽  
Xuejing Kang
Keyword(s):  
Power Spectrum ◽  
Fractional Power ◽  
Nonuniform Sampling ◽  
Fractional Power Spectrum

Fractional Power Spectrum

2008 ◽  
Vol 56 (9) ◽  
pp. 4199-4206 ◽  
Author(s):  
Ran Tao ◽  
Feng Zhang ◽  
Yue Wang
Keyword(s):  
Power Spectrum ◽  
Fractional Power ◽  
Fractional Power Spectrum

scholarly journals Sensing Fractional Power Spectrum of Nonstationary Signals with Coprime Filter Banks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xiaomin Li ◽  
Huali Wang ◽  
Wanghan Lv ◽  
Haichao Luo
Keyword(s):  
Fourier Transform ◽  
Power Spectrum ◽  
Filter Banks ◽  
Fractional Fourier Transform ◽  
Linear Time ◽  
Sampling Rate ◽  
Fractional Power ◽  
Fourier Domain ◽  
Wide Sense ◽  
Fractional Power Spectrum

The coprime discrete Fourier transform (DFT) filter banks provide an effective scheme of spectral sensing for wide-sense stationary (WSS) signals in case that the sampling rate is far lower than the Nyquist sampling rate. And the resolution of the coprime DFT filter banks in the Fourier domain (FD) is 2π/MN, where M and N are coprime. In this work, a digital fractional Fourier transform- (DFrFT-) based coprime filter banks spectrum sensing method is suggested. Our proposed method has the same sampling principle as the coprime DFT filter banks but has some advantages compared to the coprime DFT filter banks. Firstly, the fractional power spectrum of the chirp-stationary signals which are nonstationary in the FD can be sensed effectively by the coprime DFrFT filter banks because of the linear time-invariant (LTI) property of the proposed system in discrete-time Fourier domain (DTFD), while the coprime DFT filter banks can only sense the power spectrum of the WSS signals. Secondly, the coprime DFrFT filter banks improve the resolution from 2π/MN to 2π sin α/MN by combining the fractional filter banks theory with the coprime theory. Simulation results confirm the obtained analytical results.

The on-line use of histogram data for high-speed correction and alignment of electron microscope images

1984 ◽  
Vol 42 ◽  
pp. 556-557
Author(s):  
William Krakow
Keyword(s):  
Power Spectrum ◽  
High Speed ◽  
Direct Memory Access ◽  
Digital Television ◽  
Contrast Transfer Function ◽  
The Past ◽  
High Resolution Tem ◽  
On Line ◽  
Correction Of Astigmatism ◽  
The Fourier Transform

In the past few years on-line digital television frame store devices coupled to computers have been employed to attempt to measure the microscope parameters of defocus and astigmatism. The ultimate goal of such tasks is to fully adjust the operating parameters of the microscope and obtain an optimum image for viewing in terms of its information content. The initial approach to this problem, for high resolution TEM imaging, was to obtain the power spectrum from the Fourier transform of an image, find the contrast transfer function oscillation maxima, and subsequently correct the image. This technique requires a fast computer, a direct memory access device and even an array processor to accomplish these tasks on limited size arrays in a few seconds per image. It is not clear that the power spectrum could be used for more than defocus correction since the correction of astigmatism is a formidable problem of pattern recognition.

Log-log scale roughness spectroscopy of surfaces

1993 ◽  
Vol 51 ◽  
pp. 224-225
Author(s):  
P. Fraundorf ◽  
B. Armbruster
Keyword(s):  
Power Spectrum ◽  
Autocorrelation Function ◽  
Power Spectra ◽  
Scanning Force Microscopy ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
Scanning Force ◽  
Lateral Structure ◽  
Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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