Short-Time Fractional Fourier Transform and Its Applications

2010 ◽  
Vol 58 (5) ◽  
pp. 2568-2580 ◽  
Author(s):  
Ran Tao ◽  
Yan-Lei Li ◽  
Yue Wang
2020 ◽  
Vol 68 ◽  
pp. 3280-3295 ◽  
Author(s):  
Jun Shi ◽  
Jiabin Zheng ◽  
Xiaoping Liu ◽  
Wei Xiang ◽  
Qinyu Zhang

Author(s):  
Dinesh Bhatia ◽  
Animesh Mishra

The role of ECG analysis in the diagnosis of cardio-vascular ailments has been significant in recent times. Although effective, the present computational algorithms lack accuracy, and no technique till date is capable of predicting the onset of a CVD condition with precision. In this chapter, the authors attempt to formulate a novel mapping technique based on feature extraction using fractional Fourier transform (FrFT) and map generation using self-organizing maps (SOM). FrFT feature extraction from the ECG data has been performed in a manner reminiscent of short time Fourier transform (STFT). Results show capability to generate maps from the isolated ECG wavetrains with better prediction capability to ascertain the onset of CVDs, which is not possible using conventional algorithms. Promising results provide the ability to visualize the data in a time evolution manner with the help of maps and histograms to predict onset of different CVD conditions and the ability to generate the required output with unsupervised training helping in greater generalization than previous reported techniques.


2021 ◽  
Vol 24 (3) ◽  
pp. 667-688
Author(s):  
Ramanathan Kamalakkannan ◽  
Rajakumar Roopkumar ◽  
Ahmed Zayed

Abstract In this paper, we introduce a short-time coupled fractional Fourier transform (scfrft) using the kernel of the coupled fractional Fourier transform (cfrft). We then prove that it satisfies Parseval’s relation, derive its inversion and addition formulas, and characterize its range on ℒ 2(ℝ2). We also study its time delay and frequency shift properties and conclude the article by a derivation of an uncertainty principle for both the coupled fractional Fourier transform and short-time coupled fractional Fourier transform.


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