Time–Frequency Concentration, Heisenberg Type Uncertainty Principles and Localization Operators for the Continuous Dunkl Wavelet Transform on $$\mathbb {R}^{d}$$ R d

2017 ◽  
Vol 14 (4) ◽  
Author(s):  
Hatem Mejjaoli ◽  
Khalifa Trimèche
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principles ◽  
Localization Operators ◽  
Time Frequency ◽  
Heisenberg Type

Localization operators, time frequency concentration and quantitative-type uncertainty for the continuous wavelet transform associated with spherical mean operator

2019 ◽  
Vol 17 (04) ◽  
pp. 1950022 ◽  
Author(s):  
Hatem Mejjaoli ◽  
Nadia Ben Hamadi ◽  
Slim Omri
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Finite Measure ◽  
Continuous Wavelet ◽  
Uncertainty Principles ◽  
Localization Operators ◽  
Spherical Mean Operator ◽  
Von Neumann ◽  
Time Frequency ◽  
Spherical Mean

We consider the continuous wavelet transform [Formula: see text] associated with the spherical mean operator. We investigate the localization operators for [Formula: see text], in particular, we prove that they are in the Schatten-von Neumann class. Next, we analyze the concentration of this transform on sets of finite measure. In particular, Donoho-Stark and Benedicks-type uncertainty principles are given. Finally, we prove many versions of quantitative uncertainty principles for [Formula: see text].

Localization Operators and Uncertainty Principles for the Hankel Wavelet Transform

2021 ◽  
Vol 58 (3) ◽  
pp. 335-357
Author(s):  
Saifallah Ghobber ◽  
Siwar Hkimi ◽  
Slim Omri
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principles ◽  
Localization Operators ◽  
Localization Operator ◽  
Uncertainty Inequalities

The aim of this paper is to prove some uncertainty inequalities for the continuous Hankel wavelet transform, and study the localization operator associated to this transformation.

Time-Frequency Analysis of Partial Discharge Phenomena in SF6 gas using Wavelet Transform

1997 ◽  
Vol 117 (3) ◽  
pp. 338-345 ◽  
Author(s):  
Masatake Kawada ◽  
Masakazu Wada ◽  
Zen-Ichiro Kawasaki ◽  
Kenji Matsu-ura ◽  
Makoto Kawasaki
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Partial Discharge ◽  
Time Frequency Analysis ◽  
Time Frequency

Image encryption based on Fractional wavelet transform, Arnold transform with the double random phases in HSV color domain

2020 ◽  
Vol 13 ◽  
Author(s):  
Aarushi Shrivastava ◽  
Janki Ballabh Sharma ◽  
Sunil Dutt Purohit
Keyword(s):  
Wavelet Transform ◽  
Image Encryption ◽  
Fractional Fourier Transform ◽  
Color Image ◽  
Random Phase ◽  
Arnold Transform ◽  
Time Frequency ◽  
Key Space ◽  
Secret Keys ◽  
Fractional Wavelet Transform

Objective: In the recent multimedia technology images play an integral role in communication. Here in this paper, we propose a new color image encryption method using FWT (Fractional Wavelet transform), double random phases and Arnold transform in HSV color domain. Methods: Firstly the image is changed into the HSV domain and the encoding is done using the FWT which is the combination of the fractional Fourier transform with wavelet transform and the two random phase masks are used in the double random phase encoding. In this one inverse DWT is taken at the end in order to obtain the encrypted image. To scramble the matrices the Arnold transform is used with different iterative values. The fractional order of FRFT, the wavelet family and the iterative numbers of Arnold transform are used as various secret keys in order to enhance the level of security of the proposed method. Results: The performance of the scheme is analyzed through its PSNR and SSIM values, key space, entropy, statistical analysis which demonstrates its effectiveness and feasibility of the proposed technique. Stimulation result verifies its robustness in comparison to nearby schemes. Conclusion: This method develops the better security, enlarged and sensitive key space with improved PSNR and SSIM. FWT reflecting time frequency information adds on to its flexibility with additional variables and making it more suitable for secure transmission.

scholarly journals Automatic ECG Classification Using Continuous Wavelet Transform and Convolutional Neural Network

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 119
Author(s):  
Tao Wang ◽  
Changhua Lu ◽  
Yining Sun ◽  
Mei Yang ◽  
Chun Liu ◽  
...  
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Convolutional Neural Network ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Ecg Signals ◽  
Rr Interval ◽  
Frequency Components ◽  
Fully Connected

Early detection of arrhythmia and effective treatment can prevent deaths caused by cardiovascular disease (CVD). In clinical practice, the diagnosis is made by checking the electrocardiogram (ECG) beat-by-beat, but this is usually time-consuming and laborious. In the paper, we propose an automatic ECG classification method based on Continuous Wavelet Transform (CWT) and Convolutional Neural Network (CNN). CWT is used to decompose ECG signals to obtain different time-frequency components, and CNN is used to extract features from the 2D-scalogram composed of the above time-frequency components. Considering the surrounding R peak interval (also called RR interval) is also useful for the diagnosis of arrhythmia, four RR interval features are extracted and combined with the CNN features to input into a fully connected layer for ECG classification. By testing in the MIT-BIH arrhythmia database, our method achieves an overall performance of 70.75%, 67.47%, 68.76%, and 98.74% for positive predictive value, sensitivity, F1-score, and accuracy, respectively. Compared with existing methods, the overall F1-score of our method is increased by 4.75~16.85%. Because our method is simple and highly accurate, it can potentially be used as a clinical auxiliary diagnostic tool.

scholarly journals An innovative image fusion algorithm based on wavelet transform and discrete fast curvelet transform

2011 ◽  
Vol 1 (3) ◽  
Author(s):  
T. Sumathi ◽  
M. Hemalatha
Keyword(s):  
Wavelet Transform ◽  
Image Fusion ◽  
Curvelet Transform ◽  
Relevant Information ◽  
Good Time ◽  
Discrete Wavelet ◽  
Fusion Algorithm ◽  
Time Frequency ◽  
Fused Image

AbstractImage fusion is the method of combining relevant information from two or more images into a single image resulting in an image that is more informative than the initial inputs. Methods for fusion include discrete wavelet transform, Laplacian pyramid based transform, curvelet based transform etc. These methods demonstrate the best performance in spatial and spectral quality of the fused image compared to other spatial methods of fusion. In particular, wavelet transform has good time-frequency characteristics. However, this characteristic cannot be extended easily to two or more dimensions with separable wavelet experiencing limited directivity when spanning a one-dimensional wavelet. This paper introduces the second generation curvelet transform and uses it to fuse images together. This method is compared against the others previously described to show that useful information can be extracted from source and fused images resulting in the production of fused images which offer clear, detailed information.

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