scholarly journals Frame Spectral Pairs and Exponential Bases

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Christina Frederick ◽  
Azita Mayeli
Keyword(s):  
Spectral Pairs ◽  
Exponential Bases

WAVELET PACKETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF LINE

2013 ◽  
Vol 06 (01) ◽  
pp. 1350007 ◽  
Author(s):  
Vikram Sharma ◽  
P. Manchanda
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packets ◽  
Half Line ◽  
State University ◽  
Spectral Pairs ◽  
Funct Anal ◽  
Positive Half

Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform multiresolution analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied multiresolution analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform multiresolution analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.

scholarly journals A simple construction of exponential bases in L2 of the union of several intervals

1995 ◽  
Vol 38 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Kristian Seip
Keyword(s):  
Riesz Basis ◽  
Partial Result ◽  
Simple Construction ◽  
Real Numbers ◽  
Exponential Bases ◽  
Several Intervals

It is proved that every space L2 (I1, ∪ I2), where I1 and I2 are finite intervals, has a Riesz basis of complex exponentials , {λk} a sequence of real numbers. A partial result for the corresponding problem for n≧3 finite intervals is also obtained.

Interpolation of Subspaces and Applications to Exponential Bases

2015 ◽  
pp. 509-532
Author(s):  
Fritz Gesztesy ◽  
Gilles Godefroy ◽  
Loukas Grafakos ◽  
Igor Verbitsky
Keyword(s):  
Exponential Bases

Speech Perception Hash Authentication Algorithm Based on Immittance Spectral Pairs

2014 ◽  
Vol 610 ◽  
pp. 385-392
Author(s):  
Yi Bo Huang ◽  
Qiu Yu Zhang ◽  
Zhan Ting Yuan ◽  
Peng Fei Xing
Keyword(s):  
Matrix Factorization ◽  
Gaussian White Noise ◽  
Speech Communication ◽  
Time Requirement ◽  
Parameter Matrix ◽  
Spectral Pairs ◽  
Mean And Variance ◽  
Speech Authentication ◽  
Perceptual Hashing ◽  
Non Negative Matrix Factorization

According to the situation that traditional speech authentication algorithms don’t be appropriated for present speech communication, we proposed a speech authentication algorithm of perceptual hashing based on Immittance Spectral Pairs. It can satisfy the requirement of the efficiency and the robustness for speech authentication. Firstly, the speech signal pre-processing, for framing, adding window, obtained for each speech frame immittance spectral Pairs parameters, constitute an immittance spectral Pairs parameter matrix. Then process cepstral mean and variance normalization for immittance spectral Pairs parameter matrix, cepstral mean and variance normalization can effectively improve the robustness of the Gaussian white noise. And parameter matrix for non-negative matrix factorization. Finally, quantifying the formed weight matrix and getting perceptual hashing sequences.Experiments show that the proposed algorithm has good robustness for content preserving operations, and it doesn’t reduce the efficiency while meeting robustness, it can satisfy the real-time requirement of speech communication.

Exponential bases in L2

1971 ◽  
Vol 5 (1) ◽  
pp. 31-38 ◽  
Author(s):  
V. �. Katsnel'son
Keyword(s):  
Exponential Bases
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