scholarly journals Generalized convolution theorem associated with fractional Fourier transform

2012 ◽  
Vol 14 (13) ◽  
pp. 1340-1351 ◽  
Author(s):  
Jun Shi ◽  
Xuejun Sha ◽  
Xiaocheng Song ◽  
Naitong Zhang
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Generalized Convolution

scholarly journals TEOREMA KONVOLUSI PADA TRANSFORMASI FOURIER FRAKSIONAL QUATERNION SISI KIRI DAN SIFAT-SIFATNYA

2019 ◽  
Vol 16 (1) ◽  
pp. 1-12
Author(s):  
N H Wibowo ◽  
S Musdalifah ◽  
Resnawati Resnawati
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Quaternion Algebra ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Quaternion Fourier Transform

Fourier transform (FT) is growing very rapidly and applying in various fields such as analyzing and decomposing signals in the frequency domain. FT has been extended to quaternion algebra known as the Quaternion Fourier Transform (QFT). The purpose of this paper are to formulate the definition and properties of the left sided Quaternion Fractional Fourier Transform (QFFT), to formulate the definition and convolution theorem for left sided QFFT. Firstly, the results showed the formulation of the left sided QFFT definition and some of the properties such as linearity, translation, modulation and scalar. Secondly, its showed the formulation of convolution theorem for left sided QFFT and also the left sided QFFT of conjugate and translation convolution.

scholarly journals Quaternionic fractional Fourier transform for Boehmians

2020 ◽  
Vol 72 (6) ◽  
pp. 812-821
Author(s):  
R. Roopkumar
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Convolution Theorem

UDC 517.9 We construct a Boehmian space of quaternion valued functions using the quaternionic fractional convolution. Applying the convolution theorem, the quaternionic fractional Fourier transform is extended to the context of Boehmians and its properties are established.

Fractional convolution

1998 ◽  
Vol 40 (2) ◽  
pp. 257-265 ◽  
Author(s):  
David Mustard
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Convolution Operators ◽  
Double Integral ◽  
Integral Formulas ◽  
Wigner Distributions ◽  
Fractional Unit

AbstractA continuous one-parameter set of binary operators on L2(R) called fractional convolution operators and which includes those of multiplication and convolution as particular cases is constructed by means of the Condon-Bargmann fractional Fourier transform. A fractional convolution theorem generalizes the standard Fourier convolution theorems and a fractional unit distribution generalizes the unit and delta distributions. Some explicit double-integral formulas for the fractional convolution between two functions are given and the induced operation between their corresponding Wigner distributions is found.

Logarithmic uncertainty principle, convolution theorem related to continuous fractional wavelet transform and its properties on a generalized Sobolev space

2017 ◽  
Vol 15 (05) ◽  
pp. 1750050 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Sobolev Space ◽  
Inversion Formula ◽  
Uncertainty Relation ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Inner Product ◽  
Fractional Wavelet Transform ◽  
Product Relation

The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the Riemann–Lebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CFrWT are provided. Thereafter, a logarithmic uncertainty relation for the CFrWT is investigated and the convolution theorem related to the CFrWT is established using the convolution of the FrFT. The CFrWT on a generalized Sobolev space is introduced and its important properties are presented.

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