A convolution-based fractional transform

Dou, Jiayin; He, Qian; Yu, Ping; Sun, Qiang; Liu, Shutian; Liu, Zhengjun

doi:10.1007/s11082-016-0685-9

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…The earlier work on the linear canonical wavelet transform was published by authors [15,30,43,44]. The wavelet transform has major applications in the field of image and signal processing, mathematical analysis, communications, radar and other [7,13,19,21,37,39,40]. Let (W A ψ 1 ϕ)(β, α) and (W A ψ 2 ϕ)(ρ, γ) be two LCWT of a function ϕ ∈ L 2 (R) w.r.t.…”

Section: Definition 21 (Admissibility Condition)mentioning

confidence: 99%

The composition of linear canonical wavelet transforms on generalized function spaces

Prasad

Ansari

2020

Filomat

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Section: Definition 21 (Admissibility Condition)mentioning

confidence: 99%

The composition of linear canonical wavelet transforms on generalized function spaces

Prasad

Ansari

2020

Filomat

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“…The random phase masks serve as ciphering keys are employed in image/Fourier planes. Since then, several optical image cryptosystems have been considered like holography [13], optical transforms [1][2][3][4][5][8][9][10][11][12][13][14][15], and interference [18]. In [19], the authors present a virtual optics scheme to encrypt digital audio using the virtual optical scheme parameters.…”

Section: Introductionmentioning

confidence: 99%

Secure Opto-Audio Cryptosystem Using XORing Mask and Hartley Transform

Faragallah

El‐Sayed

2021

IEEE Access

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This research paper proposes a secure opto-audio cryptosystem using XORing mask and Hartley transform (HT). The digital one dimensional (1D) plainaudio data is converted into two dimensional plainaudio map (2D PAM) and after that, the 2D PAM is divided into 2D plainaudio blocks (2D PABs). The basic idea of the proposed opto-audio encryption system depends on XORing each block of the 2D PABs with a single image selected from a personal image database that can be viewed as a secret key in the proposed opto-audio cryptosystem. Each block of the mixed 2D PABs is then transposed using the chaotic logistic adjusted sine map (LASM) and optically encrypted with HT. The XOR and LASM are implemented digitally while HT implemented optically. An additional XORing mask step helps to remove residual intelligibility from the 2D PABs, fill in speechless gaps in spoken conversations, and destroys both the pitch and format details. The utilization of chaotic LASM allows efficient noise immunity. A comparative study is held between the proposed opto-audio encryption system and other related audio encryption systems in terms the standard well known encryption metrics. The results have confirmed the efficiency of the introduced opto-audio encryption system. The proposed opto-audio encryption system security is explored from an accurate encryption point of view, and tests confirmed the superiority of the proposed opto-audio encryption system from the encryption point of view.

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“…Among orthogonal transforms, fractional orthogonal transforms have been extensively applied in signal processing during the past decades. They include FrFT [21, 22], fractional cosine transform [23, 24], fractional sine transform [23, 24], fractional Hartley transform [23, 24], fractional Hilbert transform [25], fractional wavelet transform [26], fractional random transform [27], fractional Mellin transform [28], fractional Gabor transform [29], fractional S transform [30], convolution‐based fractional transform [31], multiple‐parameter FrFT (MPFrFT) [32–35], and so on. Mathematically, this kind of transforms, which is a generalisation of the corresponding conventional transforms, can be regarded as a rotation of signals in the time–frequency plane and therefore has attracted much attention [23].…”

Section: Introductionmentioning

confidence: 99%

“…To date, there are a number of papers involving the fractional transforms [21–35]. However, only FrFT has been used for quaternion signal processing under the name of fractional quaternion Fourier transform (FrQFT) [11–13].…”

Section: Introductionmentioning

confidence: 99%