Duality Property of Discrete Quaternion Fourier Transform

We introduce the discrete quaternionic Fourier transform (QDFT), which is generalization of discrete Fourier transform. We establish the version discrete of duality property duality related to the QDFT

REPRESENTASI QUATERNION DALAM BENTUK MATRIKS

Perbedaan antara quaternion dengan bilangan kompleks terletak pada bagian imajiner.  Sehingga untuk merepresentasikan suatu bilangan quaternion dapat dilakukan dengan menggunakan bilangan imajiner. Pada peper ini, diperkenalkan kombinasi bilangan kompleks dalam merepresentasikan bilangan quaternion, strukturnya dalam bentuk matriks . Beberapa sifat telah dibuktikan pada paper ini termasuk juga perkalian dua bilangan quaternion

Correlation Theorem for Two-sided Quaternion Fourier Transform

In this paper we establish correlation theorem for the two-sided quaternion Fourier transform (QFT). A consequence of the theorem is also investigated

Product Theorem for Quaternion Fourier Transform

This paper presents in some detail the quaternion Fourier transform (QFT) of the product of two quaternion functions. It is shown that the proposed product for the QFT is closely related to the convolution in the quaternion Fourier domain

Relationships between Convolution and Correlation for Fourier Transform and Quaternion Fourier Transform

In this paper we introduce convolution theorem for the Fourier transform (FT) of \ud two complex functions. We show that the correlation theorem for the FT can be \ud derived using properties of convolution. We develop this idea to derive the \ud correlation theorem for the quaternion Fourier transform (QFT) of the two \ud quaternion functions

Convolution and Correlation Based on Discrete Quaternion Fourier Transform

In this paper we present the generalized convolution and correlation for the two-dimensional discrete quaternion Fourier transforn (DQFT). We provide several new properties of the generalization. These results can be considered as the extensions of the correlation and convolution properties of real and complex Fourier transform to the DQFT domai

A quantum wavelet uncertainty principle

The aim of this paper is to derive a new uncertainty principle for the generalized $q$-Bessel wavelet transform studied earlier in \cite{Rezguietal}. In this paper, an uncertainty principle associated with wavelet transforms in the $q$-calculus framework has been established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is exploited next to explore a wavelet uncertainty principle already in the $q$-calculus framework.Comment: 16 page

TRANSFORMASI FOURIER DAN TRANSFORMASI FOURIER QUATERNION

pada paper ini menjelaskan transformasi Fourier baik yang bernilai real maupun yang bernilai quaternion. Perbedaan mendasarnya terletak pada kernel transformasi, dimana pada transformasi Fourier quaternion dibedakan menjadi tiga jenis, yaitu sisi kiri, sisi kanan dan dua sisi. Adapun sifat-sifat yang dibuktikan seperti pergeseran, modulasi, pengskalaan dan lain-lain (TFQ sisi kanan)