2022/06/30 by Aamir H. Dar, Dar, Aamir H., M. Younus Bhat +1 · 1 citation
Computer Science · Mathematics · #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2207.09926
openalex publication_date 2022/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier transform. In this paper, we generalize the quadratic phase Fourier transform to quaternion valued signals, known as the quaternion QPFT QQPFT. We initiate our investigation by studying the QPFT of 2D quaternionic signals, then we introduce the QQPFT of 2D quaternionic signals. Using the fundamental relationship between the QQPFT and quaternion Fourier transform QFT, we derive the inverse transform and Parseval and Plancherel formulas associated with the QQPFT. Some other properties including linearity, shift and modulation of the QQPFT are also studied. Finally, we formulate several classes of uncertainty principles UPs for the QQPFT, which including Heisenberg type UP, logarithmic UP, Hardys UP, Beurlings UP and Donohon Starks UP. It can be regarded as the first step in the applications of the QQPFT in the real world.