Discrete biquaternion linear canonical transform

Abstract

The landscape of signal processing has witnessed significant advancements over the years, driven by the need for efficient and accurate techniques to analyze and manipulate complex data. While traditional Fourier-based methods have been instrumental, they often struggle to capture the intricate nuances of signals that exhibit non-linearity, non-stationarity, or dual characteristics. To address these limitations, a novel approach namely the Discrete Biquaternion Linear Canonical Transform (DBiQLCT) is introduced in this paper. Because of the inherent non-commutativity of biquaternion algebra multiplication, the Discrete Biquaternion Linear Canonical Transform (DBiQLCT) has three unique forms: left-sided DBiQLCT, right-sided DBiQLCT, and two-sided DBiQLCT. We first introduce a notion of DBiQLCT and subsequently investigate the connections between these transformations. Following that, we investigate the two-sided discrete biquaternion linear canonical transform (TDBiQLCT), revealing important fundamental features such as linearity, time shift, conjugate, and modulation. We also establish the Plancherel and convolution theorems associated with the two-sided DBiQLCT. Furthermore, applications of the proposed transform are discussed at the end.