The well-known quaternion algebra is a four-dimensional natural extension of the field of complex numbers and plays a significant role in various aspects of signal processing, particularly for representing signals wherein several instincts are to be controlled simultaneously. For efficient analysis of such quaternionic signals, we introduce the notion of linear canonical wavelet transform in quaternion domain by invoking the elegant convolution structure associated with the quaternion linear canonical transform. The preliminary analysis encompasses the study of fundamental properties of the proposed linear canonical wavelet transform in quaternion domain including the Rayleigh’s theorem, inversion formula and a characterization of the range. Subsequently, we formulate three uncertainty principles; viz, Heisenberg-type, logarithmic and local uncertainty inequalities associated with the linear canonical wavelet transform in quaternion domain.

众所周知的四元数代数是复数领域的四维自然扩展，在信号处理的各个方面发挥着重要作用，特别是在表示同时控制几种本能的信号方面。为了有效分析此类四元数信号，我们通过调用与四元数线性正则变换相关的优雅卷积结构，在四元数域中引入了线性正则小波变换的概念。初步分析包括在四元数域中研究所提出的线性正则小波变换的基本性质，包括瑞利定理、反演公式和范围的表征。随后，我们制定了三个不确定性原则；即，海森堡型，