In terms of this influential but rarely discussed theory, this thesis seeks to explore and generalize the linear canonical transform (LCT) to quaternionvalued signals. we call it the quaternionic linear canonical transform (QLCT). In a communication theory setting, an uncertainty principle states that a signal cannot be arbitrarily confined in both the spatial and frequency domains. Many efforts have been devoted to extend the uncertainty principle to various types of functions and Linear canonical transforms. We establish an uncertainty principle for the QLCT by using the properties of the LCT and describe a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains by applying the uncertainty principle established in the first part, pointing out that only a Gaussian quaternionic signal can minimize the uncertainty. One of the basic problems encountered in signal representations using the conventional LCT is the ineffectiveness of the LCT kernel to represent and compute location information. One method to overcome such a problem is the windowed Linear canonical transform (WLCT). Following this method we define windowed quaternionic linear canonical transform(WLCT). The QWLCT has the similar properties with QLCT. Finally we established uncertainty principle of QWLCT.