A Variation on Inequality for Quaternion Fourier Transform, Modified Convolution and Correlation Theorems for General Quaternion Linear Canonical Transform

The quaternion linear canonical transform is an important tool in applied mathematics and it closely related to the Fourier transform. In this work, using a symmetric form of two-sided (QFT), we first derive variation on Heisenberg-type uncertainty principle transformation. We then consider general It may be considered as extension Based orthogonal plane split, develop convolution theorem that associated with its correlation theorem. finally discuss how apply study generalized swept-frequency filters.