The novel quadratic-phase wavelet transform in the Clifford-valued domain

To represent Clifford-valued signals more efficiently in the time-frequency domain, we establish the notion of novel integral transform known as Clifford quadratic-phase wavelet transform (CQPWT) by invoking the convolution theory associated with the Clifford quadratic-phase Fourier transform (CQPFT). We begin our discussion by establishing the definition of CQPWT and some fundamental properties, few of them include linearity, translation, and parity. We then proceed to the derivation of some mathematical formulae including the orthogonality relation, inversion formula, and reproducing kernel by formulating the relationship between the CQPFT and Clifford Fourier transform (CFT) of an analyzing function. We then investigate the Heisenberg's and logarithmic uncertainty principles corresponding to the proposed transform. Finally, we conclude our discussion by displaying the validity of transform via illustrative examples.