Commutative quaternion algebra and DSP fundamental properties: Quaternion convolution and Fourier transform

•We introduce a novel so-called (2,2)-model or algebra with associative and commutative multiplication properties for signal /image processing applications.•We describe two discrete quaternion Fourier transforms working on the (2,2)-model.•We present an effective procedure for computing the aperiodic quaternion convolution in the frequency domain.•We show the benefits and validate of our concept on 1-D signal filtering applications.