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In this paper, we study the convolution structure in the special affineFourier transform domain to combine the advantages of the well known specialaffine Fourier and Stockwell transforms into a novel integral transform coinedas special affine Stockwell transform and investigate the associated constant Qproperty in the joint time frequency domain. The preliminary analysisencompasses the derivation of the fundamental properties, Rayleighs energytheorem, inversion formula and range theorem. Besides, we also derive a directrelationship between the recently introduced special affine scaled Wignerdistribution and the proposed SAST. Further, we establish Heisenbergsuncertainty principle, logarithmic uncertainty principle and Nazarovsuncertainty principle associated with the proposed SAST. Towards theculmination of this paper, some potential applications with simulation arepresented.

Special Affine Stockwell Transform Theory, Uncertainty Principles and Applications