Efficient implementation of discrete Pascal transform using difference operators

Introduction: Transformations are vital to any engineering subject, in particular, to electrical engineering. Fourier series, Laplace transform, Fourier transform and their counterparts in the discrete-time domain, are the fundamental tools for signal processing, communication and control engineering. Recently, the discrete Pascal transform (DPT) has been introduced to process discrete signals [1]. The transform has found applications in edge detection [2], bump detection and watermarking [1]. Various features of the DPT, such as computational complexity [3, 4], hardware implementation [5], interpolation using DPT [6] and the link between Poisson sequences and Laguerre polynomials [7], have been reported. The major contributions of this Letter are: (i) to provide an alternative definition of the transform using the difference operator, (ii) to provide efficient modularised implementations, and (iii) to extend the transform to non-square 2D applications.