Interpolation Using the Discrete Pascal Transform

We present new techniques for performing upsampling and interpolation on discrete-time signals using the Pascal transform. These methods can be classified into two general categories: global interpolation and local interpolation by windowing. Global interpolation fits the entire signal to one continuous polynomial, which is evaluated to fill in the intermediate points. Local interpolation chooses only a subset of the signal to fit to a polynomial of lower degree, and the position of the window is shifted so as to eventually cover the entire signal. We will compare the global and local methods of Pascal interpolation to a more common technique that uses the Fourier transform.