We use the name ‘fast Padé transform’ (FPT) for the Padé approximant (PA) applied to signal processing. This is done to highlight the so-called ‘transform’ feature of the PA by which the shape spectrum is obtained non-parametrically as reminiscent of the fast Fourier transform (FFT). In contrast to the FFT, the FPT can perform parametric analysis. This chapter examines resolution improvement of the FPT relative to the FFT for signal processing. Numerical examples are given to illustrate the two variants of the diagonal FPT.