Enhanced Frequency Resolution in Data Analysis

We present a numerical study of the resolution power of Padé Approximations to the Z-transform, compared to the Fourier transform. As signals are represented as isolated poles of the Padé Approximant to the Z-transform, resolution depends on the relative position of signal poles in the complex plane i.e. not only the difference in frequency (separation in angular position) but also the difference in the decay constant (separation in radial position) contributes to the resolution. The frequency resolution increase reported by other authors is therefore an upper limit: in the case of signals with different decay rates frequency resolution can be further increased.