TITLE:
Enhanced Frequency Resolution in Data Analysis
AUTHORS:
Luca Perotti, Daniel Vrinceanu, Daniel Bessis
KEYWORDS:
Frequency Resolution; Z-Transform; Padé Approximations
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.3 No.3,
September
5,
2013
ABSTRACT: 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.