Enhancement of Poles in Spectral Analysis

This paper presents a new technique for detecting a small pole in the presence of a nearby strong pole. By simultaneously applying the chirp z-transform (CZT) and a recently developed window, the new technique is shown to be able to detect and resolve a small pole. The CZT is efficient since it employs the fast Fourier transform (FFT) to evaluate a convolution. But unlike the FFT which is limited to the evaluation of the spectrum on the jw-axis, the CZT can evaluate the z-transform on the whole complex plane. And with the use of the new window, which is designed to have a near-sidelobe level of any specified value, the CZT is shown to be able to resolve two closely spaced poles with a large difference in amplitudes. Unlike the Prony's method, the new technique does not require predetermining the system order. No matrix inversion or solution of polynomial roots is required. Further, the new technique is a linear operation. Thus even under noisy environments it yields accurate, stable results for extraction of poles from transient response data.