Secondary information from filter bank may not yield higher resolution of line

Abstract

The entropy based Hirschman optimal transform (HOT) is superior to the energy based discrete Fourier transform (DFT) in terms of its ability to separate or resolve two limiting cases of localization in frequency, viz pure tones and additive white noise. In this paper, we implement a stationary line spectral estimation method using filter banks, which are constructed with the HOT and the DFT. We combine these filter banks with the classic interpolating procedure developed by Barry Quinn to develop our line estimation algorithm. We call the resulting algorithm the smoothed HOT-DFT line periodogram. We compare its performance (in terms of frequency resolution) to Quinn's smoothed periodogram. In particular, we compare the performance of the HOT-DFT with that of the DFT in resolving two close frequency components in additive white Gaussian noise (AWGN). We find the HOT-DFT to be superior to the DFT in frequency estimation, and ascribe the difference to the HOT's relationship to entropy. It is well-known that the frequency estimation (i.e. the secondary inference that is desired from the signal model) is highly related with the modeling performance. In fact, we will show that while the residual energy is lower for the DFT filter bank, the frequency estimation error might be higher.