Performance Analysis of Basis Functions in TVAR Model

In this paper Time-varying Auto regressive model (TVAR) based approach for instantaneous frequency (IF) estimation of the nonstationary signal is presented. Time-varying parameters are expressed as a linear combination of constants multiplied by basis functions. Then, the time-varying frequencies are extracted from the time-varying parameters by calculating the angles of the estimation error filter polynomial roots. Since there were many existing basis functions that could be used as basis for the TVAR parameter expansion, one might be interested in knowing how to choose them and what difference they may cause. The performance of different basis functions in TVAR modeling approach is tested with synthetic signals. Our objective is to find an efficient basis for all testing signals in the sense that, for a small number of basis (or) expansion dimension, the basis yields the least error in frequency. In this paper, the optimal basis function of TVAR Model for the instantaneous frequency (IF) estimation of the test signals was obtained by comparing IF estimation precise and anti-noise performance of several types basis functions through simulation.