International Journal of Signal Processing, Image Processing and Pattern Recognition Vol.7, No.3 (2014), pp.317-338 http://dx.doi.org/10.14257/ijsip.2014.7.3.26 ISSN: 2005-4254 IJSIP Copyright ⓒ 2014 SERSC Performance Analysis of Basis Functions in TVAR Model G. Ravi Shankar Reddy 1 and Dr. Rameshwar Rao 2 1 Dept.of ECE, CVR College of Engineering, Hyderabad, India 2 Vice - Chancellor, JNT University, Hyderabad, India 1 ravigosula_ece39@yahoo.co.in, 2 rameshwar_rao@hotmail.com Abstract 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. Keywords: Instantaneous frequency estimation, basis functions, Time-varying autoregressive model, nonstationarysignal 1. Introduction Nonstationary signal modeling is a research topic of practical interest, because most temporal signals encountered in real applications, such as speech, biomedical, seismic and radar signals have time-varying statistics[1, 2].The problem of time dependency was usually circumvented by assuming local stationary over a relatively short time interval, in which stationary system identification and analysis techniques are applied. However, this assumption is not always suitable, and methods for nonstationary processes are needed. Nonstationary signal analysis methods can be categorized into nonparametric and parametric [3]. The nonparametric approaches are based on time-dependent spectral representations, and include the short-time Fourier transform, the time frequency distribution and the evolutionary spectrum due to the uncertainty principle, one cannot get both high time and frequency resolutions using these nonparametric methods[4] The parametric approaches are based on the linear time-varying (TV) model, in which a nonstationary process is represented using an AR, MA or ARMA model with parameters changing with time. The TV spectrum can be estimated from the TV model parameters, and the instantaneous frequency of the nonstationary signal can be extracted. In contrast with nonparametric approaches, good accuracy in signal representation and high frequency resolution in spectral estimation can be obtained by using parametric approaches even for short data sequences [5] Online Version Only. Book made by this file is ILLEGAL.