Application of F-test method on model order selection and related problems

Download
2015
Yazar, Alper
Signal modeling is one of the important topics of signal processing area. The input signal should be modeled with a suitable mathematical model first. In statistics related disciplines, there are information theory based criteria for model order selection topic. In this thesis work, F-test based methods are proposed on model order selection and related problems. F-test is used in statistics related disciplines. However, it is not so widely used in signal processing related problems. Solution approaches for signal processing related problems based on known F-test are contributions of this thesis work. This work is focused on signals in linear spaces. Fundamentally, F-test is a test of significance. It is used to test whether a signal model is sufficient to model the signal of interest or higher order models are needed. This test is made by using two nested models with different orders. RSS (Residual Sum of Squares) values are calculated for each model and they are compared using F-test. According to the test result, it is determined that whether the lower order model is almost good as the higher order model or the higher order model improves the accuracy significantly. The proposed method is basically an iterative application of F-test. It selects the suitable model order by applying F-test many times. In this work, some problems related with model order selection topic are solved using F-test based approaches. An analysis window length selection method for zero-crossing point estimation problem using line fit is proposed as the first example. Secondly, a method is proposed for the segmentation of multi tone signals. Similar approach is given as the third example for segmentation of FM signals. As the fourth example, a number of pole selection algorithm is proposed for all-pole signal modeling using Prony's method. Lastly, a segmentation method for damped sinusoidal signals with Prony's method is proposed. Simulation results are provided for each five problems.