Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Joint fundamental frequency and order estimation using optimal filtering | Christensen et al. EURASIP Journal on Advances in Signal Processing 2011 2011 13 http content 2011 1 13 o EURASIP Journal on Advances in Signal Processing a SpringerOpen Journal RESEARCH Open Access Joint fundamental frequency and order estimation using optimal filtering Mads Gr sb0ll Christensen1 Jesper Lisby H0jvang3 Andreas Jakobsson2 and S0ren Holdt Jensen3 Abstract In this paper the problem of jointly estimating the number of harmonics and the fundamental frequency of periodic signals is considered. We show how this problem can be solved using a number of methods that either are or can be interpreted as filtering methods in combination with a statistical model selection criterion. The methods in question are the classical comb filtering method a maximum likelihood method and some filtering methods based on optimal filtering that have recently been proposed while the model selection criterion is derived herein from the maximum a posteriori principle. The asymptotic properties of the optimal filtering methods are analyzed and an order-recursive efficient implementation is derived. Finally the estimators have been compared in computer simulations that show that the optimal filtering methods perform well under various conditions. It has previously been demonstrated that the optimal filtering methods perform extremely well with respect to fundamental frequency estimation under adverse conditions and this fact combined with the new results on model order estimation and efficient implementation suggests that these methods form an appealing alternative to classical methods for analyzing multi-pitch signals. Introduction Periodic signals can be characterized by a sum of sinusoids each parametrized by an amplitude a phase and a frequency. The frequency of each of these sinusoids sometimes referred to as harmonics is an integer multiple of a fundamental frequency. When observed such signals are commonly corrupted by observation noise and the .
