Time-frequency Cooperative Filter Algorithm Design And Analysis

Many natural and man-made signals, such as those used in radio physics, radar and sonar, exhibit instantaneous frequency and bandwidth. As for a common filter, it can only effectively filter out interference signals with different frequencies, which leads to unsatisfactory filtering effect. Based on time-frequency distribution, this paper proposes the time-frequency cooperative filter algorithm. The paper mainly research the variable filter algorithm based on time-frequency distribution and extended Fourier transform(EFT). The research of this paper will focus on the following aspects:1. It introduces different design methods of filters and time-frequency tool, including short-time Fourier transform, Wigner-Willie and Choi-Williams. Then it studies a new kind of Fourier transform, EFT, whose functional relations to exploit the newly defined differential operator and the time-varying bandpass region of a variable bandwidth filter(VBF). Depended on time-varying cut-off frequencies, the proposed EFT can be used for time-varying filtering. It analyzes the realization possibility of the filter in extended Fourier domain in theory.2. The paper analyses the energy distribution in time-frequency domain of chirp signal by using time-frequency tool, which is used in variable bandwidth filter algorithm based on time-frequency distribution.3. Time-frequency collaborative filter algorithm mainly involves two kinds, the first one based on the time-frequency analysis, and the second based on Extended Fourier transform. The first one depends on Choi-Williams or short time Fourier transform. Filtering threshold on the basis of time-frequency distribution affects filtering effect. In the paper applies minimum mean square error criterion to deciding filtering threshold. The proposed time-varying EFT filter is constructed by a newly defined differential operator with known boundaries of spectral supports in time-frequency domain. Simulation result shows that, compared with the fixed bandpass filter, the proposed three kinds of time-varying filters perform better in filtering effect.