Abstract

In this paper, we propose a method to solve the instantaneous frequency estimation problem at each point of the digital signal sequence obtained by digitizing the chirped signal by combining the projection method with the stochastic resonance method. This problem is chosen as the estimation of the instantaneous frequency (instantaneous frequency at the midpoint of a frame) at the center of the frame, and then we can solve the above problem through the orthogonal projection of a space of which dimension is equal to the frame length into a two-dimensional subspace, combined with stochastic resonance theory. Assuming this digital signal frame as a vector lying in a space of which dimension is equal to the length of the frame, we estimate the instantaneous frequency of the frame center point by finding the basis vector of the corresponding frequency that constitutes the two-dimensional subspace in which the vector is placed. By moving the center point of the frame onto each point of the digital signal sequence corresponding to a period of frequency modulation, we can obtain the overall frequency curve accurately. At this time, the basis vectors that constitute the two-dimensional subspace are constructed by reflecting the frequency modulation characteristics. The estimation results obtained in the simulation are compared with the results using the short-time Fourier transform, Wigner-Bill distribution, which are often used in the presence of noise and Doppler effects such as Doppler radar and sonar, which shows that the proposed method has very high accuracy.

Authors

Yu-Chol Jong, Jong-Gun Kim, Tok-Gil Kang, Chol-Nam Om
Kim Il Sung University, Democratic People’s Republic of Korea

Keywords

IF (Instantaneous Frequency), FM (Frequency Modulation), Stochastic Resonance, Signal Frame, Basis Vector