Analysis of Oscillation Components in Instantaneous Frequency Estimation by Finite Order 2-D Hilbert Transformer

The Hilbert transformer (HT) is widely used in the field of signal processing. The HT is also used for estimating instantaneous frequency (IF) and is utilized in the analysis of non-stationary signals. This paper describes the IF estimation using 2-D HT. An analytic image is generated from the input image and the output image by the 2-D HT. From this analytic image, the instantaneous phase and IF can be derived. In the case of finite order 1-D HT, it is known that the estimated IF includes components that are even multiples of the input signal's angular frequency, due to approximation errors occurring during filter design. It is considered that similar errors are included in the estimation of IF using the 2-D HT. Therefore, this paper analyzes the errors by the 2-D HT in the estimated IF theoretically and through simulation.