Cheng, Chun Hing

The discrete two‐dimensional (2D) S‐transform (ST‐2D) is a space‐frequency representation that provides the local spectrum at each pixel in an image. The inherent localisation properties of the ST‐2D make it a preferred candidate for space‐frequency analysis. However, the ST‐2D is sensitive to the image rotation. This limits its use in many image processing applications such as texture analysis. This study describes the rotational sensitivity of the ST‐2D, and explains how this limits its application. To overcome these problems, a novel rotationally invariant S‐transform (RIST) is formulated, and its rotational invariance is investigated. The RIST can provide approximate rotational invariance for magnitudes and complex values over a wide range of rotation angles, but with a trade‐off of higher computation time. The RIST may be useful for many medical, scientific and industrial applications.

S ‐transform (ST) is a time–frequency representation (TFR) that is popularly used in a variety of applications, but prohibitive in both storage and computation for large time series. This study proposes a one‐dimensional fast time–frequency transform (FTFT‐1D) which generates a highly compressed form of the ST directly, without the need to compute the complete ST matrix initially and compress it subsequently. The compression technique used in the FTFT‐1D helps in storage, transmission and visualisation of the ST. The FTFT‐1D encodes the TFR information uniformly and finds the local spectrum instantaneously and accurately. It is useful for real‐time applications such as monitoring, control and filtering. In addition, the FTFT‐1D is memory efficient, robust and adaptive in nature.