Scaled window decompositions for reduced interference time–frequency distributions

Abstract

The reduced interference distribution (RID) is a time–frequency distribution (and a member of Cohen’s class) which enjoys a number of desirable properties. A simple design procedure, which allows one to start with a simple primitive function, h(t) is provided. When h(t) is equipped with certain constraints, a full RID kernel within Cohen’s class can easily be constructed. RID computation has traditionally been achieved by the ‘‘outer-product methods,’’ wherein the kernel is convolved with the local autocorrelation of the signal along time for each lag value. Amin, Cunningham, and Williams and others have provided alternative methodologies; the ‘‘inner-product methods.’’ This involves decomposition of the kernel into an orthonormal set of windows. Each window is used to form an STFT. We have found that a truncated set of windows can be used to closely approximate RIDs. Wavelet and scale-related windows can be used to generate a discrete time–frequency distribution that closely approximates RIDs. Illustrations of the contributions of each of the windows will be provided. This method of decomposition of the RID leads to new insights into the nature of time–frequency distributions as well as providing a method for very fast computation.