A four-parameter quadratic distribution

Quadratic distributions such as time-frequency distributions and ambiguity functions have many useful applications. In some cases it is desirable to have a quadratic distribution of more than two variables. Using the technique of applying operators to variables, general quadratic distributions of more than two variables can be developed. We use this technique to develop a four-parameter quadratic distribution that includes variables of time, frequency, lag, and doppler. A general distribution is first developed and some of the mathematical properties are discussed. The distribution is then applied to the improvement of an adaptive time-frequency distribution. An example signal is shown to evaluate the performance of the technique.