Characteristic functions in radar and sonar

We often encounter problems that involve either nonlinear or multi-dimensional combinations of random variables. One would like to be able to determine the probability density function of these combinations. The individual components that contribute to the combination are assumed known, but the combination is not known. Computations to determine this combined PDF axe tedious and difficult to accomplish in most cases. We propose a simpler means to bypass many of these difficulties. By using Fourier analysis and application of the definition of the Dirac delta function, the proper form the combined PDF is obtained with considerable simplification. The motivation for this is engineering applications that occur frequently in radar applications that involve combinations of probability density functions.