An exploratory investigation of the applicability of wavelets and wavelet transforms to signals that are encountered in high speed radar has been performed. The wideband cross ambiguity function (WBCAF) is calculated for two signals, the original signal and scaled and translated versions of the second. In an active sensing problem such as encountered in radar, the first signal will be known transmission and the second will be a reflected, refracted and/or reradiated version of the transmitted signa. When the two signal are correlated, a single correlation coefficient is calculated at each scale and translation value. These values can be interpreted as a representation of the actual scattering process. The approach used to calculate the WBCAF utilizes wavelet transforms, in this case splines, and can be expressed as an integral oeprator acting on the two signal wavelet transforms. The WBCAF is thus calculated entirely in the wavelet transform domain. A significant point of this formulation is that the wavelet transforms for each signal are with respect to an arbitrary mother wavelet which can be chosen a priori with the mathematical model of its time scaling and translation also known. For the work described herein, a linear chirp signal (i.e. sinusoidal wave with increasing frequency) served as the test case of transmission. Provision is made for the target or return signal generator to have significant velocities and accelerations as well.
George D. Catalano,
"Exploratory investigation of the application of wavelets to high-speed radar signals", Proc. SPIE 3723, Wavelet Applications VI, (22 March 1999); doi: 10.1117/12.342927; https://doi.org/10.1117/12.342927