Computing the ambiguity surface

The computation of the discrete ambiguity function is considered. Two straightforward methods are developed depending upon whether we write the discrete ambiguity as a filter or as a discrete Fourier transform. A modification of the transform method produces an approximation to the discrete ambiguity function, but has increased computational efficiency. This method is based on a recent work [1]. In most major applications, we need to compute limited portions of the DFT description of the discrete ambiguity function. To do so, we first pass a long sequence of "data" through a decimated FIR filter, and then use the FFT algorithm on the results. The Remez algorithm is employed to control the resulting aliasing errors. In the final section, approximation theory is applied directly to the problem of computing the discrete ambiguity function. The algorithm required to carry out the necessary computations turns out to be the same as on the prevoius approximation method based on a decimating FIR filter.