The article describes the typical problems of the Doppler frequency shift (DFS) and its sign determination in a continuous-wave and pulse radars using radiophotonic technologies in single- and multi-target tracking modes. The structure of the hardware-software spectrum analyzer and the variants of its mathematical implementation for solving these problems are proposed. The analyzer is functionally universal, however, its main purpose is to solve the problems of the magnitude and sign determination of the DFS using a radiophotonic device based on tandem single-port amplitude and phase modulators (TAPM) in the radar. For the single-target continuous radar tracking mode, a hardware linear filter method with an oblique frequency response and analysis of pairwise beat frequencies is proposed, and for multi-target tracking, it is supplemented by an FFT with further analysis of all received components by scanning with a software ultra-narrow band filter. The absolute error in the DFS determination by the frequency of information signals depends on the bandwidth of the software ultra-narrow band filter (units of Hz). The relative error in the amplitudes of information signals determination does not exceed ±10 -3 in almost the entire range of amplitudes of the hardware linear filter. The ratio D of the obtained amplitudes for a pair of DFS information frequencies assigned to a specific target allows determining its sign: with D<1, the target is receding, with D>1, the target is approaching. Using a method similar to the method for multi-target tracking of a continuous radar, typical problems of the DFS and its sign determination in the pulse radars can be solved.