The Spectrum Sliding Analysis (SSA) is a dynamic spectrum analysis in which the next analysis interval differs from the previous one by including the next signal sample and excluding the first one from the previous analysis interval (Dillard 1967, 1973, 1977). Such spectrum analysis is necessary for time-frequency localization of analyzed signals with given peculiarities (Tolimieri and An 1998). Using the well-known Fast Fourier Transform towards this aim is not effective. Recursive algorithms which use one complex multiplication for computing one spectrum sample during each analysis interval are more effective. The author improved one such algorithm so that it becomes possible to use one complex multiplication for computing two, four, and even eight (for complex signals) spectrum samples simultaneously. Problems of realization and application of the SSA are considered in the book, which is intended for students and specialists in Digital Signal Processing.