The spectral digital signal processing methods for narrow-band acoustic signals are considered. One of the main parameters of spectral signal processing, spectral analyze resolution, is optimized earlier but only by using the energy criterion of optimality---the signal/noise ratio. In the present work, an optimization problem for the spectral analyze resolution was formulated and solved by using probability criterion of optimality, false-alarm probability for signal detection. It was considered a mixture of narrow-band signals and noisy interference and two important practical cases: (1) known center frequencies of signals; (2) unknown center frequencies of signals. A new nontraditional common results is obtained; it is shown that under final signal duration, optimum resolution mismatches substantially with a width of spectral signal density which allows considerable simplification hardware realization of spectral digital signal processing methods.