A statistical treatment of the frequency spectrum intensity distribution and its characteristics of a specklegram is presented in this paper. The specklegram is assum-ed to be taken by a generalized compound-shearing photographic system without any cross overlap between the apertures at recording the shearing images. Attentions are particularly paid to the action of each "basic correlation spectrum" component and to the peripheral distribution of each spectral region. Typical experimental verifications are given. Eesults shown in this paper may be beneficial to the improvement in the filter design, the filtering operation, and tho design of aperture in a componnd-sliear-ing photographic system.