This paper presents a linear shift-invariant system euqivalent to morphological dilation for a memoryless uniform source in the sense of the power spectral density function, and comares it with dialtion. This equivalent LSI system is found through spectral decomposition and, for dilation and with windwo size L, it is shown to be a finite impulse response filter composed of L-1 delays, L multipliers and three adders. Th ecoefficients of the equivalent systems are tabulated. The comparisons of dilation and its equivalent LSI system show that probability density functions of the output sequences of the two systems are quite different. In particular, the probability density functon from dilation of an independent and identically distributed uniform source over the unit interval (0, 1) shows heavy probability in around 1, while that from the equivalent LSI system shows probability concentration around themean vlaue and symmetricity about it. This difference is due to the fact that dilation is a non-linear process while the equivalent system is linear and shift-ivariant. In the case that dikation is fabored over LSI filters in subjective perforance tests, one of the factors can be traced to this difference in the probability distribution.