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This paper presents random permutations and their effects when they are applied to a random sequence. Random permutations are the digital implementation of continuous time "Periodic Clock Changes". Continuous periodic clock changes have been already applied for multiple access and modulation purposes. It is shown that a random permutation applied to an input sequence with band-limited power spectrum can give a spreaded sequence with white power spectrum. Closed forms of the power spectral density of the interleaved sequences are given and simulations are presented. When the length of the permutation is large, it is shown that the new interleaved sequence power spectrum converges towards a white noise except for the null frequency, where the power spectrum remains the same as the input sequence. These results have an application to interleaving (random or deterministic), chip interleaving and more generally in spread spectrum techniques.