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We prove that mixtures of continuous alphabet constant modulus sources can be identified with probability 1 with a finite number of samples (under noise-free conditions). This strengthens earlier results which only considered an infinite number of samples. The proof is based on the linearization technique of the analytical constant modulus algorithm (ACMA), together with a simple inductive argument. We then study the finite-alphabet case. In this case, we provide a subexponentially decaying upper bound on the probability of nonidentifiability for a finite number of samples. We show that under practical assumptions, this upper bound is tighter than the currently known bound. We then provide an improved exponentially decaying upper bound for the case of L-PSK signals (L is even).