This paper considers a cost function level analysis of the Sum-squared Autocorrelation Minimization (SAM) channel shortening algorithm. We point out that the actual cost the blind adaptive stochastic gradient descent algorithm is minimizing is only indirectly related to the sum squared autocorrelation. We study the asymptotic regimes under which the actual cost yields a reliable surrogate for the sum squared autocorrelation. We investigate the relationship between the minima of the actual cost and sum squared autocorrelation. We also study the upper bound of the approximate cost as a function of the window size used in the approximate autocorrelation calculation.