Advances in digital computers have been spectacular but increasingly complex to model. Even the cycle-accurate simulators, which are costly to develop and run have questionable accuracy. This thesis provides a simple, accurate, scientifically proven, and analytic model to accurately predict the performance of real applications. The method creates two profiles as a function of time or problem sizes. The first profile, Hardware Signature, that reveals computer hardware speed, is obtained by running a universal benchmark, HINT or by running an analytical model, AHINT. The second profile, Application Signature (APPMAP), that divulges intrinsic application requirements, can be obtained by four different methods outlined in the thesis. The convolution of these two profiles are used to predict real application performance. The model was tested using 25000 performance measurements and was validated by determining Pearson's correlation, Spearman's rank correlation and maximum deviation from linearity. Furthermore, through the Hardware Signature of the analytical models, one can obtain precise answers to questions about optimum size of memory, caches, and the numerical precision for a given clock rate.