The continuous Hermite functions have been used for continuous signal approximations for some time. Vectors called discrete dilated Hermite functions are presented in this paper that model digital signals in a similar way, often with excellent compression capabilities. The dilation feature is important for many applications, and the ability to generate orthonormal vectors efficiently that approximate dilated Hermite functions is first reported in this paper. Computationally efficient approximations to the QRS complex of ECG signals are presented as particular examples.