Basis Selection Problems for different Performance Measures - Fundamental Limits

The questions whether or not a system can be approximated by an orthonormal filter bank, and how complex and robust such an approximation will be, are of great interest in different areas such as system-, control-, and information theory. However, every discipline has a different view with different performance criteria on these problems. This paper investigates the basis selection problem for different applications, starting with a stability problem from system theory, looking on entropy based methods from the information theory, and investigates the peak-to-average power ratio problem in communication systems.