Warped linear time invariant systems and their application in audio signal processing

The main goal behind coordinate transformation (warping) of a Linear Time Invariant (LTI) system is to represent its signals in terms of new basis functions that better suit the application in hand. Unitary operators simplify the analysis considerably; therefore, they are used to derive the relations between variables in the original and warped domains. These relations show that an LTI system can be warped by processing its input signals with a unitary warping transformation. An efficient implementation of this warping transformation, that is based on a nonuniform sampling theorem, is given; which allows applying the warping principle in real-time applications. As an example of exploiting this technique, it is shown that sampling an audio signal at exponentially spaced moments changes the underlying coordinates of its signal processing system to suit those of the human auditory system.