Mu ltirate Signal Processing Concepts in Digital Commu nications Bojan Vrcelj In Partial Fu lfillment of the Requ irements for the Degree of Doctor of Philosophy California Institu te of Technology Pasadena, California 2004 (Su bmitted Ju ne 2, 2003) Abstract Multirate systems are building blocks commonly used in digital signal processing (DSP). Their function is to alter the rate of the discrete-time signals, which is achieved by adding or deleting a portion of the signal samples. Multirate systems play a central role in many areas of signal processing, such as filter bank theory and multiresolution theory. They are essential in various standard signal processing techniques such as signal analysis, denoising, compression and so forth. During the last decade, however, they have increasingly found applications in new and emerging areas of signal processing, as well as in several neighboring disciplines such as digital communications. The main contribution of this thesis is aimed towards better understanding of multirate systems and their use in modern communication systems. To this end, we first study a property of linear systems appearing in certain multirate structures. This property is called biorthogonal partnership and represents a terminology introduced recently to address a need for a descriptive term for such class of filters. In the thesis we especially focus on the extensions of this simple idea to the case of vector signals (MIMO biorthogonal partners) and to accommodate for nonintegral decimation ratios (fractional biorthogonal partners). Some of the main results developed here pertain to a better understanding of the biorthogonal partner relationship. These include the conditions for the existen...
