Number theory based signal conversion and processing techniques - Vun, Chan Hua. (2012)
While number theory has often been shown to possess great potentials for simplifying the execution of sophisticated signal processing routines, its practical applications typically need powerful computing resources and frequently rather complicated hardware circuitry in actual implementations. One such example is the residue number system (RNS) that theoretically can allow computations that involve large numbers to be performed using multiple small numbers in a parallel and independent manner, hence enabling faster processing speed and higher throughput. However, its practical applications are usually deterred by various implementation issues such as the difficulties in performing the binary-to-RNS forward conversion process, the inconvenience encountered during the execution of the modulo operation and the complication involved in performing the RNS-to-binary reverse conversion process. In this thesis, we propose novel applications of the RNS principles in two areas related to signal processing that circumvent some of these practical problems encountered when executing RNS based signal processing functions.