This thesis is concerned with the issues of design and optimisation of digital filters and multirate filter banks. The main focus and contribution of this thesis is to apply the genetic algorithm (GA) technique and to draw some comparison with the standard gradient and non-gradient based optimisation methods. The finite word length (FWL) constraint affects the accuracy of a real-time digital filter requency response. For the case of digital filters, this study is concerned with the optimisation of FWL coefficients using genetic algorithms. Some comparative study with the simple hill climber algorithms is also included. The outcome of this part of the study demonstrates a substantial improvement of the new results when compared with the simply rounded FWL coefficient frequency response. The FWL coefficient optimisation process developed in the earlier Chapters is extended to the field of multirate filter banks. All multirate filter banks suffer from the problems of amplitude, phase and aliasing errors and, therefore, constraints for perfect reconstruction (PR) of the input signal can be extensive. The problem, in general, is reduced to relaxing constraints at the expense of errors and finding methods for minimising the errors. Optimisation techniques are thus commonly used for the design and implementation of multirate filter banks. In this part of the study, GAs have been used in two distinct stages. Firstly, for the design optimisation so that the overall errors are minimised and secondly for FWL coefficient optimisation of digital filters that form the sub-band filters of the filter bank. This process leads to an optimal realisation of the filter bank that can be applied to specific applications such as telephony speech signal coding and compression. One example of the optimised QMF bank was tested on a real-time DSP target system and the results are reported. The multiple M-channel uniform and non-uniform filter banks have also been considered in this study for design optimisation. For a comparative study of the GA optimised results of the design stage of the filter bank, other standard methods such as the gradient based quasi-Newton and the non-gradient based downhill Simplex methods were also used. In general, the outcome of this part of study demonstrates that a hybrid approach of GA and standard method was the most efficient and effective process in generating the best results.

Global Positioning Systems (GPS) is undergoing stunning changes and upgrades which will enhance the Civil and Military users. This modernization included new satellite signals for Civil and Military purposes which benefits the fundamental signal acquisition and tracking of the GPS receiver. These new signals enable a new family of alternatives for mitigating the ionospheric errors that currently limit the GPS accuracy [16]. A new Civil signal L2 Civil (L2C) was commissioned on the L2 frequency which could have ionospheric error elimination capability, with better cross correlation, Data recovery performance, and threshold tracking. The complex structure of the signal calls for new Acquisition approaches which are implementable with limited computational burden. This thesis proposes an Acquisition methodology to acquire the Code phase offset and Carrier frequency offset of the L2C signal which can be implemented in real time. The algorithm employs a serial code search for Code Phase by retaining the original sampling frequency `fs' and implements a FFT search for carrier frequency offset with a reduced sampling frequency of `fs/M' where `M' is the decimation rate. Multirate Filters are employed for reducing the sampling frequency. After the Acquisition is performed, the values are passed onto the Phase Lock Loop (PLL) and Delay Lock Loop (DLL) to further synchronize the Code Phase and Carrier frequency. The algorithm was tested on a real data set for the performance evaluation of Acquisition and Tracking, and the navigation bits were extracted and the results discussed.