Multirate systems have been an active research area in recent years due to their wide range of applications in control, digital signal processing (DSP) and communication systems. This thesis aims to carry over control-theoretic methodologies to develop design and estimation methods for multirate DSP and communication systems.

A composite error criterion is proposed to capture all three traditional distortions for the multirate filterbank-based transceiver model that is a unifying framework able to encompass existing modulation and equalization schemes. Incorporating noise attenuation and filter bandlimiting properties into this error criterion, an optimal design procedure is developed and applied to the transceiver design, yielding a finite impulse response (FIR) transceiver th at has good frequency-selectivity properties and is close to perfect reconstruction. A least squares solution is given in closed form in each iteration for which the algorithm is easy to implement. Next, the stopband energy and passband magnitude constraints are directly incoporated into transmultiplexers design, thus taking a step forward in addressing practical issues about frequency selectivity. Further, in order to design transmultiplexers with low implementation complexity, a novel method is developed and it can not only achieve close-to-perfect reconstruction but also obtain most appropriate filter length. The recursive feature of the algorithm greatly improves the computation efficiency.

For crosstalk estimation in digital subscriber line (DSL) services, a multi-channel multirate DSL model is proposed and a multirate recursive least squares identification algorithm is developed. and an upper bound of the parameter estimation error is given. When the model order is unknown, a recursive algorithm is developed to identify the crosstalk model order and parameters simultaneously.

Finally, several open problems are listed as our future research directions.