This course covers advanced Digital Signal Processing (DSP) concepts that play a key role in state of the art technologies. Specifically, we first introduce the theory of multirate DSP such as decimators, interpolators, delay chains, blocking/unblocking operators, decimation and interpolation filters, the polyphase representation and perfect reconstruction filter banks. We also study lossless systems, linear periodically time varying systems, time-frequency representations and wavelets. We then discuss a number of related research topics such as transform and subband coding in data compression, advanced sampling theory in oversampled A/D converters, transmultiplexers and precoders in broadband wireline communication systems (e.g. xDSL systems), fractionally spaced and non-uniformly spaced equalizers in digital communications and, (multirate) DSP and wavelet applications in genomics signal processing. The course has the dual role of presenting advanced DSP tools to the general class body while preparing the more specialized student for pursuing research in the DSP area.