New Techniques for Design and Implementation of One- Dimensional and Two-Dimensional Multirate Digital Filter Banks

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The proposed effort is focused on study of multirate digital filter bank systems for application in one-dimensional and two-dimensional signal processing. The basic philosophy behind these systems is that if a discrete-time signal is split into a number of adjacent frequency bands, then the information in each of these bands can be coded separately. This often results in improved efficiency in storage/transmission of such signals. The improvement is a consequence of the fact that, the peculiarities of each frequency band (such as the average energy, the impact on human perception, etc.) can be exploited in the process of judging the precision required for each sub-band. In this way a signal can be compressed even if it is not ban-limited, simply by exploiting the fact that some frequency bands are more important than others. Effort will be directed towards the design and implementation of the set of filters which will perform the band-splitting and reconstruction. This is a very unconventional filter-design problem, because of aliasing and other types of distortions which result from the use of non-ideal band-splitting filters and decimators. Because of these, more complicated algebraic tools (such as paraunitariness and losslessness) are required in the design and implementation phase. In addition to its application in a number of engineering problems, the multirate filter bank structure is closely related to fundamentals of signal sampling, reconstruction, and block processing. A thorough understanding of this will therefore unify several aspects of interest to the signal- processing scientific community.