The role of integer matrices in multidimensional multirate systems

The basic building blocks in a multidimensional (MD) multirate system are the decimation matrix M and the expansion matrix L. For the D-dimensional case these are D×D nonsingular integer matrices. When these matrices are diagonal, most of the one-dimensional (ID) results can be extended automatically. However, for the nondiagonal case, these extensions are nontrivial. Some of these extensions, e.g., polyphase decomposition and maximally decimated perfect reconstruction systems, have already been successfully made by some authors. However, there exist several ID results in multirate processing, for which the multidimensional extensions are even more difficult. An example is the development of polyphase representation for rational (rather than integer) sampling rate alterations. In the ID case, this development relies on the commutativity of decimators and expanders, which is possible whenever M and L are relatively prime (coprime). The conditions for commutativity in the two-dimensional (2D) case have recently been developed successfully in [1]. In the MD case, the results are more involved. In this paper we formulate and solve a number of problems of this nature. Our discussions are based on several key properties of integer matrices, including greatest common divisors and least common multiples, which we first review. These properties are analogous to those of polynomial matrices, some of which have been used in system theoretic work (e.g., matrix fraction descriptions, coprime matrices, Smith form, and so on)

Vector space framework for unification of one- and multidimensional filter bank theory

A number of results in filter bank theory can be viewed using vector space notations. This simplifies the proofs of many important results. In this paper, we first introduce the framework of vector space, and then use this framework to derive some known and some new filter bank results as well. For example, the relation among the Hermitian image property, orthonormality, and the perfect reconstruction (PR) property is well-known for the case of one-dimensional (1-D) analysis/synthesis filter banks. We can prove the same result in a more general vector space setting. This vector space framework has the advantage that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case. Many results in 1-D filter bank theory are hence extended to the multidimensional case, with some algebraic manipulations of integer matrices. Some examples are: the equivalence of biorthonormality and the PR property, the interchangeability of analysis and synthesis filters, the connection between analysis/synthesis filter banks and synthesis/analysis transmultiplexers, etc. Furthermore, we obtain the subband convolution scheme by starting from the generalized Parseval's relation in vector space. Several theoretical results of wavelet transform can also be derived using this framework. In particular, we derive the wavelet convolution theorem

POWER REDUCTION BY DYNAMICALLY VARYING SAMPLING RATE

In modern digital audio applications, a continuous audio signal stream is sampled at a fixed sampling rate, which is always greater than twice the highest frequency of the input signal, to prevent aliasing. A more energy efficient approach is to dynamically change the sampling rate based on the input signal. In the dynamic sampling rate technique, fewer samples are processed when there is little frequency content in the samples. The perceived quality of the signal is unchanged in this technique. Processing fewer samples involves less computation work; therefore processor speed and voltage can be reduced. This reduction in processor speed and voltage has been shown to reduce power consumption by up to 40% less than if the audio stream had been run at a fixed sampling rate

Analysis and characterization of wireless smart power meter

2014 Summer.No supplementary documents submitted.Includes bibliographical references.Recent increases in the demand for and price of electricity has stimulated interest in monitoring energy usage and improving efficiency. This research work supports development of a low-cost wireless smart power meter capable of measuring RMS Values of voltage and current, real power, and reactive power. The proposed smart power meter features include matching by-device rate of consumption and usage patterns to assist users in monitoring the connected devices. The meter also includes condition monitoring to detect harmonics of interest in the connected circuits which can give vital clues about the defects in machines connected to the circuits. This research work focuses on estimating communicational and computational requirements of the smart power meter and optimization of the system based on the estimated communication and computational requirements. The wireless communication capabilities investigated here are limited to existing wireless technologies in the environment where the power meters will be deployed. Field tests are performed to measure the performance of selected wireless standard in the deployment environment. The test results are used to understand the distance over which the smart power meters can communicate and where it is necessary to utilize repeaters or range extenders to reduce the data loss. Computational requirements included analysis of smart meter front-end sampling of analog data from both current and voltage sensors. Digitized samples stored in a buffer which is further processed by a microcontroller for all the desired results from the power meter. The various stages for processing the data require computational bandwidth and memory dependent on the size of the data stream and calculations involved in the particular stage. A Simulink-based system model of the power meter was developed to report a statistic of computational bandwidth demanded by each stage of data processing. The developed smart meter works in an environment with other wireless devices which include Wi-Fi and Bluetooth. The data loss caused when the smart power meter transmits the data depends on the architecture of the wireless network and also pre-existing wireless technology working in the same environment and while operating in the same frequency band. The best approach in developing a wireless network should reduce the hardware cost of the network and to reduce the data loss in the wireless network. A wireless sensor network is simulated in OMNET++ platform to measure the performance of wireless standard used in smart power meters. Scenarios involving the number of routers in the network and varying throughput between devices are considered to measure the performance of wireless power meters. Supplementary documents provided with the electronic version of this thesis contain program codes which were developed in Simulink and OMNET++

A System Approach to the Design of Multirate Filter Banks.

This dissertation studies the design of multirate filter banks by adopting a so-called system approach. The design issue of Johnston\u27s method is first investigated in which an explicit expression of the reconstruction error is derived using Lyapunov stability theory, and new convergent iterative algorithms are proposed through non-linear optimization. The results are extended to the two-dimensional filter banks. The design issue of more general multirate filter banks is also investigated through model matching method. Using standard results from modern control theory, new design algorithms are developed which minimize the reconstruction error while completely eliminating the aliasing error. State-space realizations, inner-outer factorizations, and optimal Hankel norm approximation are used to reduce the complexity of computation and improve the accuracy of the proposed design algorithms