| Abstract: |
In this thesis, smoothness of sampled real-world signals is exploited through the applicationof polynomial predictive filters. The principal reason for employing the polynomial signalmodel is principally twofold: firstly, assuming that the sampling rate is adequate, all real-world signals exhibit piecewise polynomial-like behavior, and secondly, polynomial-basedsignal processing is computationally efficient. By definition, polynomial predictive filtersprovide estimates of future values of polynomial-like signals. Thus, the potential applicationsof this research include a vast number of different delay sensitive operations on measurementslike temperature, position, velocity, or power, especially in control engineering field.The polynomial-based predictive signal processing is a well-known technique, but polyno-mial-predictive filters have had severe drawbacks, which have hindered their application;their white noise attenuation is generally low, or they exhibit considerable passband gainpeaks, rendering them unattractive for most applications. It has been possible to design HRpolynomial predictors, which exhibit applicable magnitude response properties, but the se-vere problem with them, as well as with the FIR polynomial predictors, has been that theyhave generally not been implementable in low-precision fixed-point environments becauseof their coefficient quantization sensitivity. In this thesis, coefficient quantization error-freedesigns of both FIR and HR polynomial predictors are presented, thus providing methodsfor overcoming the above drawbacks and design problems.Polynomial differentiators are closely related to polynomial predictors; they are derived in asimilar fashion, have design problems of a similar nature, and have applications in the con-trol field. Both of these two filter types are discussed in this thesis; the proposed designmethods are applicable to both of them.The implementation aspects of polynomial predictors and differentiators investigated hereare also connected to the practical requirements of the application, namely delay alleviationin closed loop transmitter power control of multi user mobile communications systems. Par-ticularly, if predictive received power level estimation is implemented in handheld mobileterminals, this application specifies the implementation criteria as requirements on low im-posed computational burden, low power consumption, and compact hardware size. Allthese criteria are met by providing the desired functionality using a small number of fixed-point arithmetic operations. Taking into account the results presented in this thesis, poly-nomial prediction fulfills these criteria.In this thesis, digital filter design methodologies are advanced by first-time introduction ofexact low-degree polynomial prediction and discrete time differentiation in low-precisionfixed-point computing environments, with, for example, 8 or 16 bits. Polynomial predictionis shown advantageous in the closed loop transmitter power control system application, andin comparisons with more complex and flexible predictors, it is shown to be a highly effi-cient method for this particular application.This thesis is seen as contributing to advances in practical polynomial predictor and differ-entiator design methods, and thereafter studies the application of polynomial predictors inmobile communications system transmitter power control. This research will be of interestto signal processing, control, and communications engineers and researchers alike.
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