Selected topics in frequency estimation
Abstract: Frequency estimation has been studied for a number of years.One reason for this is that the problem is easy to understand,but difficult to solve. Another reason, for sure, is the largenumber of applications that involves frequency estimation, e.gradar applications using frequency modulated continuous wave(FMCW) techniques where the distance to the target is embeddedin the frequency, resonance sensor system where the outputsignal is given as the frequency displacement from a nominalfrequency, in radio frequency identification systems (RFID)where frequency modulation is used in the communication link,etc. The requirement on the frequency estimator varies with theapplication but typical issues are: accuracy, processing speedor complexity, and ability to handle multiple signals. Many ofthe problems have been solved but there still exist severalopen questions.The first part of this thesis addresses the problem offrequency estimation using low complexity algorithms. One wayof achieving such an algorithm is to use 1-bit quantizedsamples of the input signal. Frequency estimation using look-uptables has been studied and the properties of such an estimatorare presented. By analyzing the look-up tables using theHadamard transform a novel type of low-complexity frequencyestimators is proposed. They use operations such as binarymultiplication and addition of precalculated constants. Thisfact makes it suitable in applications where low complexity isa major issue. A hardware demonstrator using the table look-uptechnique has been build and a short description of it isincluded in the thesis.Today, the interest of using digital signal processinginstead of analog processing is almost absolute. Accordingly,analog-to-digital converters (ADC) are used in order todigitalize the analog input before digital processing is takenplace. The ADC performance is measured according to the IEEEStandard 1241. The waveform fitting method included in thestandard has been studied in some detail. A criterion for modelselection has been derived using the parsimony principle.Further, an algorithm has been derived for estimation of theparameters of multiple sinusoids using the standardizedwave-fitting method, in combination with the expectationmaximization (EM) algorithm. The performance of the algorithmhas been studied and it is shown to produce statisticallyefficient estimates.
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