Selected Topics in Frequency Estimation

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 large number of applications that involves frequency estimation, e.g radar applications using frequency modulated continuous wave (FMCW) techniques where the distance to the target is embedded in the frequency, resonance sensor system where the output signal is given as the frequency displacement from a nominal frequency, in radio frequency identification systems (RFID) where frequency modulation is used in the communication link, etc. The requirement on the frequency estimator varies with the application but typical issues are: accuracy, processing speed or complexity, and ability to handle multiple signals. Many of the problems have been solved but there still exist several open questions. The first part of this thesis addresses the problem of frequency estimation using low complexity algorithms. One way of achieving such an algorithm is to use 1-bit quantized samples of the input signal. Frequency estimation using look-up tables has been studied and the properties of such an estimator are presented. By analyzing the look-up tables using the Hadamard transform a novel type of low-complexity frequency estimators is proposed. They use operations such as binary multiplication and addition of precalculated constants. This fact makes it suitable in applications where low complexity is a major issue. A hardware demonstrator using the table look-up technique has been build and a short description of it is included in the thesis. Today, the interest of using digital signal processing instead of analog processing is almost absolute. Accordingly, analog-to-digital converters (ADC) are used in order to digitalize the analog input before digital processing is taken place. The ADC performance is measured according to the IEEE Standard 1241. The waveform fitting method included