Sine wave fit algorithm based on total least-squares method with application to ADC effective bits measurement

Sinewave fit is a fundamental task in many test and measurement systems. The characterizations of analog-digital converters and digital oscilloscopes are two examples. In this paper, we present a high-performance (i.e., high-precision and high-speed) algorithm to estimate the four parameters of a sinewave from a sample data record. By the use of trigonometric identity, we propose a frequency estimator that turns the nonlinear estimation problem into a linear one. Thus, the difficulty of the traditional nonlinear least-squares sinewave fit method is attenuated. The total least-squares method is used to estimate four parameters of a sinewave in order to minimize the estimation errors in the sense of l₂ norm. Simulation results exhibit that the proposed method gives superior performance over traditional ones and achieves excellent estimation of the true resolution of the simulated ideal ADC. This new algorithm is noniterative and gives swift and consistent results.