Abstract
This paper presents a sliding Goertzel algorithm to accurately estimate the Fourier coefficients of multifrequency (MF) sinusoidal signals buried in noise. The algorithm is based on second-order digital resonators that are tuned at the desired frequencies. The proposed method provides the following advantages when compared with the conventional Goertzel algorithm. Firstly, it computes Fourier coefficients in less than one signal period. Therefore, faster detection time is achieved, particularly when the greatest common divisor (GCD) of the input frequencies is small. Secondly, it is less prone to numerical overflow problems in fixed-point arithmetic implementation. Thirdly, the algorithm is quite suitable for time varying sinusoidal signal estimation. An analysis is undertaken to provide additional insight into the issue of required acquisition time versus the desired accuracy for the proposed algorithm. Extensive simulation tests are also included to demonstrate its performance.
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