Simulation experiments to compare the signal detection properties of DFT and MEM spectra

Abstract

Four simulation experiments have been carried out to compare the statistics of threshold detection of a complex sinusoid in additive noise using the Burg maximum entropy method (MEM) and the discrete Fourier transform (DFT) technique. The results indicate that, in the presence of additive white noise, the DFT consistently provides a higher signal detection probability P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> and a more accurate estimate of signal frequency than the MEM. In the presence of colored noise, the DFT provides a higher P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> when signal-to-noise ratio (SNR) is high, or when signal detection is carried out in the low false-alarm probability P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</inf> region. Only in the very restricted case of low SNR together with a high P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</inf> and the signal far away from the center of the noise band does the MEM provide a higher P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> than the DFT.