Improved bispectrum estimation based on modified group delay

Abstract

This article proposes an improved estimation method for the bispectrum of a system or signal, by applying the modified group delay (MMGD) in the bispectrum domain. To achieve a higher frequency resolution, the bispectrum is computed in frequency domain and further to reduce the variance preserving the frequency resolution, MMGD is applied in the bispectrum domain. The proposed method due to its better frequency resolution not only properly detects the phase coupled frequencies but also reduces the bispectrum magnitude estimate’s variance significantly compared to that of biperiodogram. Compared to the proposed method, though the windowed bispectrum (WB) provides a better reduction in variance, it is unable to detect the coupled frequencies due to its poor frequency resolution. For an AR process in the presence of noise (SNR = 4 dB), the system magnitude estimate by the proposed method has a 27.63% lower normalized sum sample mean square error (NSSMSE) than that by the WB. Also for a non-minimum phase system in presence of noise (SNR = 7 dB), the phase estimation by the new approach has 8.6% lower NSSMSE than that by WB and also it is marginally better than that obtained by applying MMGD in system group delay domain.