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This paper investigates the circularity of Short Time Fourier Transform (STFT) coefficients noise only, and proposes a modified STFT such that all coefficients coming from white Gaussian noise are circular. In order to use the spectral kurtosis (SK) as a Gaussianity test to check if signal points are present in a set of STFT points, we consider the SK of complex circular random variables, and its link with the kurtosis of the real and imaginary parts. We show that the variance of the SK isdoi:10.1109/tsp.2010.2081986 fatcat:2bpwxh6syna7jmqdvwsvzz2v5q