On circularity of complex-valued radar signals

Tapering Promotes Propriety for Fourier Transforms of Real-Valued Time Series

“…This statement is quite vague and the purpose of the current paper is to explore the issue much further, and in particular look at the interaction between tapering and propriety. (Tapering is not mentioned in [9] or [16].) We find that impropriety is worse at frequencies where power is relatively low in comparison to any high power peaks in the spectrum, i.e., those frequencies where the spectral estimate is subject to 'side-lobe leakage.'…”

“…(Only positive frequencies are shown because of the symmetry about zero.) B is calculated using (16). Half this width, B/2, is also marked by a vertical dashed line in each plot.…”

“…Propriety of J(f ) was briefly considered in [9], (and used by [16] in the context of radar signals), where it was concluded that "Unless the noise is white, the circular anomaly will usually not be zero, and the second-order statistics must take a prescribed form that is not circular." This statement is quite vague and the purpose of the current paper is to explore the issue much further, and in particular look at the interaction between tapering and propriety.…”