As with the analyses in the Lv’s distribution,^{25} the principle of the stationary phase is utilized. Display Formula
$Dp1,p2,cros,2(ft\tau ,f\tau ,\xi )=Ds,cros,2\u2032\u2032(ft\tau ,f\tau ,\xi )+Ds,cros,2\u2032\u2032\u2032(ft\tau ,f\tau ,\xi )=4\xi |f\tau \Delta \gamma p1,p2||\xi 2ft\tau 2+\Delta \gamma p1,p22|3/2\xb7cos{sgn(\Delta \gamma p1,p2)\pi 4[1+sgn(\xi 2ft\tau 2+4\Delta \gamma p1,p22)]+2f\tau 2\Delta \gamma p1,p2\xi 2ft\tau 2+\Delta \gamma p1,p22\u2212\Delta fp1,p222\Delta \gamma p1,p2}.$(27)
Then the 2-D convolution theorem is utilized to obtain Display Formula$Ds,cros(ft\tau ,f\tau ,\xi )=8Ap1Ap2\xi |f\u02dc\tau \Delta \gamma p1,p2||\xi 2f\u02dct\tau 2+\Delta \gamma p1,p22|3/2\xb7cos{sgn(\Delta \gamma p1,p2)\pi 4[1+sgn(\xi 2f\u02dct2+\Delta \gamma p1,p22)]+2f\u02dc\tau 2\Delta \gamma p1,p2\xi 2f\u02dct\tau 2+\Delta \gamma p1,p22\u2212\Delta fp1,p222\Delta \gamma p1,p2}.$(28)