Note that we have two cross-terms $LPAFpq,cross(\omega 1,\omega 2)$ and $LPAFqp,cross(\omega 1,\omega 2)$, and we only take $LPAFpq,cross(\omega 1,\omega 2)$ as an example to analyze. Obviously, $LPAFpq,cross(\omega 1,\omega 2)$ is with the form Display Formula
$LPAFpq,cross(\omega 1,\omega 2)=Dpq,cross\u222b\u2212\u221e+\u221eexp{\u2212j2\pi [\omega 1\u2212(\varphi p,1\u2212\varphi q,1)\u221212(\varphi p,2+\varphi q,2)\u221218(\varphi p,3\u2212\varphi q,3)]t}\xd7exp{\u2212j2\pi [\omega 2\u221212(\varphi p,2\u2212\varphi q,2)\u221214(\varphi p,3+\varphi q,3)]t2}\xd7exp{j2\pi [16(\varphi p,3\u2212\varphi q,3)]t3}dt,$(23)
where $Dpq,cross$ is irrelevant to the variable $t$.