Hãy tìm Y ( e j ω ) nếu biết. F T [ x ( n ) ] = X ( e j ω ) ; F T [ y ( n ) ] = Y ( e j ω ) với y ( n ) = j . x

$Y\left(e{}^{j\omega }\right)=\frac{1}{2}X\left(e{}^{j\left(\omega -\omega {}_0\right)}\right)-\frac{1}{2}X\left(e{}^{j\left(\omega +\omega {}_0\right)}\right)$

$Y\left(e{}^{j\omega }\right)=\frac{1}{2}X\left(e{}^{j\left(\omega +\omega {}_0\right)}\right)+\frac{1}{2}X\left(e{}^{j\left(\omega -\omega {}_0\right)}\right)$

$Y\left(e{}^{j\omega }\right)=\frac{1}{2}X\left(e{}^{j\omega }\right)+\frac{1}{2}X\left(e{}^{j\omega {}_0}\right)$

$Y\left(e{}^{j\omega }\right)=\frac{1}{2}X\left(e{}^{j\omega }\right)-\frac{1}{2}X\left(e{}^{j\omega {}_0}\right)$