Suprajitno and Greenhalgh (1985) used contour-slice filtering in the FK domain to separate up-going and down-going wavefields to facilitate vertical seismic profile (VSP) data processing. Berkhout (2014a; 2014b; 2014c) exploited the wavefield separation idea by directly resorting to a Bremmer's series-like concept in the modeling engine and so proposed two new seismic imaging technologies, namely full-wavefield migration (FWM) and joint migration inversion (JMI). Liu et al. (2011) pointed out the origin of the low-frequency noise in reverse-time migration (RTM) images and then proposed an imaging condition, based upon wavefield separation, to suppress such low-frequency noise. Fei et al. (2015) and Wang et al. (2016) used wavefield separation by double Hilbert transformations to remove false structures in RTM images. Zheng et al. (2018) used double Hilbert transformations to do up/down separation of wavefields in 3D forward modelling. To our knowledge wavefield separation has been limited to either vertical or horizontal propagation directions, and the industry lacks a general theoretical framework that is capable of handling wavefield separation at an arbitrary propagation direction. In this abstract we show that with the input data properly organized, FK filtering is capable of separating wavefields at an arbitrary propagation direction. We design this FK filter explicitly, and mathematically show that wavefield separation via double Hilbert transformations is equivalent to using the same FK filter.