Widely linear (WL) receivers are able to fulfill single antenna interference cancellation (SAIC) of one rectilinear (R) (ASK, BPSK) or quasi-rectilinear (QR) (MSK, GMSK, OQAM) co-channel interference (CCI). In the presence of residual frequency offsets (FO), standard SAIC/MAIC receivers lose their efficiency and have to be extended using WL frequency shifted (FRESH) filtering, which has been done recently. However, in practice the observations are low-pass filtered before sampling and processing, which may degrade the performance. In this context, the purpose of the paper is twofold. The first one is to extend the previous pseudo MLSE-based WL FRESH receiver, for sources with differential FO, to observations which are low-pass filtered. The second one is to analyze, both analytically and by simulations, the impact of the low-pass filtering on the performance of the extended pseudo MLSE-based WL FRESH receiver