The　multiple　second-order　generalized　integrator　(MSOGI),　which　is　composed　of　parallel　second-order　generalized　integrators　(SOGI),　is　widely　used　in　grid　synchronization　and　signal　extraction,　and　it　usually　suffers　from　dc　offset　issue.　In　continuous　domain,　low-pass　filter　(LPF)　can　be　added　to　SOGI　to　eliminate　the　dc　offset　in　its　quadrature　channel.　However,　in　digital　implementation,　directly　discretized　LPF-based　methods　may　not　be　able　to　eliminate　dc　offset　and　ac　discretization　error　simultaneously,　where　the　steady-state　error　will　also　be　introduced　by　the　conventional　frequency-locked　loop　(FLL).　In　this　article,　a　modified　impulse　invariant　method　is　adopted　to　discretize　SOGIs,　which　presents　zero　ac　errors　and　good　dynamics,　but　shows　dc　offset　in　both　output　channels.　Then,　an　LPF　is　introduced　to　eliminate　the　dc　offset　of　the　discrete　SOGI,　forming　a　discrete　SOGI-LPF.　And,　a　discrete　MSOGI-LPF　(DMSOGI-LPF)　is　formed　by　paralleling　multiple　DSOGI-LPFs,　which　can　extract　different　frequency　components.　Furthermore,　a　discrete　FLL　is　proposed　to　estimate　the　frequency　of　the　input　signal,　which　suppresses　the　influence　of　the　dc　offset　and　achieves　good　dynamics.　Finally,　the　stability　analysis　of　the　proposed　method　based　on　discrete　linear-time　periodic　(LTP)　model　is　provided.　The　effectiveness　of　the　proposed　method　and　its　discrete　LTP　model　are　validated　through　experimental　results.　©　1986-2012　IEEE.