Conventional　analog-to-information　converter　(AIC)　frameworks　employ　a　discrete-time　synthesis　sparse　model　to　deal　with　analog　signals,　which,　however,　induces　a　challenging　basis　mismatch　problem.　In　this　paper,　we　propose　a　novel　AIC　framework,　called　generalized　AIC　(G-AIC),　to　tackle　this　issue.　In　the　new　method,　an　analysis　sparse　model　is　taken,　for　the　first　time,　as　the　prior　information　of　analog　signals　being　sampled　at　sub-Nyquist　rate.　Through　the　joint　optimization　for　the　discretization　operator　and　its　analysis　sparse　operator,　the　C-AIC　removes　the　model　error　between　an　analog　signal　and　its　equivalent　discrete　samples.　To　validate　the　C-AIC　framework,　we　design　a　single　channel　G-AIC　system　based　on　switched-capacitor　(SC)　circuits.　The　circuit　design　is　presented　at　the　theoretical-level,　the　system-level,　and　the　transistor-level.　Numerical　simulations　demonstrate　the　C-AIC　system　can　well　restore　an　analog　signal　from　its　sub-Nyquist　measurements,　even　though　its　sparse　basis　is　unknown.　Compared　with　two　state-of-the-art　AIC　systems,　the　new　design　can　achieve　at　least　2d　B　reconstruction　gain.　In　brief,　the　proposed　method　provides　a　promising　alternative　to　exploit　analog　signals　in　sub-Nyquist　sampling　systems.