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Improving the lifetime of wireless sensor networks (WSNs) is directly related to the energy efficiency of computation and communication operations in the sensor nodes. Compressive sensing (CS) theory suggests a new way of sensing the signal with a much lower number of linear measurements as compared to the conventional case provided that the underlying signal is sparse. This result has implications on WSN energy efficiency and prolonging network lifetime. In this paper, the effects of acquiring, processing, and communicating CS-based measurements on WSN lifetime are analyzed in comparison to conventional approaches. Energy dissipation models for both CS and conventional approaches are built and used to construct a mixed integer programming framework that jointly captures the energy costs for computation and communication for both CS and conventional approaches. Numerical analysis is performed by systematically sampling the parameter space (i.e., sparsity levels, network radius, and number of nodes). Our results show that CS prolongs network lifetime for sparse signals and is more advantageous for WSNs with a smaller coverage area.