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Capacitive touch screens are ubiquitous in today's electronic devices. Improved touch screen responsiveness and resolution can be achieved at the expense of the touch screen controller analog hardware complexity and power consumption. This paper proposes an alternative compressive sensing based approach to exploit the sparsity of simultaneous touches with respect to the number of sensor nodes to achieve similar levels of responsiveness. It is possible to reduce the analog data acquisition complexity at the cost of extra digital computations with less total power consumption. Using compressive sensing, in order to resolve the positions of the sparse touches, the number of measurements required is related to the number of touches rather than the number of nodes. Detailed measurement circuits and methodologies are presented along with the corresponding reconstruction algorithm.