A touch sensing circuit is configured to supply touch drive signals to electrodes of a touch sensitive display device and detect corresponding touch sense signals from the electrodes in response to the supplied touch drive signals, a touch sense signal indicating a change in self-capacitance of a driven electrode in response to a touch input on the driven electrode. The touch sensing circuit is further configured to integrate, for a first predetermined duration of time, a measure of each of the touch sense signals, to generate a first integrated signal corresponding to each touch sense signal; integrate, for a second predetermined duration of time, the first integrated signal, to generate a second integrated signal corresponding to each touch sense signal; and determine presence of one or more touch inputs on one or more of the electrodes based on the second integrated signal.