We experimentally demonstrate, for the first time, a chirped microwave pulses generator based on the processing of an incoherent optical signal by means of a nonlinear dispersive element. Different capabilities have been demonstrated such as the control of the timebandwidth product and the frequency tuning increasing the flexibility of the generated waveform compared to coherent techniques. Moreover, the use of differential detection improves considerably the limitation over the signalto-noise ratio related to incoherent processing.