The Nth Power Nonlinear Transform(NPT) is a common method for automatic modulation classification, especially for Phase Shift Keying(PSK) signals. Nevertheless，the sampling rate required in the NPT method is typically much greater than Nyquist rate，which causes heavy burden for the Analog to Digital Converter(ADC). Taking advantage of the sparse property of Phase Shift Keying signals spectrum under NPT，the NPT method is developed for PSK signals with Sub-Nyquist rate samples. Combining the NPT method with Compressive Sensing(CS) theory，frequency spectrum reconstruction of the Nth Power Nonlinear Transform of PSK signals is presented, which can be further applied to Automation Modulation Recognition(AMR) and rough estimations of unknown carrier frequency and symbol rate.