  Sampling rate required in the Nth Power Nonlinear Transformation (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
PSK signals' spectrum under NPT, we develop the NPT method for PSK signals with
Sub-Nyquist rate samples. In this paper, combined the NPT method with
Compressive Sensing (CS) theory, frequency spectrum reconstruction of the Nth
power nonlinear transformation of PSK signals is presented, which can be
further used for AMR and rough estimations of unknown carrier frequency and
symbol rate.
