Apparatus and methods for demodulating a signal

An apparatus for demodulating an analogue input signal comprises a hard limiter stage for converting the signal to a two level signal. A digital down converter/low pass filter stage converts the signal to a base band signal, and a symbol synchronization stage extracts symbol timing. An instantaneous phase detector calculates the instantaneous phase of the one or more symbols associated with the input signal. If the input signal has been modulated according to a pi/4DQPSK, pi/2DBPSK, GMSK, or a GFSK modulation scheme, a differential detector determines a difference in the phase between adjacent symbols, a coarse frequency offset compensation stage applies a compensation signal to compensate for frequency offset, and a frequency offset estimation stage updates this compensation signal. A demapper generates a demodulated output signal after compensation by the frequency offset compensation stage.