The present invention pertains to demodulation of GMSK signals by estimating a carrier frequency of the signal having a carrier residual, basebanding the signal, tracking the signal's carrier frequency, removing the carrier residual, detecting a data burst, generating a bank of poly-bit matched filters, applying the bank of poly-bit matched filters to the signal, determining a magnitude and phase of the output of each poly-bit filter of the bank of poly-bit matched filters, determining a maximum magnitude, determining the location of a baud center, generating a plurality of correlation signals by applying the bank of poly-bit matched filters at the baud center, estimating a carrier phase, removing the estimated carrier phase, applying a Viterbi decoding algorithm to the signal, and estimating the transmitted data sequence.