An optimum predetection Gaussian bandpass filter for differential detection of MSK is derived theoretically with numerical techniques. The optimum product of bandwidth

and bit duration

, compromising the noise reduction effect with the intersymbol interference effect, is calculated at a given bit error rate (BER). It is shown that the optimum

product is 1.21 with 4.02 dB degradation at 10
-6BER where the degradation is defined as the increase in

relative to ideal coherent detection of MSK.