Abstract: A method of synthesizing a finite impulse response digital filter includes a phase of calculating the impulse response g(t) of an analog filter the transfer function of which is defined by a predetermined bandwidth B, shape factor SF and out-band attenuation level A. The coefficients of the digital filter are extracted by sampling the resulting impulse response. The calculation phase consists in expanding the impulse response into an integer number M of Hermite functions predetermined in accordance with the shape factor SF. The coefficient extraction phase includes sampling of the expanded impulse response after the calculation phase in a time window the duration of which is dependent on the out-band attenuation level A using a sampling period At that is dependent on the bandwidth B.