An approach for demodulating a frequency-modulated signal involves processing a frequency-modulated signal with a phase shifter network to provide a demodulated signal that has a relatively constant amplitude around the center frequency of the frequency-modulated signal and that exhibits a relatively linear phase change over an operational frequency range. Embodiments of the invention include a phase shifter network comprising N number of all-pass filters and a phase shifter network comprising a low-pass bessel filter.