Suppose that the phase-modulated signal of Problem has an arbitrary value for the maximum phase deviation β_p. This modulated signal is applied to an ideal band-pass filter with mid-band frequency ƒ_c and a pass-band extending from ƒc – 1.5ƒ_m to ƒ_c + 1.5ƒ_m. Determine the envelope, phase, and instantaneous frequency of the modulated signal at the filter output as functions of time.