An FM modulator is followed by an ideal band pass filter having a center frequency of 500 Hz and a bandwidth of 70 Hz. The gain of the filter is 1 in the pass band. The unmodulated carrier is given by 10 cos(1000πt), and the message signal is m(t) = 10 cos (20πt). The transmitter frequency-deviation constant f_d is 8 Hz/V.

(a) Determine the peak frequency deviation in hertz.
(b) Determine the peak phase deviation in radians.
(c) Determine the modulation index.
(d) Determine the power at the filter input and the filter output
(e) Draw the single-sided spectrum of the signal at the filter input and the filter output. Label the amplitude and frequency of each spectral component.