An / and Q modulator for minimum-shift keying requires that the two baseband modulators be precisely matched in time delay and carrier phase. At very high data rates, perhaps above 100 Mbps, this can be difficult. An alternative, and somewhat subtle, MSK modulator is the serial MSK modulator. It consists of a BPSK waveform (with rectangular pulses of bit duration Tb) modulated onto an offset carrier frequency fo - 1/47b, which is then passed through a passband filter with impulse response g(t) (Notice that the apparent frequency of the passband filter and the frequency of the BPSK waveform are offset in opposite directions.) a. Sketch a functional block diagram of the serial MSK modulator. b. Prove that the serial MSK modulator does indeed give an MSK waveform. (Hint: Work with only the first bit, and show in the Fourier transform domain that the right Fourier transform is obtained, then extend this to the other bits.) sin 27 (fo + 1/4Tz)t 0 t To otherwise. c. What is the relationship between the bit stream that is modulated into the BPSK waveform and the apparent datastream in the land Q components of the final MSK waveform?