ELEC0006 - Signal and Systems
PROBLEM SET 4
2. Digital Communications
4.1 The data b(t) consists of the bitstream 0 0 1 0 1 0 0 1 1 0 1 0. Assuming that the bitrate fb is equal to the carrier frequency and sketch vBPSK(t).
4.2 The bit stream d(t) is to be transmitted using DPSK. If d(t) is 0 0 1 0 1 0 0 1 1 0 1 0 determine b(t) (the bit stream actually encoded onto the carrier). Show that b(t) b(t-Ts) yields the original data. Also show that if the fourth bit of b(t) is in error then the fourth and fifth data bits will also be in error.
4.3 The bit stream 0 0 1 0 1 0 0 1 1 0 1 0 is to be transmitted using FSK. Sketch the transmitted waveform assuming that fL =fb and fH = 2fb.
4.4 Both binary FSK and binary PSK signals have a constant envelope. Binary FSK signals can be noncoherently detected, whereas binary PSK signals cannot. What are the reasons for this difference.
4.5 The binary sequence 1 0 1 1 0 1 0 0 1 1 is transmitted over a communication channel using DPSK. The channel introduces a 180˚ phase reversal.
(a) Sketch the transmitted DPSK waveform, assuming an initial bit of 1.
What is the effect of changing the initial bit to a 0?
(b) Assuming that the channel is noise free, show that the DPSK detector in
the receiver reproduces the original binary sequence, despite the 180˚ phase reversal in the channel.
4.6 Sketch the QPSK waveform for the sequence 1 0 1 1 0 1 0 0 1 1. You may assume the following:
(a) The carrier frequency equals the bitrate.
(b) The dibits 00, 10, 11 and 01 are represented by phase shifts equal to 0, π/2, π, 3π/2 radians.