Let yt denote the random process corresponding to the

Question

Let Y(t) denote the random process corresponding to the transmission of one symbol over the QPSK communications system of Example 10.6. What is the sample space of the underlying experiment? Sketch the ensemble of sample functions.

Examples 10.6

In a quaternaryphase shift keying (QPSK) communications system, one of four equally probable symbols s₀,...,s₃ is transmitted in T seconds. If symbol si is sent, a waveform x(t,si) = cos(2π f₀t + π/4 + iπ/2) is transmitted during the interval [0, T ]. In this example, the experiment is to transmit one symbol over [0, T] seconds and each sample function has duration T. In a real communications system, a symbol is transmitted every T seconds and an experiment is to transmit j symbols over [0, j T] seconds. In this case, an outcome corresponds to a sequence of j symbols and a sample function has duration j T seconds.