probability and stochastic process, Basic Statistics

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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(2p f0t + p/4 + ip/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.

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