3.2. A random process π₯(π‘) consists of an ensemble of sample functions, each of which is a square wave of amplitude ±π and period π, Fig. 3.8(π). The "phase" of each sample is defined as the time π‘ = π at which the sample first switches from +π to −π (for π‘ > 0 ). π varies randomly from sample to sample with a uniform probability distribution of the form shown in Fig. 3.8(b). Show that the time history of a single sample function may be represented by the Fourier series expansion π₯(π‘) = 4π π ∑ π=1.3,5,… 1 2ππ sinβ‘ (π − π‘) π π and hence calculate the ensemble average πΈ[π₯(π‘)π₯(π‘ + π)] to find the autocorrelation function for the π₯(π‘) process. Verify that this agrees with the result shown in Fig. 3.9 Hint. The Fourier series "recipe" is given by equations (4.1) and (4.2 1