Lab 4: Binary PCM Processes Solution

Description

1. Let us analyze the NRZ-L scheme. Let X(t) denote the stochastic process that generates random NRZ-L code signals, with pulse-width T sec.

1. 1. Simulate the stochastic process X(n) = X(nT_s) in Python, assuming independent bit stream.

1. 2. Compute the mean m_X and Auto-correlation matrix R_X, and verify (approxi-mately) whether X(n) is wide-sense stationary or not.

1. 3. Let d U[0, T] be a uniformly distributed RV that models a random starting

point for the PCM scheme. Let X₁(t) = X(t d) denote the same NRZ-L signal with random initial delay d (begin with 0 for t 2 [0 d]). Repeat the above step with X₁(n) = X₁(nT_s).

(d) Compute the PSD of X(n) (or/and X₁(n)) for different pulse-widths T.

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