Theory

For Wide-Sense Stationary (WSS) processes, the Autocorrelation Function (ACF) and the Power Spectral Density (PSD) are fundamental tools for analysis. They are related by the Wiener-Khinchin Theorem, which states that the PSD is the Fourier transform of the ACF.

• Autocorrelation Function (ACF): Shows how a signal correlates with a time-shifted version of itself. It reveals the internal "memory" or repetitive structure of the process.
• Power Spectral Density (PSD): Shows how the power of a signal is distributed over different frequencies. It reveals the frequency content of the process.

Procedure

1. A description of a physical random process will be shown. Analyze the description to understand its nature.
2. Step 1: Select the mathematical equation that best models the described process.
3. Step 2: Based on the process, identify the correct ACF plot from a set of options.
4. Step 3: Identify the correct PSD plot that corresponds to the ACF.
5. After completing all steps, a detailed observation will explain the connections between the description, equation, ACF, and PSD.