By the end of this virtual lab, learners will be able to:

• Perform and interpret matrix operations, decompositions, and factorizations that underpin signal processing algorithms.
• Characterize the statistical behavior of a system's output when driven by a wide sense stationary (WSS) input — under LTI systems, linear systems with Gaussian input, and AR/MA/ARMA system models.
• Compute and compare spectral estimates — Correlogram, Blackman–Tukey, Windowed Periodogram, Bartlett, Welch, and Daniell and evaluate their statistical properties across different signal parameters.
• Apply parametric spectral estimation methods (Yule-Walker, Min-Norm, Least Squares, MUSIC) to broadband, narrowband, and sum-of-sinusoid signals, and study how model order affects estimate quality.
• Design and evaluate a Wiener filter to estimate a signal from noisy observations, analyzing estimation error across filter lengths, noise distributions, signal types, and a real-world speech enhancement application.
• Build the statistical and mathematical foundation needed to progress to adaptive algorithms (LMS, RLS, Kalman filtering) and their applications in prediction, noise cancellation, and equalization.