Adaptive and statistical signal processing form the backbone of modern signal analysis and communication systems, powering applications such as noise cancellation, channel equalization, prediction, and signal modeling. However, these concepts — rooted in linear algebra, random processes, and optimal estimation theory — are often difficult for students to internalize through lectures alone, since their behavior depends heavily on statistical properties that are hard to visualize analytically. The Adaptive Signal Processing Virtual Lab addresses this gap by offering a structured, simulation-based environment where students can experiment directly with the mathematical and statistical foundations of the field. The lab takes learners through a carefully sequenced set of experiments: it begins by building fluency with the matrix operations and decompositions that underlie signal processing algorithms, then examines how a system's statistical output behaves when driven by a wide sense stationary (WSS) input under different modeling assumptions (LTI, Gaussian, AR/MA/ARMA). It then introduces spectral estimation — covering both classical (Correlogram, Blackman–Tukey, Periodogram, Bartlett, Welch, Daniell) and parametric (Yule-Walker, Min-Norm, Least Squares, MUSIC) techniques — and studies how estimator performance varies with signal type. The sequence concludes with the Wiener filter, where students design a mean-square-error-optimal linear filter and study its estimation error under different noise distributions, signal types, and filter lengths, including an application to enhancing the SNR of real recorded speech. By working through these experiments, students move from foundational mathematical tools to a working, hands-on understanding of statistical signal characterization and optimal filtering — the essential groundwork for later coursework in adaptive filtering (LMS, RLS, Kalman filtering) and its applications.