An Initiative of Ministry of Education under the National Mission on Education through ICT

Adaptive Signal Processing Virtual Lab I

Broad Areas of Virtual Labs
Electronics & Communications
IIT DELHI
Introduction

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.

Objective

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.

Reference Books

No reference books available.

Lab Contact Person

Prof. Suresh Bhalla,
Professor,
Civil Engineering