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6.011

Introduction to Communication, Control, and Signal Processing

Undergraduate · Historical course

Spring 2018 · Signals, Systems and Inference

Topics

  • Introduction
  • Transforms
  • Energy Spectral Density
  • State-Space Models
  • State-Space Models, Equilibrium, Linearization
  • Modal Solution of Undriven CT and DT LTI State-Space Models
  • Full Modal Solution, Asymptotic Stability, Reachability, and Observability
  • Matrix Exponential, ZIR+ZSR, Transfer Function, Hidden Modes, Reaching Target States
  • Observers for State Estimation
  • Observers, State Feedback
  • State Feedback, Observer-Based Feedback
  • Probabilistic Models, Random Variables
  • Vector Picture for First- and Second-Order Statistics; MMSE and LMMSE Estimation
  • LMMSE Estimation, Orthogonality
  • Normal Equations, Random Processes
  • Wide-Sense Stationary Processes; LTI Filtering of WSS Processes
  • LTI Filtering of WSS Processes
  • Power Spectral Density (PSD)
  • Einstein-Wiener-Khinchin Theorem, PSD Applications, Modeling Filters
  • Wiener Filtering
  • Wiener Filtering Illustrations
  • Hypothesis Testing
  • Neyman-Pearson Testing, Signal Detection
  • Matched Filtering

Readings

  • All readings are from Signals, Systems and Inference [SSI] unless otherwise noted.
    Listed reading
  • Hardcover : Oppenheim, Alan, and George Verghese. Signals, Systems and Inference . Pearson, 2015. ISBN: 9180133943283
    Listed reading
  • Softcover : Oppenheim, Alan, and George Verghese. Signals, Systems and Inference . Pearson, 2017. ISBN: 9781292156200
    Listed reading
  • Refamiliarize yourself with Chapters 1, 2, 4–7, 9 of Signals and Systems
    Listed reading
  • Oppenheim, Alan, and Alan Willsky, with S. Hamid Nawab. Signals and Systems . 2nd ed. Prentice-Hall, 1996.
    Listed reading
  • [SSI] Finish chapter 5
    Listed reading
  • Topic: Probablistic Models, Random Variabls · Reading: [SSI] Chapters 7 and 8
    Reading assignment
  • Topic: MMSE and LMMSE Estimation · Reading: [SSI] Finish sections 8.1–8.3.1
    Reading assignment
  • Topic: WSS Processes · Reading: [SSI] Chapter 10
    Reading assignment
  • Topic: LTI Filtering of WSS Processes, Power Spectral Density · Reading: [SSI] Sections 12.1–12.4
    Reading assignment
  • Topic: Wiener Filtering · Reading: [SSI] Finish sections 12.1–12.4
    Reading assignment
  • Topic: Hypothesis Testing · Reading: [SSI] Sections 9.2–9.31
    Reading assignment
  • Topic: Signal Detection · Reading: [SSI] Chapter 13
    Reading assignment
Spring 2010

Topics

  • Warming up.
  • Introduction and overview. Linear, time-invariant (LTI) systems.
  • Discrete-time Fourier transforms (DTFT), continuous-time Fourier transforms (CTFT): definitions and operations.
  • Classes of DTFT, CTFT; energy spectral density.
  • Spectral factorization.
  • Sampling, interpolation, discrete-time (DT) processing of continuous-time (CT) signals.
  • Fractional delay in DT systems.
  • Group delay.
  • State-space models.
  • Obtaining state-space models.
  • Equilibria and linearization. Modes of LTI state-space models.
  • Linearization, eigenvalues, eigenvectors, modes.
  • Reachability, observability, hidden modes, minimality.
  • Reachability, observability, hidden modes.
  • State observers and feedback.
  • Observers and feedback.
  • Observer-based feedback; DT control of CT systems.
  • Probability review.
  • Minimum mean-square-error (MMSE) and linear MMSE (LMMSE) estimation; orthogonality.
  • MMSE and LMMSE estimation.
  • Random processes, wide-sense stationarity (WSS).
  • Correlation/covariance functions.
  • Ergodicity. LMMSE prediction from finite data.
  • LTI filtering of WSS processes.
  • Power spectral density (PSD).
  • PSD. Modeling and whitening filters.
  • Unconstrained (noncausal) Wiener filtering.
  • Unconstrained Wiener filtering.
  • Oversampled noise modulation.
  • More PSD and Wiener filter practice.
  • Pulse-amplitude modulation (PAM); Nyquist condition for zero intersymbol interference (ISI).
  • PAM. Nyquist condition.
  • Binary PAM, hypothesis testing, minimum probability of error.
  • Optimal detection, false alarm, miss.
  • Likelihood ratio; Neyman-Pearson detection.
  • Receiver operating characteristic (ROC).
  • Quadrature amplitude modulation (QAM); modems.
  • Signal detection in white Gaussian noise.
  • Matched filtering.
  • Pulse compression.
  • Signal detection in colored noise.
  • (Causal) Wiener prediction.
  • Wiener prediction.
  • Spectral estimation, periodogram averaging.
  • Review.
  • Notions of information theory and coding.
  • Clinical monitoring, estimation and prediction.

Readings

Sources