# Academics  /  Courses  /  DescriptionsELEC_ENG 395: Adaptive Signal Processing and Learning

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### Prerequisites

ELEC_ENG 202, ELEC_ENG 302

### Description

CATALOG DESCRIPTION: discrete-time random process, second-order statistics, autoregressive and moving average processes, linear prediction, Wiener filter, stochastic gradient (Least Mean Square) algorithm, least squares estimation, introduction to Kalman filter.

REQUIRED TEXT: S. Haykin, "Adaptive Filter Theory", Prentice-Hall, 2013.

COURSE DIRECTOR: Prof. Mike Honig

COURSE GOALS: To provide an introduction to adaptive signal processing methods with applications to compression, prediction, model estimation (learning), and array processing.

PREREQUISITES BY COURSES: 202, 302

PREREQUISITES BY TOPIC:

ITEM 1: Probability

ITEM 2: Frequency-domain (spectral) analysis

ITEM 3: Familiarity with z-transforms.

COURSE TOPICS:

1. Applications: speech compression, financial forecasting, array processing
2. Discrete-time random process, second-order statistics, filtering
3. Autoregressive and Moving Average processes
4. Linear prediction, Wiener filter
6. Least squares estimation and filtering
7. Introduction to Kalman filter

GRADES: A weighted combination of homework, midterm, and project.

COURSE OBJECTIVES:  When a student completes this course, s/he should be able to:

1. Characterize a wide-sense stationary discrete-time random process in terms of second-order statistics and spectral desnity.
2. Model a given signal or time-series as an AR, MA, or ARMA random process.
3. Compute the optimal (Wiener) predictor or filter from second-order input statistics.
4. Design a stochastic gradient algorithm to satisfy particular performance criteria.
5. Compute a Least Squares approximation of the Wiener filter from measurements.
6. Simulate adaptive signal processing algorithms to compare relative performance.
7. Apply a state-space model and the Kalman filter to solve a basic tracking problem.