Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Yule Walker Equations: Efficient Implementation and Correlation Analysis

In course

COM-500: Statistical signal and data processing through applications

Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, with an application oriented approach and hands-on numeri ...

Description

This lecture covers the Yule Walker equations for efficient implementation and correlation analysis in signal processing. It discusses the computation of empirical correlation, biased vs. unbiased correlation, and issues with extreme lags and non-zero mean signals. The instructor challenges students to propose efficient implementations and reduction of estimation issues. The lecture also delves into linear estimation of AR parametric models, Levinson's algorithm, and the computational burden involved. Practical examples and Matlab practices are provided to enhance understanding.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Andrea Ridolfi

I am a professor of Signal Processing and Communication Technologies at Bern University of Applied Sciences. Since 2004 I hold a lecturer position at EPFL, teaching “Mathematical Principles of Signal Processing” (Doctoral School, 2004 – 2011), “Statistical Signal and Data Processing through Applications” (Master Program, (2004 – ongoing), and Signal Processing and Machine Learning for Digital Humanities (Master, 2017 – 2019, co-taught with Mathieu Salzmann). Previously, I have been working as Project Manager and R&D Engineer at EPFL (2011-2014), coordinating the LCAV activities within the NSF – Nanotera project Opensense, and as Project Manager and R&D Engineer with the biomedical signal processing group at CSEM (2006-2011).

Official source

Ontological neighbourhood

Statistics

Data analysis: Time series

Related concepts (32)

Spectral density estimation

In statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also known as the power spectral density) of a signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Autoregressive model

In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation).

Intraclass correlation

In statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.

Related lectures (40)

Time Series: Fundamentals and Models

Explores the fundamentals of time series analysis, including stationarity, linear processes, forecasting, and practical aspects.

Time Series: Linear Filtering and Spectral Estimation

Explores linear filtering, spectral estimation, and second-order stationarity in time series analysis.

Spectral & Parametric Estimation: Time Series

Covers spectral estimation techniques like tapering and parametric estimation, emphasizing the importance of AR models and Whittle likelihood in time series analysis.

Red bus/Blue bus paradox

Explores the Red bus/Blue bus paradox, nested logit models, and multivariate extreme value models in transportation.

Probabilistic Models for Linear Regression