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

Lecture

Causal Systems & Transforms: Delay Operator Interpretation

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 discusses the concept of z Variable as a Delay Operator in the context of LTI causal systems and transforms. It covers the interpretation of z-1 as a delay operator, the implementation of realizable systems, and the distinction between FIR and IIR systems. The lecture also explores random variables, cumulative distribution functions, moments, and correlation in the context of probability theory. Additionally, it delves into the properties of discrete time stochastic processes, including stationarity, correlation, covariance, and power spectral density. The lecture concludes with an overview of Hilbert Spaces, explaining the inner product, norm, and projection theorem.

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

Statistical inference: Mathematical statistics

Mathematics

Analysis: Functional analysis

Information engineering

Signal processing: Fourier analysis

Related concepts (32)

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

Hilbert space

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space.

Empirical distribution function

In statistics, an empirical distribution function (commonly also called an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical measure of a sample. This cumulative distribution function is a step function that jumps up by 1/n at each of the n data points. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value.

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

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.

Related lectures (56)

Probability and Statistics

Covers probability, statistics, independence, covariance, correlation, and random variables.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Variance and Covariance: Properties and Examples