Lecture

Linear Time Invariant Filters: Time Series

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In course

MATH-342: Time series

A first course in statistical time series analysis and applications. ...

Description

This lecture covers the estimation of sample mean consistency, ergodicity, and stationarity in time series. It delves into the concepts of sampling, aliasing, and spectral representation, emphasizing the properties of linear time invariant filters. The lecture also explores the transfer function, frequency response function, and the spectral representation of stationary processes.

Instructor

Sofia Charlotta Olhede

I am a professor of Statistics at EPFL. I did my PhD in Mathematics at Imperial College London, and graduated in 2003. I was an assistant professor (lecturer) at Imperial College London 2002-2006, and an associate professor (senior lecturer) 2006-2007. In 2007 I moved to University College London and became a full professor. I moved to EPFL in 2019, and in 2018 I became an Institute of Mathematical Statistics Fellow with citation “For seminal contributions to the theory and application of large and heteroge

Official source

Related concepts (32)

Sampling (statistics)

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

Frequency response

In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations.

Stratified sampling

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population.

Linear filter

Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions.

Convenience sampling

Convenience sampling (also known as grab sampling, accidental sampling, or opportunity sampling) is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand. This type of sampling is most useful for pilot testing. Convenience sampling is not often recommended for research due to the possibility of sampling error and lack of representation of the population. But it can be handy depending on the situation. In some situations, convenience sampling is the only possible option.

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