Lecture

Properties of Time-Frequency Domain Signals

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In course

EE-350: Signal processing

Dans ce cours, nous présentons les méthodes de base du traitement des signaux. ...

Description

This lecture covers the main properties of time-frequency domain signals, including linearity, correlation, convolution, and limitations for signals of unlimited duration. It also discusses the convolution of long signals by short signals using sectioned addition.

Instructors (2)

Jean-Philippe Thiran

Jean-Philippe Thiran was born in Namur, Belgium, in August 1970. He received the Electrical Engineering degree and the PhD degree from the Université catholique de Louvain (UCL), Louvain-la-Neuve, Belgium, in 1993 and 1997, respectively. From 1993 to 1997, he was the co-ordinator of the medical image analysis group of the Communications and Remote Sensing Laboratory at UCL, mainly working on medical image analysis. Dr Jean-Philippe Thiran joined the Signal Processing Institute (ITS) of the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in February 1998 as a senior lecturer. He was promoted to Assistant Professor in 2004, to Associate Professor in 2011 and is now a Full Professor since 2020. He also holds a 20% position at the Department of Radiology of the University of Lausanne (UNIL) and of the Lausanne University Hospital (CHUV) as Associate Professor ad personam. Dr Thiran's current scientific interests include Computational medical imaging: acquisition, reconstruction and analysis of imaging data, with emphasis on regularized linear inverse problems (compressed sensing, convex optimization). Applications to medical imaging: diffusion MRI, ultrasound imaging, inverse planning in radiotherapy, etc.Computer vision & machine learning: image and video analysis, with application to facial expression recognition, eye tracking, lip reading, industrial inspection, medical image analysis, etc.

Pascal Frossard

Teaching & PhD PhD Students Yiming Qin, Alba Carballo Castro, Elisa Messori, Ke Wang, Sevda Ögüt, Tuna Alikasifoglu, William Cappelletti, Manuel Madeira, Mahdi Amiri, Ortal Yona Senouf, Vasiliki Rizou, Cem Bilaloglu, Abdellah Rahmani, Amel Abdelraheem, Jérémy Jean Philippe Baffou, Adam Hazimeh, Vincent Jung, Yike Zhao Past EPFL PhD Students Dan Jurca, Jean-Paul Wagner, Ivana Radulovic, Ivana Tosic, Effrosyni Kokiopoulou, Zafer Arican, Vijayaraghavan Thirumalai, Tamara Tosic, Eirina Bourtsoulatze, Elif Vur

Official source

Ontological neighbourhood

Information engineering

Signal processing: Fourier analysis

Related concepts (31)

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

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.

Non-uniform discrete Fourier transform

In applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.

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.

Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.

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