Time-Frequency Characterization of Resting-State Brain Function Reveals Overlapping Components with Specific Topology and Frequency Content

Even at rest, functional magnetic resonance imaging (fMRI) data displays exquisitely complex temporal dynamics. Here, we deployed a time-frequency analysis to track the modulus of fMRI signals over time, across space (a set of 341 brain areas) and frequency (45 uniformly distributed bins in the 0.01-0.25 Hz range). Decomposing the data into a set of temporally overlapping building blocks by Principal Component Analysis, we exposed diverse functional components with their own modulus pattern across brain locations and frequency sub-ranges. In particular, the component explaining most data variance showed homogeneous modulus across space at low frequencies, fitting with the marked whole-brain signal fluctuations seen in the time courses subjected to analysis. Other components showed topologically well-defined modulus patterns (e.g., contrasting the default mode and visual networks), with characteristic frequency properties and subject-specific activation profiles.

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Dimitri Nestor Alice Van De Ville, Thomas William Arthur Bolton
2019
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https://infoscience.epfl.ch/record/268422?ln=en

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Digital Signal Processing I

Basic signal processing concepts, Fourier analysis and filters. This module can be used as a starting point or a basic refresher in elementary DSP

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Digital Signal Processing III

Advanced topics: this module covers real-time audio processing (with examples on a hardware board), image processing and communication system design.

Time–frequency analysis

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.

Time–frequency representation

A time–frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency Distribution", abbreviated as TFD. TFRs are often complex-valued fields over time and frequency, where the modulus of the field represents either amplitude or "energy density" (the concentration of the root mean square over time and frequency), and the argument of the field represents phase.

Principal component analysis

Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data.

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