https://github.com/marco-congedo/fourieranalysis.jl
A Julia package for the Fourier analysis of Multivariate Data in the Frequency and Time-Frequency Domain
https://github.com/marco-congedo/fourieranalysis.jl
coherence fft spectra synchronization time-frequency time-series
Last synced: 5 months ago
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A Julia package for the Fourier analysis of Multivariate Data in the Frequency and Time-Frequency Domain
- Host: GitHub
- URL: https://github.com/marco-congedo/fourieranalysis.jl
- Owner: Marco-Congedo
- License: other
- Created: 2019-09-21T07:59:01.000Z (almost 7 years ago)
- Default Branch: master
- Last Pushed: 2026-02-16T20:16:18.000Z (5 months ago)
- Last Synced: 2026-02-17T02:47:27.413Z (5 months ago)
- Topics: coherence, fft, spectra, synchronization, time-frequency, time-series
- Language: Julia
- Homepage:
- Size: 4.55 MB
- Stars: 62
- Watchers: 7
- Forks: 13
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
| **Documentation** |
|:---------------------------------------:|
| [](https://Marco-Congedo.github.io/FourierAnalysis.jl/stable) |
**Related Publications**
[Technical report](https://hal.science/hal-01868538/document)
**FourierAnalysis** is a signal-processing [**Julia**](https://julialang.org/) package for
performing the analysis of *real multivariate data* (e.g., multivariate time series)
in the *frequency* domain and in the *time-frequency* domain. It is based upon the
[DSP.jl](https://github.com/JuliaDSP/DSP.jl), [FFTW.jl](https://github.com/JuliaMath/FFTW.jl) and [AbstractFFTs.jl](https://github.com/JuliaMath/AbstractFFTs.jl) packages.
In the frequency domain *FourierAnalysis* computes **spectra**, *linear* and
*non-linear* **cross-spectral matrices** and several *linear* and *non-linear* **coherence matrices** using the sliding-windows [Welch method](https://en.wikipedia.org/wiki/Welch%27s_method).
Time-frequency representations are obtained applying a
[filter-bank](https://en.wikipedia.org/wiki/Filter_bank) and the
[Hilbert transform](https://en.wikipedia.org/wiki/Hilbert_transform).
This way *FourierAnalysis* computes the **analytic signal**, from which the **instantaneous amplitude** (envelope) and **instantaneous phase** are obtained, along with several popular *linear* and *non-linear*, *weighted*, *univariate* and *bivariate* statistics, such as
- **mean amplitude**
- **mean direction**
- **phase concentration** (the non-linear version of which is the directional statistic *circular mean resultant length*)
- **comodulation**
- **coherence** (the non-linear version of which is known as *phase-locking values* or *phase coherence*).
All these measures are provided in a simple and unified fashion, following the conceptual approach previously illustrated in
in the context of electroencephalography ([Congedo, 2018](https://hal.archives-ouvertes.fr/hal-01868538v2/document)), for which all default settings have been tailored. The package has been written with the *do-it-with-one-line* spirit, but without sacrificing full control over relevant options.
## Installation
Execute the following command in Julia's REPL:
]add FourierAnalysis
## About the Author
[Marco Congedo](https://sites.google.com/site/marcocongedo) is
a Research Director of [CNRS](http://www.cnrs.fr/en) (Centre National de la Recherche Scientifique), working at [UGA](https://www.univ-grenoble-alpes.fr/english/) (University of Grenoble Alpes), in Grenoble (France), the city where Jean-Baptiste Joseph Fourier has served as a Prefect:).
## Contact
first name *dot* last name *at* gmail *dot* com
## Examples
```
using FourierAnalysis, Plots
# Set sampling rate (sr) and FFT window length (wl):
sr, wl = 128, 128
# Generate a sinusoidal wave at 10Hz with peak amplitude 0.5 and add some white noise:
v = sinusoidal(0.5, 10, sr, wl*16) + randn(wl*16)
# Get the power spectrum with a rectangular tapering window:
S = spectra(v, sr, wl; tapering=rectangular)
# Plot the power spectrum:
plot(S; fmax=24)
# The same syntax applies in the case of multivariate data (e.g., 4 time-series):
V = randn(wl*16, 4)
# avoid conflict with DSP.hamming
S = spectra(V, sr, wl; tapering=FourierAnalysis.hamming)
plot(S)
# Get the analytic amplitude in the time-Frequency domain:
A = TFamplitude(v, sr, wl; fmax=24)
# plot the analytic amplitude:
heatmap(A.y)
# et cetera.
```
| **Documentation** |
|:---------------------------------------:|
| [](https://Marco-Congedo.github.io/FourierAnalysis.jl/stable) |