{"id":32158683,"url":"https://github.com/marco-congedo/fourieranalysis.jl","last_synced_at":"2026-02-19T02:02:33.120Z","repository":{"id":40315988,"uuid":"209946997","full_name":"Marco-Congedo/FourierAnalysis.jl","owner":"Marco-Congedo","description":"A Julia package for the Fourier analysis of Multivariate Data in the Frequency and Time-Frequency Domain","archived":false,"fork":false,"pushed_at":"2026-02-16T20:16:18.000Z","size":4771,"stargazers_count":62,"open_issues_count":3,"forks_count":13,"subscribers_count":7,"default_branch":"master","last_synced_at":"2026-02-17T02:47:27.413Z","etag":null,"topics":["coherence","fft","spectra","synchronization","time-frequency","time-series"],"latest_commit_sha":null,"homepage":"","language":"Julia","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"other","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/Marco-Congedo.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2019-09-21T07:59:01.000Z","updated_at":"2026-02-13T07:15:41.000Z","dependencies_parsed_at":"2024-07-14T22:29:31.361Z","dependency_job_id":"da15ab35-e15a-4d0f-b3a7-ea2478361492","html_url":"https://github.com/Marco-Congedo/FourierAnalysis.jl","commit_stats":null,"previous_names":[],"tags_count":12,"template":false,"template_full_name":null,"purl":"pkg:github/Marco-Congedo/FourierAnalysis.jl","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Marco-Congedo%2FFourierAnalysis.jl","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Marco-Congedo%2FFourierAnalysis.jl/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Marco-Congedo%2FFourierAnalysis.jl/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Marco-Congedo%2FFourierAnalysis.jl/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/Marco-Congedo","download_url":"https://codeload.github.com/Marco-Congedo/FourierAnalysis.jl/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Marco-Congedo%2FFourierAnalysis.jl/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29600848,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-19T00:59:38.239Z","status":"online","status_checked_at":"2026-02-19T02:00:07.702Z","response_time":117,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["coherence","fft","spectra","synchronization","time-frequency","time-series"],"created_at":"2025-10-21T13:01:02.259Z","updated_at":"2026-02-19T02:02:33.113Z","avatar_url":"https://github.com/Marco-Congedo.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"| **Documentation**  | \n|:---------------------------------------:|\n| [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://Marco-Congedo.github.io/FourierAnalysis.jl/stable) |\n\n**Related Publications**\n[Technical report](https://hal.science/hal-01868538/document)\n\n![](/docs/src/assets/Fig1.jpg)\n\n**FourierAnalysis** is a signal-processing [**Julia**](https://julialang.org/) package for\nperforming the analysis of *real multivariate data* (e.g., multivariate time series)\nin the *frequency* domain and in the *time-frequency* domain. It is based upon the\n[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.\n\nIn the frequency domain *FourierAnalysis* computes **spectra**, *linear* and\n*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).\n\nTime-frequency representations are obtained applying a\n[filter-bank](https://en.wikipedia.org/wiki/Filter_bank) and the\n[Hilbert transform](https://en.wikipedia.org/wiki/Hilbert_transform).\nThis 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\n- **mean amplitude** \n- **mean direction** \n- **phase concentration** (the non-linear version of which is the directional statistic *circular mean resultant length*)\n- **comodulation**\n- **coherence** (the non-linear version of which is known as *phase-locking values* or *phase coherence*).\n\nAll these measures are provided in a simple and unified fashion, following the conceptual approach previously illustrated in\nin 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.\n\n## Installation\n\nExecute the following command in Julia's REPL:\n\n    ]add FourierAnalysis\n\n## About the Author\n\n[Marco Congedo](https://sites.google.com/site/marcocongedo) is\na 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:).\n\n## Contact \nfirst name *dot* last name *at* gmail *dot* com\n\n## Examples\n```\nusing FourierAnalysis, Plots\n\n# Set sampling rate (sr) and FFT window length (wl):\nsr, wl = 128, 128\n\n# Generate a sinusoidal wave at 10Hz with peak amplitude 0.5 and add some white noise:\nv = sinusoidal(0.5, 10, sr, wl*16) + randn(wl*16)\n\n# Get the power spectrum with a rectangular tapering window:\nS = spectra(v, sr, wl; tapering=rectangular)\n\n# Plot the power spectrum:\nplot(S; fmax=24)\n\n# The same syntax applies in the case of multivariate data (e.g., 4 time-series):\nV = randn(wl*16, 4)\n# avoid conflict with DSP.hamming\nS = spectra(V, sr, wl; tapering=FourierAnalysis.hamming)\nplot(S)\n\n# Get the analytic amplitude in the time-Frequency domain:\nA = TFamplitude(v, sr, wl; fmax=24)\n\n# plot the analytic amplitude:\nheatmap(A.y)\n\n# et cetera.\n\n```\n\n| **Documentation**  | \n|:---------------------------------------:|\n| [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://Marco-Congedo.github.io/FourierAnalysis.jl/stable) |\n\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmarco-congedo%2Ffourieranalysis.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmarco-congedo%2Ffourieranalysis.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmarco-congedo%2Ffourieranalysis.jl/lists"}