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FourierAnalysis is a signal-processing Julia 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, FFTW.jl and 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.
Time-frequency representations are obtained applying a filter-bank and the 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.
Execute the following command in Julia's REPL:
]add FourierAnalysis
Marco Congedo is a Research Director of CNRS (Centre National de la Recherche Scientifique), working at UGA (University of Grenoble Alpes), in Grenoble (France), the city where Jean-Baptiste Joseph Fourier has served as a Prefect:).
first name dot last name at gmail dot com
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 | Technical Details |
|---|---|
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paper |