morlet_tfr.h File Reference

Complex Morlet wavelet time-frequency representation (TFR). More...

#include "dsp_global.h"
#include <Eigen/Core>
#include <QVector>

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Classes
struct	UTILSLIB::MorletTfrResult
	Result of a Morlet TFR computation for one channel. More...
class	UTILSLIB::MorletTfr
	Complex Morlet wavelet time-frequency representation. More...

Namespaces
namespace	UTILSLIB
	Shared utilities (I/O helpers, spectral analysis, layout management, warp algorithms).

Detailed Description

Complex Morlet wavelet time-frequency representation (TFR).

SPDX-License-Identifier: BSD-3-Clause Copyright (c) 2026 MNE-CPP Authors

Author

Christoph Dinh chris.nosp@m.toph.nosp@m..dinh.nosp@m.@mne.nosp@m.-cpp..nosp@m.org

Since

2.1.0

Date

March 2026

The complex Morlet wavelet ψ(t) = π^{-1/4} · e^{i2πf₀t} · e^{-t²/2σ²} is a Gaussian-modulated complex exponential and is by far the most popular wavelet for electrophysiological time-frequency analysis. At each analysis frequency f the wavelet is dilated so the number of cycles inside the Gaussian envelope (parameter n_cycles, typically 5–7) stays approximately constant; this gives a logarithmically scaled resolution Δt ∝ 1/f, Δf ∝ f matching the wavelet uncertainty principle.

The TFR is evaluated as a convolution of the signal with each wavelet — implemented in the frequency domain via FFT × FFT multiplication — yielding a complex time-frequency tensor whose squared magnitude is the instantaneous power and whose argument is the instantaneous phase. Trial-wise averaging of the complex tensor gives the inter-trial phase coherence (ITPC / phase-locking factor); averaging the power gives the event-related spectral perturbation (ERSP).

Definition in file morlet_tfr.h.