spectral_connectivity.transforms.estimate_frequency_resolution#

estimate_frequency_resolution(sampling_frequency: float, time_window_duration: float, time_halfbandwidth_product: float) → float[source]#

Estimate the frequency resolution for given multitaper parameters.

The frequency resolution (Δf) represents the bandwidth over which spectral energy is averaged. It is determined by the time-frequency trade-off inherent in spectral analysis.

Parameters:

sampling_frequency (float) – Sampling rate in Hz of the time series data. Note: This doesn’t affect frequency resolution, only the maximum frequency (Nyquist = sampling_frequency / 2).
time_window_duration (float) – Duration in seconds of each analysis window. Longer windows provide better (finer) frequency resolution.
time_halfbandwidth_product (float) – Time-bandwidth product controlling the spectral concentration. Higher values provide more spectral smoothing (coarser resolution).

Returns:

frequency_resolution – Frequency resolution in Hz. This represents the bandwidth over which spectral estimates are averaged.

Return type:

float

Notes

The frequency resolution formula is:

\[\Delta f = \frac{2 \cdot NW}{T}\]

where: - NW is the time-halfbandwidth product - T is the time window duration in seconds

Key relationships: - Longer time windows (↑T) → Better resolution (↓Δf) - Higher time-halfbandwidth product (↑NW) → More smoothing (↑Δf)

Typical values: - For 1 Hz resolution: Use T=6s with NW=3 - For 5 Hz resolution: Use T=1.2s with NW=3 - For 0.5 Hz resolution: Use T=12s with NW=3

Examples

EEG application with 1 Hz resolution:

>>> freq_res = estimate_frequency_resolution(
...     sampling_frequency=250,
...     time_window_duration=6.0,
...     time_halfbandwidth_product=3,
... )
>>> print(f"Frequency resolution: {freq_res} Hz")
Frequency resolution: 1.0 Hz

LFP application with 5 Hz resolution:

>>> freq_res = estimate_frequency_resolution(
...     sampling_frequency=1000,
...     time_window_duration=1.2,
...     time_halfbandwidth_product=3,
... )
>>> print(f"Frequency resolution: {freq_res} Hz")
Frequency resolution: 5.0 Hz