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TF Multitaper ​

This demo demonstrates time-frequency analysis using the multitaper method for high-quality spectral estimation.

What is the Multitaper Method? ​

The multitaper method improves spectral estimates by averaging across multiple orthogonal tapers (windows):

  • Slepian tapers: Mathematically optimal windows that minimize spectral leakage

  • Multiple estimates: Each taper provides an independent spectral estimate

  • Averaging: Reduces variance while preserving spectral features

  • Time-bandwidth product (NW): Controls frequency smoothing

Key Parameters ​

Cycles:

Similar to Morlet wavelets, controls the time window length:

julia
tf_multitaper(epochs, cycles = 5)

Frequency Spacing ​

Linear spacing (frequencies = 1:1:40):

  • Equal Hz steps across range

  • Good for narrow frequency bands

Logarithmic spacing (frequencies = logrange(1, 40, length = 30)):

  • Proportional steps (constant ratios)

  • Better for wide ranges (2-80 Hz)

  • Use with ylogscale = true for visualization

Baseline Correction ​

julia
plot_tf(
    tf_data,
    baseline_interval = (-0.5, -0.2),
    baseline_method = :db
)

Isolates event-related changes relative to pre-stimulus baseline.

Workflow Summary ​

This demo shows:

  1. Synthetic validation: Known frequencies (5, 25, 35 Hz)

  2. Fixed cycles: Constant resolution analysis

  3. Linear vs log spacing: Different frequency sampling strategies

  4. Baseline correction: Event-related power changes

  5. Edge filtering: Removing edge artifacts

Practical Tips ​

Choose cycles based on needs:

  • 3-5 cycles: Better temporal resolution

  • 7-10 cycles: Better frequency resolution

  • 5 cycles: Good balance for most EEG work

Frequency sampling:

  • Dense sampling (every 0.5 Hz) for detailed spectra

  • Coarse sampling (every 2-5 Hz) for faster computation

Time steps:

  • Control temporal smoothness of the output

  • Smaller steps = smoother time course but slower computation

Further Reading ​

Cohen, M. X. (2014). Analyzing Neural Time Series Data: Theory and Practice. Chapter 16: Multitapers

Code Examples ​

Show Code
julia
# Demo: Time-Frequency Analysis - Multitaper
# Shows multitaper method for time-frequency analysis with reduced variance.

using EegFun
# Note: EegFun.example_path() resolves bundled example data paths.
# When using your own data, simply pass the file path directly, e.g.:
# dat = EegFun.read_raw_data("/path/to/your/data.bdf")

#######################################################################
@info EegFun.section("TEST 1: Synthetic Signal with Known Frequencies")
#######################################################################

# Generate synthetic signal
sample_rate = 1000.0
times, signal = EegFun.generate_signal(
    400,                                    # n_trials
    [-1.0, 3.0],                            # time_interval
    sample_rate,                            # sample_rate
    [5.0, 25, 35.0],                        # frequencies
    [5.0, 5.0, 5.0],                        # amplitudes
    [[0.1, 0.5], [0.6, 1.0], [1.1, 1.5]],   # time intervals for each freq 
    0.0,                                    # noise amplitude
);
epochs_synthetic = EegFun.signal_to_data(times, signal, :Channel1, sample_rate)
EegFun.plot_epochs(epochs_synthetic, channel_selection = EegFun.channels([:Channel1]))

spectrum = EegFun.freq_spectrum(epochs_synthetic, max_freq = 80.0)
EegFun.plot_frequency_spectrum(spectrum, channel_selection = EegFun.channels([:Channel1]))

# tf_stft_fixed
tf_data = EegFun.tf_multitaper(epochs_synthetic, frequencies = 1:1:40, cycles = 5)
EegFun.plot_tf(tf_data, ylogscale = false)

tf_data = EegFun.tf_multitaper(epochs_synthetic, frequencies = 1:1:40, cycles = 5)
EegFun.plot_tf(tf_data, ylogscale = false)

tf_data = EegFun.tf_multitaper(epochs_synthetic, frequencies = logrange(1, 40, length = 30), cycles = 5)
EegFun.plot_tf(tf_data, ylogscale = true)

tf_data = EegFun.tf_multitaper(epochs_synthetic, frequencies = logrange(1, 40, length = 30), cycles = 5)
EegFun.plot_tf(tf_data, ylogscale = true)

#######################################################################
@info EegFun.section("TEST 2: Cohen Data Chapter 13")
#######################################################################
# This is some data that was presented in Cohen: Analyzin Neural Time Series Data
data_cohen = EegFun.read_data(EegFun.example_path("data/julia/tf/tf_test_epochs.jld2"));

# Figure 13.11 A)
tf_data = EegFun.tf_multitaper(data_cohen, frequencies = logrange(2, 80, length = 30), cycles = 5, time_steps = 0.05, filter_edges = true)
EegFun.plot_tf(tf_data; baseline_interval = (-0.5, -0.2), baseline_method = :db, colorrange = (-3, 3), ylogscale = true, colormap = :jet)

See Also ​