Skip to content

Spectral Entropy divergence

Key: spectral_entropy · Family: spectral · Better: lower ↓ · Per-lead: yes · Uses: fs

Spectral entropy measures how spread out a recording's spectrum is. A clean ECG concentrates power in a few low frequencies (low entropy); noise spreads it across all frequencies (high entropy). The metric asks: do the real and synthetic sets have the same distribution of spectral entropies?

Try it

Each bar counts recordings with a given spectral entropy. The real set includes recordings with different noise levels, as real data does.

Interactive demo loading… (needs JavaScript)

What to notice:

  • Too clean or too noisy shifts the whole synthetic histogram.
  • All alike: same average noise, but no variation between recordings. The histogram becomes narrow, and the divergence rises even though the PSD average would look fine. This is what this metric adds over psd.

How it works

For each lead:

  1. Compute each recording's PSD (Welch with SciPy, FFT otherwise) and normalise it to sum to 1.
  2. Compute its Shannon entropy in bits.
  3. Histogram the real and synthetic entropies with 50 bins over their joint range.
  4. Compute the Jensen–Shannon divergence between the two histograms.

The score is the mean over leads.

The math

\[ \mathrm{SE}(x) = -\sum_f p(f)\,\log_2 p(f), \qquad p(f) = \frac{S_x(f)}{\sum_{f'} S_x(f')} \]
\[ \text{score} = \mathrm{JS}\big(\mathrm{hist}(\mathrm{SE}^{r}),\ \mathrm{hist}(\mathrm{SE}^{s})\big) \in [0, \ln 2] \]

Reading the score

  • 0 means identical entropy distributions; ln 2 ≈ 0.693 means no overlap at all.
  • With 50 bins and only a few hundred recordings, histograms are sparse and the score is noisy. Use as many recordings as possible and compare against a real-vs-real baseline.
  • Per-lead means and standard deviations of the entropies are in extra and are often easier to interpret than the divergence itself.

Use it with ECGEN-Eval

ecgen-eval eval --real real.npy --synthetic synth.npy -m spectral_entropy --fs 500 --output report.html

from ecgen_eval import load_ecg_npy, AVAILABLE_METRICS

real = load_ecg_npy("real.npy", fs=500)
synth = load_ecg_npy("synth.npy", fs=500)

se = AVAILABLE_METRICS["spectral_entropy"](fs=real.fs)
result = se.compute(real.data, synth.data, lead_names=real.lead_names)
print(result.score, result.extra)   # extra[lead]: real/synth SE mean and std

Parameters are in the Metric Reference.

Learn more

  • Inouye et al., Quantification of EEG irregularity by use of the entropy of the power spectrum, Electroencephalogr. Clin. Neurophysiol. 1991.