Stress leaves a clear mark in your breathing, but amusement does not

What a sixty-second breath trace can measure beyond rate

A sixty-second breath trace is more than a count of inhalations and exhalations. It also carries the rhythm of each cycle and the stability of that rhythm over time. Frequency analysis splits the signal into bands, from slow waves at 0.05 to 0.20 hertz up to 5 hertz. Each band tracks a different motion, from slow oscillations to common adult rates and small waveform wiggles. The dominant breathing frequency is taken as the strongest peak between 0.05 and 1.00 hertz. Narrower bands then add detail, such as power from 0 to 0.10 hertz or from 0.70 to 1.00 hertz. Wavelet tools look at how energy spreads across scales, and entropy measures say whether that spread is orderly or scattered. One wavelet feature compares the energy in a fast detail band with the rest of the signal. Another asks how evenly wavelet energy is distributed, which can reveal hidden roughness in an apparently smooth trace. Autocorrelation lags measure how the signal repeats against itself after short delays. The first crossing from positive to negative correlation is called Zpm, and the next return to positive is Zmp. These lags describe cycle length, regularity, and the shape of alternation, not just how many breaths occur. They can be computed once for the whole minute, or again inside each detected breath cycle. Median Zmp across cycles gives a typical timing scale, and its variation score shows instability. Other summaries use interquartile range, full range, slope, or last-minus-first change. The coefficient of variation divides the standard deviation across cycles by the absolute mean. That separates an average effect from instability over time. Slope and difference summaries ask whether a marker drifts upward or downward through the minute. An exploratory branch also asks how quickly short-term predictability breaks down. It builds forecasts from similar past breath patterns and tracks how prediction error grows with horizon. A steeper early rise means the trace becomes harder to forecast after only a few seconds. These nonlinear markers are optional, because simpler timing and spectral features often carry the main signal. Taken together, these descriptors turn a minute of breathing into a map of rhythm, shape, stability, and predictability.

Stress, meditation, and baseline leave different breathing marks

Stress leaves a faster and less even mark in the breathing signal. The strongest single sign was extra energy in the 0.70 to 1.00 Hz band, with a separation score of 72.70. That band sits above the usual adult breathing rate, so it points to quicker ripple components in the signal. Stress also made the timing of each breath less consistent from one cycle to the next. Variability in the inspiratory time ratio reached a score of 62.81, so inhale share shifted across cycles. Meditation left a slower and steadier mark in the same sixty-second breathing window. Its clearest single sign was a longer typical breathing-cycle timing marker, with a separation score of 79.82. Low-frequency power in the 0.05 to 0.20 Hz band also helped, because meditation deepens slower oscillations. Together, those marks gave a very strong combined separation score of 88.65 for meditation. Baseline showed a shorter whole-window timing marker, with its best single score at 57.97. That shorter lag suggests the resting breath has a quicker repeat pattern than the meditative state. When several interpretable marks were combined, baseline reached scores around 63 to 64 in both model types. These numbers show that the three states do not blur into one shared breathing pattern. Stress adds speed and jitter, meditation adds depth and regularity, and baseline sits between them with a lighter signature.

Amusement is the hardest state to catch from breath alone

Amusement leaves the weakest mark in a sixty-second breath trace. Stress and meditation make clearer changes in rhythm, timing, or frequency content. For amusement, the best single marker was breathing rate, with a Matthews correlation coefficient of only 28.19. That score is low, because it means the marker separates amused windows from other states only weakly. A higher score would show a more stable pattern that a model could rely on. When several features were combined, amusement still resisted clean separation. The strongest compact transparent models reached Matthews correlation coefficients of about 31 to 35. Those numbers are far below the scores obtained for stress or meditation in the same tests. The raw-signal network also struggled, though its reported accuracy looked respectable at first glance. For amusement against all other states, it reached an accuracy of 86.14 percent but a Matthews score of only 28.20. The high accuracy is misleading, because non-amusement windows are much more common in the data. A model can score well simply by saying most windows were not amused. The network’s precision for true amusement windows was 37.93 percent, so many positive calls were wrong. Its recall was 34.07 percent, meaning it missed most of the actual amused windows. The compact model had a different weakness: precision fell to 30.44 percent while recall rose to 69.91 percent. That means it caught more real amusement windows, but too many other windows were also flagged. Adding extra predictability measures did not turn amusement into a reliable state. They improved separation somewhat, yet the best compact model still reached only about 35.69 on the balance-aware score. The practical reading is that amusement does not have a stable respiratory signature in this data set. Breathing rate, timing variability, and spectral energy can hint at it, but the signal remains too faint for confident detection.

A compact network wins at stress, while simple markers win elsewhere

The compact network that read the raw breathing signal directly had about 0.23 million adjustable numbers inside it. It passed a normalized sixty-second waveform through four convolutional layers and then sent the result to a small classifier. For stress, that design paid off. The Matthews correlation coefficient is a balance score that penalizes both missed cases and false alarms, so it is useful when the states are unevenly common. In the test where each person was held out in turn, the network reached a Matthews score of 90.61, with accuracy at 96.72 percent. Its precision was 93.03 percent and its recall was 92.41 percent, so it caught most stress windows while making few false stress calls.

A transparent five-feature model also handled stress well, but it trailed by 7.10 points on the Matthews score, reaching 83.51. It caught almost all stress windows, with recall of 95.31 percent, yet its precision was lower at 80.26 percent. That pattern means it missed fewer stress windows but made more false stress calls. Outside stress, the simpler branch often did better. For baseline, a compact feature model reached a Matthews score of 65.34, while the network managed 52.56. The gap was 12.78 points. It used power in the 0.20 to 0.50 hertz band, variation of an autocorrelation lag across three twenty-second pieces, a short-horizon predictability measure, and sample entropy. Sample entropy is a simple way to say how uneven the waveform looks from moment to moment.

For meditation, the feature model was even clearer. It reached a Matthews score of 88.65 against 77.58 for the network, with precision at 96.49 percent and recall at 86.19 percent. In plain terms, it made very few false meditation calls, though it still missed some true ones. Its five inputs included a breath-cycle median of a longer autocorrelation lag, low-frequency power in the 0.05 to 0.20 hertz band, a wavelet entropy-like measure, mid-range spectral energy, and inspiratory timing. A threshold-style model helped here, because meditation seemed to follow a more rule-like breathing pattern than stress did. The contrast suggests two tools for different jobs. The raw-signal network is the stronger choice when speed and accuracy on stress matter most. The transparent feature branch is better when a clinician, engineer, or embedded device needs to see which breathing marker drove the decision.

A practical path from breath to state

The useful lesson is that breathing can be read as a small portable signal of mental condition. The reading must match the question. For stress, a compact network trained on raw sixty-second traces gives the strongest separation. It catches most stressed windows while keeping false alarms low enough for everyday use. That makes it a plausible candidate for quiet monitoring in phones, watches, or other wearables that already track chest movement.

For meditation and baseline, simpler feature models do better when judged by balanced accuracy. They expose which timing, variability, spectral, and waveform markers are doing the work. Those transparent models matter when a clinician needs to understand why an alert fired. They also help when the device has too little memory for a larger network.

The limits are just as instructive. Amusement resisted detection even after combining several breath features. That suggests some emotional states do not leave a stable respiratory signature in this kind of data. A high raw accuracy can be misleading when one state is rare. Balanced scores reveal how often the system actually separates the target from everything else.

The work also depends on a small public wearable dataset and careful subject-wise testing. Broader real-world use will need larger groups, more daily contexts, and sensors that record breathing consistently without asking people to wear extra equipment. The opportunity is not a single universal breath test. It is a set of tools: one fast detector for stress, another explainable screen for calmer states, and honest uncertainty where the signal fades.

If future devices can tell when they are confident and when they should stay silent, breathing may become less like a vital sign and more like a quiet window into how people are doing.