FFT and power spectral density of the PPG waveform, explained

Every pulse oximeter already produces a rich signal that most monitors throw away. The number on the screen is the oxygen saturation, but the underlying optical trace, the photoplethysmography or PPG waveform, carries far more information than a single percentage. PulSentry's approach rests on reading that waveform in the frequency domain. This article walks through how that works, in plain engineering terms.

What the PPG waveform is

A pulse oximeter shines light through tissue, usually a fingertip, and measures how much reaches the far side. With each heartbeat, arterial blood volume rises and falls, and so does the absorbed light. The result is a repeating waveform whose dominant rhythm is the heartbeat. Riding on top of that cardiac pulsation is a slower, gentler undulation that tracks breathing: intrathoracic pressure changes with each breath subtly alter venous return and the pulse amplitude. In a healthy person that respiratory effect is small. When the heart is under pressure, it grows.

From the time domain to the frequency domain

Looking at the raw waveform, the respiratory modulation can be hard to quantify by eye. The Fast Fourier Transform, or FFT, solves this by re-expressing the signal as a sum of sine waves at different frequencies. Instead of amplitude over time, you get power over frequency, the power spectral density (PSD). Two peaks dominate the result:

• A cardiac peak, near the heart rate, typically around 1 to 2 Hz (roughly 60 to 120 beats per minute).
• A respiratory peak, near the breathing rate, typically around 0.2 to 0.4 Hz (roughly 12 to 24 breaths per minute).

Because the two processes live at clearly different frequencies, the spectrum separates them cleanly. That separation is the whole point: a feature that is tangled together in time becomes two distinct, measurable peaks in frequency.

The pulsus index: a ratio of two peaks

Once the respiratory and cardiac peaks are identified, the relationship between them can be summarized as a single ratio, the respiratory spectral power divided by the cardiac spectral power. PulSentry tracks this ratio, which we call the pulsus index, continuously over time. A low, stable index reflects the small respiratory effect seen in normal physiology. A persistently rising index reflects a growing respiratory influence on the pulse, the same mechanism that produces pulsus paradoxus at the bedside. For the clinical background on that sign, see our clinician's guide to pulsus paradoxus.

Why the frequency domain helps in practice

Working in the frequency domain brings several practical advantages for a continuous monitor:

• Noise separation. Motion and other artifacts often sit at frequencies away from the cardiac and respiratory bands, so they can be down-weighted rather than mistaken for signal.
• A trend, not a snapshot. A spot reading of pulsus paradoxus depends on the moment it is taken. A spectral ratio computed on a rolling window produces a trend line, and it is the persistence of a rising trend, not any single value, that is informative.
• It uses hardware that already exists. No new sensor is required. The analysis runs on the PPG that standard pulse oximeters already generate.

What this does not do

Signal processing does not diagnose. The pulsus index is a quantitative summary of a waveform feature, not a verdict about a patient. It is designed to surface a persistent, rising respiratory effect on the pulse so a care team can investigate sooner, with the tools they already trust. PulSentry is investigational and not FDA-cleared. Any monitoring signal is meant to support clinical judgment, never to replace it.

For why this matters specifically after cardiac surgery, where the relevant collections can be hard to see on echo, see why echocardiography misses post-surgical tamponade.