Butterworth Filtering at 500 Hz Optimizes PPG-Based Heart Rate Variability Analysis for Wearable Devices: A Comparative Study

Figures

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  Figure 1. Amplitude response of Butterworth and Elliptic bandpass filters (0.8–20 Hz, 2nd-order) under single-pass (solid lines) and zero-phase forward-backward (dashed lines) implementations, with the passband shaded. (a) At 1000 Hz, Butterworth shows a flat passband (transition widths: 0.65 Hz low, 84.35 Hz high), while Elliptic has 1 dB ripple and sharper roll-off (82.80 Hz high). (b) At 500 Hz, Butterworth (0.65 Hz low, 75.36 Hz high) and Elliptic (74.18 Hz high) maintain spectral fidelity. (c) At 250 Hz, Butterworth (0.65 Hz low, 55.34 Hz high) and Elliptic (54.74 Hz high) show reduced high-frequency transitions due to lower Nyquist frequency.

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  Figure 2. Pole–zero diagrams of the 2nd-order digital Butterworth (BW, blue) and elliptic (EL, red) bandpass filters (0.8–20 Hz) at three sampling rates: (a) fs = 1000 Hz, (b) fs = 500 Hz, (c) fs = 250 Hz. The poles are marked with × and transmission zeros with ○, enclosed by a dashed unit circle. Both designs place zeros at z = +1 and z = −1 (suppressing DC and Nyquist), while the elliptic filter additionally introduces two transmission zeros positioned on the unit circle in the left half-plane, producing sharper transition bands. All poles lie inside the unit circle (stable); pole radii decrease slightly as fs decreases because with the 0.8–20 Hz passband fixed, the natural decrease in pole radii results from pole readjustment to maintain filter stability.

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  Figure 3. Agreement between PPG- and ECG-derived HRV indices across six filter–sampling configurations. The left panels show Lin’s concordance correlation coefficients (CCC) with 95% bootstrap confidence intervals, with the red dashed line indicating the 0.90 threshold for excellent agreement. The right panels present mean differences with 90% confidence intervals relative to the ±0.05 equivalence bounds (blue dotted lines) used in the TOST procedure. Results are shown for (a) ln HF, (b) ln LF, and (c) ln VLF, comparing Butterworth (BW) and Elliptic (EL) filters at sampling rates of 250, 500, and 1000 Hz.

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  Figure 4. Bland–Altman plots for log-transformed HRV indices comparing PPG- and ECG-derived measurements under six filter–sampling configurations. Results are shown for (a) ln HF, (b) ln LF, and (c) ln VLF. Each panel contains six subplots corresponding to Butterworth (BW) and Elliptic (EL) filters at sampling rates of 1000, 500, and 250 Hz. The x-axis displays the average of PPG and ECG values, and the y-axis plots the difference (PPG − ECG). Red dashed lines indicate the mean bias, while green dotted lines denote the 95% LoA (mean difference ± 1.96 SD), and blue dots represent individual measurements. These plots visualize systematic bias and random variability across filter designs and sampling frequencies.

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  Figure 5. Passing–Bablok regression comparing PPG- and ECG-derived HRV indices across filter–sampling conditions: (a) ln HF, (b) ln LF, and (c) ln VLF. Results are shown for Butterworth (BW) and Elliptic (EL) filters at 1000, 500, and 250 Hz. Scatter points represent paired measurements; the dashed line denotes the line of identity (y = x), and the red line indicates the PBR fit with slope and intercept. Blue dots represent individual HRV indices. Agreement is strongest for BW at 500 and 1000 Hz, acceptable for EL at 1000 Hz, and weakest at 250 Hz, especially for EL.

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  Figure 6. Frequency response characteristics and spectral fidelity comparison for each filter condition. Left: Comparison of frequency responses with ideal bandpass filter (black dashed line), showing that Butterworth filters exhibit flat characteristics in the passband (0.8–20 Hz, yellow region) while elliptic filters demonstrate sharp cutoff characteristics with passband ripple. Right: Spectral fidelity relative to ideal bandpass filter, where BW filters (1000 Hz: 100.0%, 500 Hz: 98.2%, 250 Hz: 89.5%) generally outperform EL filters (1000 Hz: 97.8%, 500 Hz: 91.3%, 250 Hz: 78.9%), with BW 500 Hz particularly providing high fidelity while maintaining computational efficiency.