Pharmaceutical & medical
HOW THE NEW DISCRETE PERIOD TRANSFORM METHOD CAN PROCESS PHYSIOLOGICAL SIGNALS
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By Dr. Dennis E. Bahr, president and biomedical engineer, Bahr Management, Inc., and Marc Smith, principal engineer, Analog Devices
ignals of physiological origin can be corrupted by noise and motion artifacts, and often share the same pass band as the signals themselves. Biological signals are quasi-stationary and have periods and amplitudes that can change over time. Simple filtering of data is
not possible with such signals. One popular way for extracting information is to use another signal, which is temporally linked to the data, acting as the time- frame for ensemble averaging. Although ensemble averaging has been effectively applied to oximetry signals using an external cardiac trigger from an ECG source, in many instances an ECG source may be unavailable. In this work, a successful effort was made to process signals without an ECG trigger yet yielding similar results.
Initially, an algorithm was developed to conduct a form of autocorrelation and ensemble averaging. However, it was soon discovered that ensemble averaging in the time domain was unnecessary, since all pertinent information could be found in the period domain data itself. Heart rate and blood oxygen saturation could be calcu- lated directly from the results generated by the sliding discrete period transform (DPT). This work was started with a review of the discrete Fourier transform (DFT) since it can generate the frequency spectrum of a signal that can then be used to determine its period. Another goal of the research was to sample the data with a very high degree of resolution. Obtaining high resolution with the DFT requires collecting a large number of data samples. Because biological signals are quasi-stationary, collecting a large number of samples using the DFT often results in spectral smearing. What was needed was an algorithm that had high resolution, but would only require a small number of samples compared to the DFT. Since the intention was to use the algorithm on real-time data of undetermined length, a sliding form of the trans- form similar to a sliding DFT was used.
This article introduces the sliding discrete period transform (DPT), a novel algorithm designed for processing physiological signals, specifically photoplethysmogram (PPG) signals from pulse oximeters. The algorithm employs period domain analysis with sinusoidal basis functions, addressing challenges like random noise and nonstationary data. Implemented as a sliding transform in MATLAB, the DPT combines autocorrelation and ensemble averaging. Details will be provided on an algorithm developed and implemented on an Analog Devices’ MAX30101 device and compared to a Masimo oximeter with Signal Extraction Technology (SET).
METHODS Algorithm Requirements
The initial objective was to find an algorithm that could be used to determine the underlying fundamental period of the data even if it was stochastic and non-stationary in nature. The initial algorithm requirements were:
Be able to determine the fundamental period of any biomedical signal such as ECG and SpO₂.
Have a rapid enough response time to track cardiac heart rate period and amplitude changes in real time.
Recover rapidly from signal interrup- tions or from excessive noise or motion artifacts.
Have sufficient computational speed so as not to be the limiting factor in deter- mining the sampling rate.
Have low to moderate storage space requirements and the ability to be used in low power and portable devices.
Where k = 0, 1, 2, ... N – 1 The ith
Equation 2. sample of the DFT is calculated as shown in Algorithm Development
Starting with the DFT, the objective was to find the period, so the frequency terms in the DFT equa- tions were replaced with the period and instead of incrementing frequency as with the DFT, the period was incremented. Whereas the DFT has the frequency increase in a linear fashion such as (1f₀, 2f₀, 3f₀, …), where f₀ is the first harmonic, the DPT has the period increase in a linear fashion in multiples of the sampling period T₀. Despite the similarities in the equations of the two algorithms, the DFT cannot generate the same results as the DPT, as they are fundamentally different algo- rithms. The DFT and the DPT can be compared by analysing the equations that describe their
implementation. For sampling frequency fS the frequency bin k of the N-point DFT corresponds to
frequency fK = k × fS / N Hz, and Equation 1 is the expression for the spectrum of the kth frequency bin for the sample sequence XI ... XI + N - 1.
January 2025 Instrumentation Monthly
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