- Open Access
Vital sign sensing method based on EMD in terahertz band
© Xu and Liu; licensee Springer. 2014
- Received: 28 February 2014
- Accepted: 6 May 2014
- Published: 22 May 2014
Non-contact respiration and heartbeat rates detection could be applied to find survivors trapped in the disaster or the remote monitoring of the respiration and heartbeat of a patient. This study presents an improved algorithm that extracts the respiration and heartbeat rates of humans by utilizing the terahertz radar, which further lessens the effects of noise, suppresses the cross-term, and enhances the detection accuracy. A human target echo model for the terahertz radar is first presented. Combining the over-sampling method, low-pass filter, and Empirical Mode Decomposition improves the signal-to-noise ratio. The smoothed pseudo Wigner-Ville distribution time-frequency technique and the centroid of the spectrogram are used to estimate the instantaneous velocity of the target's cardiopulmonary motion. The down-sampling method is adopted to prevent serious distortion. Finally, a second time-frequency analysis is applied to the centroid curve to extract the respiration and heartbeat rates of the individual. Simulation results show that compared with the previously presented vital sign sensing method, the improved algorithm enhances the signal-to-noise ratio to 1 dB with a detection accuracy of 80%. The improved algorithm is an effective approach for the detection of respiration and heartbeat signal in a complicated environment.
- Empirical Mode Decomposition
- Smoothed pseudo Wigner-Ville distribution
- Respiration and heartbeat rates detection
- Performance analysis
Respiration and heartbeat rates detection is required for health examinations, particularly with aging society , which is becoming an increasingly important issue. Traditional products and methods are of the contact type, that is, these approaches require contact with or attachment of some sensors to the patient's body. These techniques include electrocardiography (ECG), oximetry, respiration belt, and so on. Such methods are difficult to employ for infants and for severely scalded or burned patients. Microwave technology can be utilized for non-contact respiration and heartbeat rates detection, which is not confronted by the aforementioned problems [2–5]. This technology supports respiration and heartbeat rates detection in an out-of-hospital environment and facilitates remote monitoring in a hospital to improve user satisfaction. Meanwhile, the detection process is unnoticeable and avoids the user's respiration and heartbeat rates change caused by mood swing.
The terahertz (THz) radar has unique advantages in the field of non-contract respiration and heartbeat rates detection. The THz wave has a shorter wavelength than other bands. The Doppler shift is inversely proportional to the wavelength. A shorter wavelength will generate a larger micro-Doppler frequency for the same micro-motion. The THz radar makes the features of the micro-Doppler more visible and can thus improve the detection accuracy . The THz photon has minimal energy. The THz wave differs from X-ray in that it has no ionization effect and does not destroy the original structure of the material . Thus, the THz wave will not damage the human body. Moreover, the THz wave can penetrate some non-metallic materials and can be reflected back from human targets. The terahertz radar can be used to detect respiration and heartbeat rates of survivors trapped in earthquakes and avalanches .
The Empirical Mode Decomposition (EMD) can filter the noise from ECG signals [9, 10]. Basing from EMD, we propose an improved respiration and heartbeat rates detection algorithm with THz radar that can further enhance the signal-to-noise ratio (SNR). This approach can effectively detect respiration and heartbeat signals in complicated environments with low SNR.
Section 2 introduces the heartbeat and respiration signal model. Section 3 introduces the Empirical Mode Decomposition and presents the steps of the improved respiration and heartbeat rates detection algorithm. Section 4 discusses the performance analysis of the improved respiration and heartbeat rates detection algorithm. Section 5 presents the conclusion.
where c is the speed of light, and the delay of the radar echo is 2R(t)/c. This assumption is known as the start-stop approximation. The speed of light is significantly faster than that of the subject body. Thus, the correctness of the assumption becomes more accurate to a higher degree.
where λ = c/fc is the wavelength of the radar wave.
for a = 1/2 - r ⋅ f2, where r is the heartbeat radius.
The respiration and heartbeat signal model parameters
Carrier frequency fc
Fixed distance R0
Respiration displacement r1
Heartbeat displacement r2
Respiration rate f1
Heartbeat rate f2
Heartbeat radius r
Heart rate shift τ
Combining the EMD and the previously reported respiration and heartbeat rates detection algorithm  significantly improves the latter.
3.1 EMD method
EMD, a new adaptive and effective data decomposition method aiming at non-linear and non-stationary data, was presented by NE Huang in 1998 . The decomposition process involves the sifting of the intrinsic oscillatory modes with their characteristic time scales in the signal, which is fully driven by the data. Any given signal can be decomposed into a series of intrinsic mode functions (IMFs). Every IMF confirms a certain frequency band of the signal s(t). The IMF sifted earlier represents a higher frequency band than that sifted later. The IMF should satisfy two conditions: (1) the number of local extrema and that of zero crossings can differ by one at most for the whole data, and (2) the mean value of the envelope defined by the local maxima and that defined by the local minima should be zero at any point . These conditions indicate that the intrinsic mode function is a single-component signal. That is, any given multi-component signal s(t) can be decomposed into several single-component signals with the EMD approach.
For any given signal s(t), the EMD process is as follows:
Step 3: r1(t) is regarded as s(t). Step 1 and step 2 are repeated to identify other IMFs imf2(t), imf3(t)…, and residuals r2(t), r3(t)…, in sequence. If the amplitude of imf N (t) is small enough or the number of extrema of r N (t) is less than a predetermined number, the whole decomposition process stops.
The IMF is not a single-component signal but contains a certain frequency band of the noised SMR(t) (Figure 1) because of the interpolation error and end effect.
3.2 The improved respiration and heartbeat rates detection algorithm
where λ is the signal wavelength. Thus, the Doppler shift in the received radar signal is proportional to the velocity of the target .
The smoothed pseudo Wigner-Ville distribution (SPWVD) time-frequency technique is applied to the respiration and heartbeat signal to measure the Doppler frequency of the target. The centroid of the spectrogram estimates the instantaneous velocity of target's cardiopulmonary motion . Finally, the centroid curve undergoes a second time-frequency analysis to extract the respiration and heartbeat rates of the individual.
where λ is fixed. In practice, the ceiling limit values of f1, r1, and r2 exist , the lower limit value of r exists. Thus, the maximum of the Doppler frequency fD max can almost be confirmed.
The over-sampling method is employed in the echo signal as pre-treatment. When the signal passes through the first time-frequency analysis, the sampling frequency is larger than the maximal frequency component in the signal. Noise components can be filtered out by a low-pass filter, which can help improve the SNR of the initial analysis of the weak signal and lessen the effects of noise on the signal band.
where imf1(t) ⋯ imfL - 1(t) are the eliminated IMFs, the frequency band confirmed by imf L (t) includes fD max, is the time-frequency result of imf i (t), and is the time-frequency result of the residue rN(t).
where x(f) is the weighting function of the frequency, and the default value is f for simplicity.
Before the second time-frequency analysis is executed, we extracted the centroid curve, which is close to the speed signal of the human body to a certain extent. Down-sampling is adopted to obtain a sampling frequency down to 10 Hz, which also satisfies the Nyquist sampling theorem. If the sampling frequency of the second time-frequency analysis does not undergo down-sampling, the final time-frequency diagram will exhibit serious distortion.
In the second time-frequency analysis of the centroid curve, the respiration and heartbeat frequencies become separated.
Carrier frequency fc
Sampling rate 1 fo
Sampling rate 2 fd
Window 1 h = hamming
Window 2 g = hamming
Frequency points N
Signal-to-noise ratio SNR
High spectral energy density areas and their corresponding frequencies in Figure 6
High spectral energy density areaσ i
Corresponding frequencyf i (Hz)
Average of normalized spectral energy density
As shown in Table 3, the respiration and heartbeat frequencies are 0.230 and 1.003 Hz, respectively.
The frequency band confirmed by imf4 is close to the practical maximum of the Doppler frequency, and the detection result shown in Figure 7c is better.
Compared with the previously presented vital sign sensing method, the improved algorithm enhances the SNR to 1 dB with a detection accuracy of 80%.
In this paper, a vital sign sensing method based on the EMD in THz band is proposed. The over-sampling method and low-pass filter sift out the noise components. The EMD further improves the SNR, and the down-sampling method prevents serious distortion. Combining the SPWVD and the centroid curve method facilitates the extraction of the respiration and heartbeat rates with low SNR. Meanwhile, the detection performance of this method is analyzed. The improved respiration and heartbeat rates detection method is an effective approach for the analysis of the THz radar signal for vital sign sensing in a complicated environment.
This work is supported by the National Natural Science Foundation of China under Project 61371048, the Fundamental Research Funds for the Central Universities under Project ZYGX2012J029, and the Fundamental Research Funds for the Central Universities under Project ZYGX2012Z001.
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