See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/257690632
`
`Spectral analysis of photoplethysmographic signals: The importance of
`preprocessing
`
`Article(cid:100)(cid:100)in(cid:100)(cid:100)Biomedical Signal Processing and Control · January 2013
`
`DOI: 10.1016/j.bspc.2012.04.002
`
`CITATIONS
`38
`
`4 authors:
`
`Saime Akdemir Akar
`
`22 PUBLICATIONS(cid:100)(cid:100)(cid:100)242 CITATIONS(cid:100)(cid:100)(cid:100)
`
`SEE PROFILE
`
`Fatma Latifoglu
`Erciyes Üniversitesi
`
`45 PUBLICATIONS(cid:100)(cid:100)(cid:100)486 CITATIONS(cid:100)(cid:100)(cid:100)
`
`SEE PROFILE
`
`READS
`4,086
`
`Kara S
`University of North Texas HSC at Fort Worth
`
`223 PUBLICATIONS(cid:100)(cid:100)(cid:100)1,582 CITATIONS(cid:100)(cid:100)(cid:100)
`
`SEE PROFILE
`
`Vedat Bilgiç
`
`27 PUBLICATIONS(cid:100)(cid:100)(cid:100)233 CITATIONS(cid:100)(cid:100)(cid:100)
`
`SEE PROFILE
`
`Some of the authors of this publication are also working on these related projects:
`
`Non-invasive diagnosis of stress urinary incontinence (SUI) View project
`
`Hyperthermia Applicator View project
`
`All content following this page was uploaded by Kara S on 05 July 2015.
`
`The user has requested enhancement of the downloaded file.
`
`APPLE 1025
`
`1
`
`

`

`This article appeared in a journal published by Elsevier. The attached
`copy is furnished to the author for internal non-commercial research
`and education use, including for instruction at the authors institution
`and sharing with colleagues.
`Other uses, including reproduction and distribution, or selling or
`licensing copies, or posting to personal, institutional or third party
`websites are prohibited.
`In most cases authors are permitted to post their version of the
`article (e.g. in Word or Tex form) to their personal website or
`institutional repository. Authors requiring further information
`regarding Elsevier’s archiving and manuscript policies are
`encouraged to visit:
`http://www.elsevier.com/copyright
`
`2
`
`

`

`Author's personal copy
`
`Biomedical Signal Processing and Control 8 (2013) 16– 22
`
`Contents lists available at SciVerse ScienceDirect
`
`Biomedical Signal Processing and Control
`
`j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / b s p c
`
`Spectral analysis of photoplethysmographic signals:
`The importance of preprocessing
`Saime Akdemir Akar a,∗, Sadık Kara a, Fatma Latifo˘glu b, Vedat Bilgic¸ c
`
`a Institute of Biomedical Engineering, Fatih University, Istanbul, Turkey
`b Biomedical Engineering Department, Erciyes University, Kayseri, Turkey
`c Bakırköy Mental and Nervous Diseases Training and Research Hospital, Istanbul, Turkey
`
`t
`
`c
`
`
`
`a
`
`r
`
`
`
`t
`
`
`
`s
`
`b
`
`
`
`a
`
`o
`
`f
`
`i
`
`
`
`n
`
`
`
`a
`
`
`
`r
`
`
`
`t
`
`
`
`i
`
`
`
`c
`
`
`
`l
`
`
`
`e
`
`
`
`Article history:
`Received 1 November 2011
`Received in revised form 30 March 2012
`Accepted 3 April 2012
`Available online 30 April 2012
`
`Keywords:
`Photoplethysmography
`Heart rate variability
`Butterworth filtering
`Myriad filtering
`Detrending
`Spectral analysis
`
`Heart rate variability (HRV) is an important and useful index to assess the responses of the autonomic
`nervous system (ANS). HRV analysis is performed using electrocardiography (ECG) or photoplethysmog-
`raphy (PPG) signals which are typically subject to noise and trends. Therefore, the elimination of these
`undesired conditions is very important to achieve reliable ANS activation results. The purpose of this
`study was to analyze and compare the effects of preprocessing on the spectral analysis of HRV signals
`obtained from PPG waveform. Preprocessing consists of two stages: filtering and detrending. The perfor-
`mance of linear Butterworth filter is compared with nonlinear weighted Myriad filter. After filtering, two
`different approaches, one based on least squares fitting and another on smoothness priors, were used
`to remove trends from the HRV signal. The results of two filtering and detrending methods were com-
`pared for spectral analysis accomplished using periodogram, Welch’s periodogram and Burg’s method.
`The performance of these methods is presented graphically and the importance of preprocessing clar-
`ified by comparing the results. Although both filters have almost the same performance in the results,
`the smoothness prior detrending approach was found more successful in removing trends that usually
`appear in the low frequency bands of PPG signals. In conclusion, the results showed that trends in PPG
`signals are altered during spectral analysis and must be removed prior to HRV analysis.
`© 2012 Elsevier Ltd. All rights reserved.
`
`1. Introduction
`
`Photoplethysmography (PPG) is a simple, noninvasive and use-
`ful technique that detects blood volume changes in the blood
`vessels by optical methods. The PPG sensor consists of an infrared
`emitter, which passes light through the blood vessels, and a detec-
`tor, which detects light reflected from the vessels. Typically the
`emitter and detector are located in a transducer placed on the fin-
`ger or earlobe [1]. The PPG waveform reflects fluctuations in blood
`volume and is synchronized with the beating of the heart [2,3].
`Because the PPG signal contains information about heart rate
`and heart rate variability (HRV), it can be used instead of the ECG
`signal in analysis. HRV is defined as the variation of ECG R-wave
`intervals (RR) with respect to time and is an important index used in
`autonomic nervous system (ANS) analysis [3–5]. For the PPG signal,
`peak-to-peak (PP) intervals could replace the RR intervals detected
`from ECG signal [6,7] in HRV analysis. Many studies [2,8–10] verify
`
`∗ Corresponding author at: Institute of Biomedical Engineering, Fatih University,
`34500 Istanbul, Turkey. Tel.: +90 212 8663300x2643; fax: +90 212 8663412.
`E-mail address: saimeakar@fatih.edu.tr (S. Akdemir Akar).
`
`1746-8094/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.
`
`http://dx.doi.org/10.1016/j.bspc.2012.04.002
`
`the high correlation between the RR intervals obtained from ECG
`signals and PP intervals obtained from PPG signals.
`Although PPG signals are more simple and useful than ECG sig-
`nals, difficulties in analysis arise due to noise usually caused by
`motion artifacts and a quasi DC signal component that corresponds
`to the changes in the venous pressure [7]. Therefore, HRV wave-
`forms obtained from PPG signals include both noise and slowly
`changing trends from this DC component [4,7]. These undesired
`components must be removed due to their detrimental effect on
`the spectral analysis results of HRV.
`Spectral analysis of HRV gives information about ANS activ-
`ity. While the
`low frequency band reflects sympathetic and
`parasympathetic activity, the high frequency band is related to
`parasympathetic activity [11]. The power spectral density (PSD)
`is a spectral analysis method to find the power distribution over a
`frequency band contained in a signal. In several studies [6,7], non-
`parametric and parametric PSD estimation methods are applied to
`HRV data obtained from PPG signals to interpret variations of ANS.
`Because the PPG signal includes various sources of noise, such
`as the patient’s motion or respiration, both linear and adaptive fil-
`ters have been used by researchers for removing these artifacts
`from PPG signals [12–14]. To remove slow non-stationary trends
`in the signal, various methods have been proposed [15–18]. While
`
`3
`
`

`

`Author's personal copy
`
`S. Akdemir Akar et al. / Biomedical Signal Processing and Control
`
`
`
`8 (2013) 16–22
`
`
`
`17
`
`distributions [23]. Given a set of N weights (w1, w2, . . . , wN) the
`output of a weighted Myriad filter is [23]
`
`
` x1, . . . , wN ◦ˆˇk,w = myriad{k; w1 ◦
` xN}
`N(cid:3)
`
`
`ˆˇk,w =
` argmin
`ˇ
`
`[k2 + wi(xi −
` ˇ)2]
`
`
`
`(2)
`
`(3)
`
`i=1
`where ˇ is the real-valued location parameter, k is the dispersion of
`[x1, x2, . . . , xN]T is the observation vector.
`the distribution, and x
`Here, wi ◦ xi represents the weighting operation.
`
`
`=
`
`3.3. Detrending with linear least-squares fitting
`
`To solve the equations of the overdetermined or inexactly
`specified systems in an approximate sense, the least-squares are
`frequently used. A very common source of least squares problems
`is curve fitting. Minimizing the sum of the squares of the resid-
`uals, which are defined as the difference between observed and
`predicted modal values, fit parameters are calculated. The linear
`least-squares fitting technique, is the simplest and most commonly
`applied form of linear regression, yields a line that best fits to
`the data [24]. On the other hand, the least-squares polynomial fit
`method computes the coefficients of the n-th order polynomial that
`best fits the input data in the least-squares sense. The equation for
`a polynomial line is
`ˆu = a0xn + a1xn−1 + a2xn−2 +
`
`
`an−1x
` . . .
`where a0, a1, . . . are the coefficients. Here, straight line is polyno-
`mials of one order and is given as
`
`an
`
`+
`
`+
`
`(4)
`
`(5)
`
`a1
`
`+
`
`a0x
`
`=
`
`ˆu
`
`is the line with a0 and a1 parameters which minimizes the quantity
`
`(ui − ˆui)2
`
`i=1
`where ui is the ith element in the input vector. A distinct set of n + 1
`coefficients is computed for each column of the M-by-N input, u.
`The MATLAB detrend function generally operates to remove linear
`trend. It computes the least-squares fit of a straight line to the data
`and subtracts the resulting function from the data [24].
`
`(6)
`
`M(cid:4)
`
`3.4. Detrending with smoothness priors
`
`To remove slow non-stationary trends from the HRV signal,
`smoothness priors, an approach that performs like a time-varying
`FIR high-pass filter, was used [19]. According to this method, the
`RR interval time series is given as
`
`
`
`(R2 − R1, R3 − R2, . . . , RN − RN−1)T ∈
` RN−1
`where N is the number of R peaks of ECG signal. The RR time series
`contains two components
`zstat +
` ztrend
`where zstat is the nearly stationary RR series component and ztrend is
`the low frequency, aperiodic trend component. ztrend can be mod-
`eled as
`ztrend =
`v
` H
`R(N−1)×M is the observation matrix, 
`RM are the regres-
`where H
`sion parameters and v is the observation error. A regularized least
`(cid:7)
`(cid:6)(cid:6)Dd(H)(cid:6)(cid:6)2
`squares solution can be used to estimate ˆ as
`argmin =
`
`∈
`
`(cid:6)(cid:6)2 +
`
` (cid:3)2
`
`
`
`z
`
`−
`
`(cid:5)(cid:6)(cid:6)H
`
`+
`
`∈
`
`=
`
`z
`
`=
`
`z
`
`=
`
`ˆ
`
`(7)
`
`(8)
`
`(9)
`
`(10)
`
`some methods analyze only non-stationary segments in HRV data
`[15], other methods, typically based on polynomial models, remove
`these trends from the signal before HRV analysis [16–18] by sub-
`tracting from the instantaneous RR interval a linear polynomial fit
`to data. One method based on smoothness priors is an advanced
`detrending method for HRV analysis and performs like a time-
`varying FIR high pass filter [19].
`The main purpose of the present study is to determine the effects
`of preprocessing on HRV signals obtained from PPG waveform.
`To this end, a linear Butterworth filter and a nonlinear weighted
`Myriad filter, as well as two different detrending methods were
`used and compared as preprocessing. The effects of denoising
`and detrending were evaluated using periodogram, Welch’s peri-
`odogram and Burg’s method, respectively. The PSD results were
`compared for data with and without trends after Butterworth or
`weighted Myriad filtering.
`To our knowledge, no study has yet analyzed and compared the
`effects of linear (Butterworth), nonlinear (weighted Myriad) filter-
`ing, and two different detrending methods on artifact reduction in
`PPG signals. Thus, this research represents one of the first studies
`that investigate the effect of combining filtering and detrending on
`PPG signals to achieve reliable ANS activation results.
`
`2. Methodology
`
`The PPG signals used in this study were recorded at the Bakırköy
`Mental and Nervous Diseases Training and Research Hospital using
`the BIOPAC MP150WSW data acquisition system and Acknowledge
`software. Fifteen healthy adults (8 female, mean age 34
`9.7 years;
`7 male, mean age 37.8
`12.3 years) volunteered to participate in
`the study. The study was approved by both the university and hos-
`pital ethics committee, and written informed consent was obtained
`from all subjects. The PPG transducer (TSD200), which consists of
`60 nm wavelength, was
`an infrared transmitter/emitter of 860
`strapped to the non-dominant hand middle finger of the subject
`and connected to the PPG amplifier (PPG100C) through a shielded
`cable to record the blood volume pulse waveform of gain 100 and
`cut-off frequencies at 0.05 Hz and 10 Hz. Data were recorded for a
`duration of two minutes with a sampling rate of 250 Hz.
`
`±
`
`±
`
`±
`
`3. Preprocessing
`
`3.1. Butterworth filtering
`
`The Butterworth filter is a simple, linear frequency domain filter.
`Due to the monotonically decreasing magnitude response and a
`highly flat magnitude response in the pass-band, the Butterworth
`method is commonly used in signal processing applications [20].
`The magnitude squared response of an N-th order analog low-pass
`Butterworth filter Ha(s) is [21]
`
`(1)
`
`1
`(˝/˝c)2N
`
`+
`
`1
`
`
`
`(cid:2)(cid:2)Ha(j˝)(cid:2)(cid:2)2 =
`
`where ˝c is the 3 dB cut-off frequency.
`
`3.2. Weighted Myriad filtering
`
`The weighted Myriad filter is a nonlinear filter. In linear filtering
`approaches, it is assumed that signal noise is normally distributed
`[22]. However, noise in biomedical signals is usually impulsive and
`therefore not well described by the Gaussian model. A filter pro-
`posed as being better equipped to eliminate this sort of impulsive
`␣-stable
`noise is the weighted Myriad filters, which is based on
`
`4
`
`

`

`Author's personal copy
`
`18
`
`S. Akdemir Akar et al. / Biomedical Signal Processing and Control
`
`
`
`8 (2013) 16–22
`
`
`
`where XN(ejw) is the discrete time Fourier transform of the N point
`data sequence xN(n)
`
`∞(cid:4)
`
`XN(ejw)
`
`=
`
`xN(n)e
`
`n=−∞
`
`−jnw = N−1(cid:4)
`
`n=0
`
`−jnw
`
`x(n)e
`
`(21)
`
`4.1.2. Welch’s periodogram
`Welch’s method is an averaging modified periodogram to esti-
`mate the power spectrum [25]. This method splits the time series
`into overlapping segments, or windows, and calculates the peri-
`odogram for each window separately. Averaging the resulting
`periodograms, the Welch periodogram is calculated. Data segments
`are given as
`
`−
`
`0, 1, . . . , L
`
`1
`
`(22)
`
`=
`
`−
`
`0, 1, . . . , M
`
`1
`
`i
`
`=
`
`+
`
`x(n
`
`iD) n
`
`=
`
`xi(n)
`where iD is the starting point for the ith sequence, M is the length
`of the segments and n is the index of segments. The windowed data
`segments are
`
`(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)M−1(cid:4)
`
`˜P(i)
`xx (f )
`
`= 1
`MU
`
`xi(n)w(n)e
`
`(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)
`
`2
`
`−j2(cid:4)fn
`
`(23)
`
`where (cid:3) is the regularization parameter and Dd shows the discrete
`approximation of dth derivative operator. The solution of Eq. (10)
`can be obtained in the form
`−1
`+
`ˆ(cid:3) =
` (cid:3)2HT DT
` (HT H
`d DdH)
`
`ˆztrend = H ˆ(cid:3)
`where ztrend is the estimated trend that must be removed. To select
`=
`the observation matrix H, a trivial choice of identity matrix H
`R(N−1)×(N−1) can be used. To solve the regularization part of Eq.
`I
`(10), an optimal Dd regularization matrix can be selected. The sec-
`ond order difference matrix D2 ∈
`R(N−3)×(N−1) is proposed as a good
`choice for estimating the aperiodic trend of the RR series. According
`to the method of smoothness priors, the detrended nearly station-
`ary RR series can be written as
`ˆzstat =
`H ˆ(cid:3) =
` (I
` z
`
`HT z
`
`
`
`∈
`
`−1)z.
`
`(cid:3)2DT
`2D2)
`
`+
`
`(I
`
`−
`
`−
`
`(11)
`
`(12)
`
`(13)
`
`4. Spectral methods
`
`Spectral methods are used to describe how the power of a time
`series is distributed with frequency.
`
`4.1. Nonparametric methods
`
`4.1.1. Periodograms
`The periodogram is the Fourier transform of the autocorrelation
`sequence and can be determined as [22]
`
`Px(ejw)
`
`=
`
`rx(k)e
`
`−jkw
`
`(14)
`
`k=−∞
`where rx(k) is the autocorrelation sequence, which may be written
`as the time average
`
`∞(cid:4)
`
`N(cid:4)
`
`(n)
`
`∗
`
`k)x
`
`+
`
`x(n
`
`1
`
`+
`
`lim
`N→∞
`
`=
`
`rx(k)
`
`n=0
`where U is a normalization factor for the power of the window
`function w and may be found
`
`M−1(cid:4)
`
`U
`
`= 1
`M
`
`w2(n)
`
`(24)
`
`n=0
`The Welch’s power spectrum is formulized from the average of
`these modified periodograms as [26]
`
`Pw
`xx(f )
`
`= 1
`L
`
`L−1(cid:4)
`
`i=0
`
`˜P(i)
`xx (f )
`
`(25)
`
`(15)
`
`4.2. Parametric methods
`
`Fourier transform based non-parametric spectral analysis meth-
`ods have some limitations such as poor frequency resolution and
`spectral leakage due to windowing [27]. Parametric analysis meth-
`ods manage to overcome these limitations of the Fourier transform,
`by estimating the parameters of a chosen signal model. Autoregres-
`sive (AR) methods are the most widely used parametric methods
`for power spectral estimation.
`
`4.2.1. Burg method
`Burg’s method [28] estimates the AR model coefficients to obtain
`the power spectrum. The Burg method finds model parameters
`that minimize the forward and backward prediction errors. These
`prediction errors for a p-th (for Rev. 2) order model are defined as
`
`i)
`
`+
`
`p
`
`−
`
`∗ p
`
`ˆa
`
`,ix(n
`
`p(cid:4)
`
`i=1
`
`p)
`
`+
`p(cid:4)
`
`−
`
`x(n
`
`=
`
`ˆeb,p(n)
`
`+
`
`x(n)
`
`=
`
`ˆef,p(n)
`
`i)
`
`−
`
`ˆap,ix(n
`
`1
`
`−
`
`1, . . . , p
`p
`
`=
`
`=
`
`i
`i
`
`∗ p
`
`−1,p−i,
`
`1)
`1)|2]
`
`−
`
`−
`
`∗ b
`
`
`
`i=1
`(cid:8)
`The AR parameters ˆap can be written by reflection coefficient ˆkp
`ˆap−1,i + ˆkp ˆa
`ˆap,i =
`ˆkp,
`(cid:10)
`The estimation of reflection coefficient is given by
`(cid:10)
`−2
`ˆef,p−1(n)ˆe
`,p−1(n
`ˆkp =
`[|ˆef,p−1(n)|2 +
`|ˆeb,p−1(n
`
`(26)
`
`(27)
`
`(28)
`
`(29)
`
`1
`2N
`
`N−1−k(cid:4)
`
`n=−N
`where * (for Rev. 1) represents the complex conjugate. When x(n) in
`Eq. (15) is only measured over a finite interval, the autocorrelation
`sequence can be estimated with a finite sum
`
`(16)
`
`(n)
`
`∗
`
`k)x
`
`+
`
`x(n
`
`n=0
`where n
`1 is the discrete time index. Then, the peri-
`0, 1, ..., N
`odogram is calculated by taking the discrete time Fourier transform
`of ˆrx(k).
`
`−
`
`=
`
`= N−1(cid:4)
`
`ˆPper(ejw)
`
`ˆrx(k)e
`
`−jkw
`
`(17)
`
`k=−N+1
`Eq. (17) may be more convenient to use when written in terms of
`the x(n). Consider the signal xN(n) of finite length N:
`=
`
`(18)
`
`(cid:9)
`
`≤
`
`x(n) 0
`n < N
`0
`otherwise
`
`(cid:8)
`
`xN(n)
`
`ˆrx(k)
`
`= 1
`N
`
`The estimated autocorrelation sequence may be written as
`(−k)
`
`∞(cid:4)
`
`ˆrx(k)
`
`= 1
`N
`
`∗
`
`xN(k)xN
`
`∗
`
`(n)
`
`= 1
`N
`
`k)xN
`
`+
`
`xN(n
`
`
`
`(cid:2)(cid:2)XN(ejw)(cid:2)(cid:2)2
`
`= 1
`N
`
`(ejw)
`
`∗ N
`
`XN(ejw)X
`
`ˆPper(ejw)
`
`n=−∞
`Finally, the periodogram, an estimate of the power spectrum,
`may be calculated by taking the Fourier transform and applying
`the convolution theorem as
`= 1
`N
`
`(19)
`
`(20)
`
`5
`
`

`

`Author's personal copy
`
`S. Akdemir Akar et al. / Biomedical Signal Processing and Control
`
`
`
`8 (2013) 16–22
`
`
`
`19
`
`Fig. 1. The raw, Butterworth filtered and weighted Myriad filtered PPG signal.
`
`Fig. 2. Detected peaks represented by circles from the Butterworth filtered PPG
`signal.
`
`number. For spectral analysis, the x-axis indicating beat number
`must be converted to time using
`
`(33)
`
`1)
`
`−
`
`t(k
`
`+
`
`PP(k)
`
`=
`
`t(k)
`
`where t is time, PP is the peak-to-peak interval and k is the num-
`ber of beats. Then, the obtained data were interpolated to obtain
`a regularly sampled series with sampling rate of 4 Hz. To remove
`the quasi DC signal that corresponds to changes in venous pressure
`[7] in the waveform, a detrending approach based on smoothness
`prior method (SPM) was applied to the resampled data. The regu-
`larization parameter was chosen as (cid:3) = 200 based on the results of a
`previous study [4]. To deduce the effects of this method for detrend-
`ing, a second method based on the MATLAB detrend function was
`applied to the resampled data. The effects of the two detrending
`methods on the PPG signal tachogram are shown in Fig. 3.
`To compare the effects of these two detrending methods on
`a variety of spectral analysis methods, the periodogram, Welch’s
`periodogram and Burg’s method were used in this study. Each spec-
`trum is limited to 2 Hz to enable the comparison of the spectrums
`before and after detrending with the detrend function and SPM.
`The default rectangular window function was used for PPG signal in
`periodogram analysis. Spectral analysis results using periodograms
`of the Butterworth low-pass filtered PPG signal and the weighted
`Myriad filtered PPG signal are given in Figs. 4 and 5. No significant
`differences for each frequency were found in both figures. Results
`showed that the periodogram-based PSD decreases at all frequen-
`cies of both detrended PPG signals. However, there are more ripples
`in detrended and spectral analyzed PPG signals because of spectral
`leakage in periodogram technique.
`The Welch’s periodogram of the low-pass Butterworth filtered
`PPG signal is calculated using a Hamming window length of 32
`and 50% overlap (Fig. 6). The Welch PSD of both detrended sig-
`
`detrend ed PPG with
`
`"SPM"
`
`0.04
`
`0.03
`
`0.02
`
`0.01
`
`0
`
`The prediction errors meet the following recursive expressions
`= ˆef,p−1(n)
`+ ˆkpˆeb,p−1(n
`= ˆeb,p−1(n
`+ ˆk
`ˆef,p−1(n)
`ˆeb,p(n)
`1)
`These prediction expressions are used to generate a recursive-
`in-order algorithm for estimating the AR coefficients. The PSD
`estimate can thus be found as [26]
`=
`ˆep
`=1 ˆap(k)e−j2(cid:4)fk|2
`|1
`where ˆep is the total least-squares error, p is the model order and
`ˆap(k) are estimates of the AR parameters.
`
`1),
`
`−
`
`∗p
`
`−
`
`ˆef,p(n)
`
`+(cid:10)
`
`p k
`
`PBU
`xx (f )
`
`(30)
`
`(31)
`
`(32)
`
`5. Results
`
`The goal of this study is to assess the effects of preprocessing of
`HRV in spectral estimations. Therefore, the effects of filtering and
`detrending in spectral estimation of PPG signals are investigated.
`PPG data are analyzed using MATLAB 7.6® software. The PPG signal
`was first filtered using Butterworth and Myriad filters, separately.
`The effects of a linear Butterworth low-pass filter of the 8th order
`(cutoff – 8 Hz) and a weighted Myriad filter on a sample PPG signal
`are shown in Fig. 1. The 8th order Butterworth filter is generally
`recommended in the literature [7,13].
`A min–max detection algorithm developed by the authors was
`implemented in MATLAB to identify the peaks and determine the
`intervals between them. Thus, systolic peaks of the PPG signal were
`detected (Fig. 2). Fig. 2 shows the peaks of the Butterworth low-
`pass filtered PPG signal. Using this min–max detection algorithm,
`peak intervals obtained from the PPG signal were used to obtain
`tachograms in which the beat intervals are plotted against beat
`
`PP interval (sec)
`
`detren
`
`ded PPG
`
` with "detren
`
`d"
`
`0.04
`
`0.03
`
`0.02
`
`0.01
`
`0
`
`-0.01
`
`-0.02
`
`-0.03
`
`PP interval (sec)
`
`PPG signa
`
`l
`
`0.87
`
`0.86
`
`0.85
`
`0.84
`
`0.83
`
`0.82
`
`0.81
`
`0.8
`
`PP interval (sec)
`
`0.79
`
`0
`
`20
`
`40
`
` (sec)
`
`80
`
`100
`
`120
`
`-0.04
`
`0
`
`20
`
`80
`
`
`
`10
`
`0
`
`120
`
`60
`40
`60
`Time (s ec)
`Time
`Fig. 3. PPG tachogram, and detrended PPG tachogram with detrend function and smoothness prior method.
`
`-0.0 1
`-0.0 2
`-0.0 3
`-0.0 4
`0
`
`20
`
`40
`
`Time (sec)
`
`60
`
`
`
`80
`
`
`
`10
`
`0
`
`
`12
`
`0
`
`6
`
`

`

`PSD without t
`
`
` (SP M)
`
`rend
`PSD via pe
`
`
`riodogram
`
`0.5
`
`1.5
`
`2
`
`Author's personal copy
`
`20
`
`S. Akdemir Akar et al. / Biomedical Signal Processing and Control
`
`
`
`8 (2013) 16–22
`
`
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`-80
`
`-100
`
`-120
`
`0
`
`Power/frequency (dB/Hz)
`
`PSD without trend (detre nd fun ction)
`
`PSD via periodogr
`
`am
`
`1.5
`
`2
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`-80
`
`-100
`
`-120
`
`Power/frequency (dB/Hz)
`
`PSD with tre nd
`
`PSD via periodogr
`
`
`am
`
`0.
`
`1
`
`1.
`
`2
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`-80
`
`-100
`
`-120
`0
`
`Power/frequency (dB/Hz)
`
`5
`
`5
`
`1
`
`Freq uency (Hz)
`Fre quency (Hz)
`Fig. 4. Periodogram PSD analysis of PPG signals with and without trends (using the detrend function and SPM) after Butterworth filtering.
`
`0
`
`0.5
`
`1
`
`Frequency (Hz)
`
`PSD without trend (detrend function)
`
`PSD without trend (SPM)
`
`PSD via periodogram
`
`0.5
`
`1.5
`
`2
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`-80
`
`-100
`
`-120
`
`0
`
`
`
`Power/frequency (dB/Hz)
`
`PSD via periodogram
`
`0.5
`
`1
`
`1.5
`
`2
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`-80
`
`-100
`
`-120
`
`Power/frequency (dB/Hz)
`
`2
`
`PSD with trend
`
`PSD via periodogram
`
`
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`-80
`
`-100
`
`-120
`
`Power/frequency (dB/Hz)
`
`0
`
`0.5
`
`1
`
`Frequency (Hz)
`
`1.5
`
`0
`
`Frequency (Hz)
`
`1
`
`Frequency (Hz)
`
`Fig. 5. Periodogram PSD analysis of PPG signals with and without trends (using the detrend function and SPM) after Myriad filtering.
`
`PSD witho ut trend (SP M)
`PSD via Welc h
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`
`
`PSD wi thout trend (de trend fun ction)
`
`
`
`PSD via Welch
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`PSD with tren d
`PSD
`
` via Welch
`
`1
`
`1.
`
`5
`
`2
`
`-80
`0
`
`
`0.
`
`5
`
`1
`
`1.5
`
`2
`
`-80
`
`0
`
`0.5
`
`1.
`
`5
`
`2
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`-80
`
`Power/frequency (dB/Hz)
`
`0.5
`
`1
`
`
`
`Frequency (Hz)
`Frequency (Hz)
`
`Fig. 6. Welch PSD analysis of PPG signals with and without trends (using the detrend function and SPM) after Butterworth filtering.
`
`Frequency (Hz)
`
`PSD without trend (detrend function)
`
`PSD without trend (SPM)
`
`20
`
`0
`
`PSD via Welch
`
`-20
`
`-40
`
`-60
`
`-80
`
`0
`
`
`
`0.5
`
`1
`
`
`Frequency (Hz)
`
`1.5
`
`2
`
`Power/frequency (dB/Hz)
`
`PSD via Welch
`
`0.5
`
`1
`
`
`Frequency (Hz)
`
`1.5
`
`2
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`-80
`0
`
`
`
`PSD with trend
`
`PSD via Welch
`
`0.5
`
`1
`
`
`Frequency (Hz)
`
`1.5
`
`2
`
`Fig. 7. Welch PSD analysis of PPG signals with and without trends (using the detrend function and SPM) after Myriad filtering.
`
`0
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`-80
`0
`
`
`
`7
`
`

`

`Author's personal copy
`
`S. Akdemir Akar et al. / Biomedical Signal Processing and Control
`
`
`
`8 (2013) 16–22
`
`
`
`21
`
`PSD without trend (detrend function)
`
`PSD without trend (SPM)
`
`PSD via Burg
`
`60
`
`40
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`PSD via Burg
`
`60
`
`40
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`PSD with trend
`
`PSD via Burg
`
`0.5
`
`Frequency (Hz)
`
`1
`
`1.5
`
`2
`
`-80
`
`0
`
`0.5
`
`1
`
`Frequency (Hz)
`
`1.5
`
`2
`
`-80
`0
`
`
`0.5
`
`1
`
`Frequency (Hz)
`
`1.5
`
`2
`
`Fig. 8. Burg PSD analysis of PPG signals with and without trends (using the detrend function and SPM) after Butterworth filtering.
`
`PSD with trend
`
`PSD without trend (detrend function)
`
`PSD without trend (SPM)
`
`PSD via Burg
`
`60
`
`PSD via Burg
`
`60
`
`PSD via Burg
`
`60
`
`40
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`-80
`
`0
`
`60
`
`0.5
`
`1
`
`Frequency (Hz)
`
`1.5
`
`2
`
`40
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`-80
`0
`
`
`
`0.5
`
`1
`
`
`Frequency (Hz)
`
`1.5
`
`2
`
`40
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`-80
`0
`
`
`
`0.5
`
`1
`
`
`Frequency (Hz)
`
`1.5
`
`2
`
`40
`
`20
`
`0
`
`-20
`
`-40
`
`-60
`
`Power/frequency (dB/Hz)
`
`-80
`0
`
`
`
`Fig. 9. Burg PSD analysis of PPG signals with and without trends (using the detrend function and SPM) after Myriad filtering.
`
`Table 1
`Average Butterworth filtered PPG signal powers for differing periodogram methods.
`
`Average power
`(0–2 Hz)
`
`Periodogram
`Welch’s periodogram
`Burg’s periodogram
`
`With
`trend
`
`0.2207
`2.53e−4
`3.0e−4
`
`Without trend via
`detrend function
`
`Without trend
`via SPM
`
`0.0188
`1.35e−4
`1.28e−4
`
`0.0007
`1.28e−5
`1.21e−5
`
`Table 2
`Average weighted Myriad filtered PPG signal powers for differing periodogram
`methods.
`
`Average power
`(0–2 Hz)
`
`Periodogram
`Welch’s periodogram
`Burg’s periodogram
`
`With
`trend
`
`0.3406
`2.47e−4
`2.57e−4
`
`Without trend via
`detrend function
`
`Without trend
`via “SPM”
`
`0.0073
`1.42e−4
`1.05e−4
`
`0.0011
`1.39e−5
`1.02e−5
`
`nals decreases nearly 40 dB between 0 and 0.5 Hz and the ripples
`between 0.5 and 2 Hz disappear. The Welch’s periodogram spec-
`tral analysis results of the weighted Myriad filtered PPG signal are
`shown in Fig. 7. While the Welch PSD of very low frequency com-
`ponents (0.01–0.04 Hz) decreased nearly 45 dB after detrending the
`Butterworth filtered PPG signal using the detrend function, the PSD
`over the same frequency range of the Myriad filtered PPG signal
`after detrending decreased even more.
`The PSD results of Burg’s method are shown in Fig. 8 for the low-
`pass Butterworth filtered PPG signal and in Fig. 9 for the weighted
`Myriad filtered PPG signal. The order of the AR model in the Burg
`method was selected as p = 16 based on [4,29], using the Akaike
`information criteria [30]. Although the PSD of signal detrended with
`the detrend function decreased nearly 80 dB between 0 and 0.05 Hz,
`over the same frequency range, the PSD of the signal detrended
`with SPM decreased 90 dB, as shown in Fig. 8. At other frequen-
`cies, no difference was obtained. Fig. 9 shows the Burg PSD of the
`weighted Myriad filtered PPG signal. The Burg PSD of very low fre-
`quency components (0.01–0.04 Hz) decreased nearly 80 dB after
`both detrending with the detrend function and with SPM.
`The average power of the Butterworth low-pass filtered and
`weighted Myriad filtered PPG signal without detrending, detrend-
`ing via the detrend function, and detrending via smoothness priors
`for the varying periodogram approaches applied to 15 subjects are
`compared in Tables 1 and 2.
`
`6. Conclusion
`
`The purpose of this study is to investigate the effects of pre-
`processing (filtering and detrending) of PPG signals on different
`spectral estimation methods. To remove noise, a linear low-pass
`Butterworth filter and adaptively weighted Myriad filter were first
`separately applied to PPG data, then two different detrending meth-
`ods (the MATLAB detrend function and smoothness prior method)
`were used to remove trends in the signal. The detrend function
`removes the linear component of a signal. It computes the least-
`squares fit of a straight line (or composite line for piecewise linear
`trends) to the data and subtracts the resulting function from the
`data [24]. The smoothness prior approach is also a simple method
`for detrending and operates like a time-varying FIR high-pass
`filter.
`The effect of the two detrending methods on the PSD of the But-
`terworth filtered PPG signal calculated with a periodogram, Welch’s
`periodogram and Burg’s method is presented in Figs. 4, 6 and 8.
`According to the differences between detrended and original PPG
`data, the periodogram does not provide effective solution for each
`frequency band because of spectral leakage. The results of Welch
`periodogram are more successful than periodogram technique. For
`Welch’s periodogram, the PSD of the low frequency components
`decreases while the value at higher frequencies is not significantly
`
`8
`
`

`

`Author's personal copy
`
`22
`
`S. Akdemir Akar et al. / Biomedical Signal Processing and Control
`
`
`
`8 (2013) 16–22
`
`
`
`affected by detrending. For Burg’s method, the PSD of very low
`frequency components decreased more for both detrended signals.
`Similarly, the periodogram-based PSD values of the Myriad fil-
`tered PPG signal decreased at all frequencies of both detrended
`signals, just as for the Butterworth filtered signal. The results of
`Welch’s and Burg’s periodogram of the Myriad filtered PPG signal
`also show a similar change with the Butterworth filtered signal pat-
`tern, such as the PSD of low frequency components decreasing after
`detrending.
`The power reduction in very low frequency and low frequency
`bands after spectral analysis of detrended PPG signal can be eval-
`uated as an important indicator of the dominant effects of trends
`in these frequency bands. This confirms the results of a previous
`study that examined the effects of trends on ECG based HRV data
`[4]. Moreover, the obtained power reduction values vary depending
`on applied spectral analysis technique and investigated frequency
`band, similarly to this previous study.
`We found that the PSD of data detrended with the smooth-
`ness prior method decreased more in comparison to that of data
`detrended with the detrend function over the 0.01–0.15 Hz fre-
`quency band for both Welch’s and Burg’s periodogram applied
`to Butterworth and Myriad filtered signals. This frequency band
`consists of very low frequency and low frequency components of
`heart rate variability analysis. In comparing the results over the
`frequency range of 0–2 Hz in Tables 1 and 2, smoothness prior
`method detrending showed a greater decrease in average power
`for all periodogram approaches. This may be due to its success
`to removing trends, which is shown in Fig. 3. So, in our study,
`the smoothness prior detrending approach was found to be more
`successful at removing trends at low frequencies. No significant
`differences at each frequency were found between the PSD results
`of the linear Butterworth filtered and adaptively weighted Myriad
`filtered PPG signals. One possible explanation is that the parame-
`ters of the Myriad filters were selected without any optimization.
`For future research in this subject, it may be useful to use an opti-
`mization algorithm for weight selection. In conclusion, the results
`showed that the spectral analysis of