Comparison of signal smoothing techniques for use in embedded system for monitoring and determining the quality of biofuels

Comparison of signal smoothing techniques for use in embedded
system for monitoring and determining the quality of biofuels
Dalton Cézane Gomes Valadares*
, Rute Cardoso Drebes,
Elmar Uwe Kurt Melcher*
, Sérgio de Brito Espínola*
,
Joseana Macêdo Fechine Régis de Araújo*
* Members of the GASIS Project (GASes Intelligent Sensing)1
Laboratório de Pesquisas em BioEnergia, Arquiteturas Dedicadas e Inteligência Artificial
(BELADIA)
Unidade Acadêmica de Sistemas e Computação
Centro de Engenharia Elétrica e Informática
Universidade Federal de Campina Grande
Campina Grande, Paraíba, Brazil
daltoncezane@gmail.com
rcdrebes@gmail.com
elmar@ computacao.ufcg.edu.br
sergiodbe@gmail.com
joseana@computacao.ufcg.edu.br
Abstract
This paper presents the study of signal smoothing techniques, in order to select the best for use in a
specific type of problem: determination of oxidative stability, by the computational calculation of
the induction period. The oxidative stability is one of the major quality parameters of biofuels.
According to some established hypotheses and metrics, the results of the study are presented,
culminating in the identification of best available techniques related to each metric. This work also
contains a case study presenting real use of the smoothing techniques in a signal collected by
Ozomat (equipment for determining the oxidative stability).
Introduction
One of the key metrics used in the evaluation process of the quality of biofuels is the oxidative
stability, which expresses the susceptibility to oxidation of the fuel. This metric is defined through
the induction period, which is the time measured between the start of the analysis and the sudden
increase in the degree of oxidation.
A new method was developed for measuring the oxidative stability, in order to obtain faster analysis
than those obtained with the main methods used in the industry [3, 16, 17]. This new method, for
purposes of this work, will be called Ozomat. The idea of the Ozomat consists in the use of the
Ozone as a catalyst for the oxidation reaction of biofuel, thereby accelerating the oxidation process,
obtaining a shorter induction period.
The Ozomat has a microfluidic measuring cell, which is responsible for reading resistances values
for calculating the induction period. Such automatic calculation is defined as the maximum point of
the second derivative of the conductivity curve (inverse of the resistance)[4]. Since there is no
analytical expression for the conductivity function, the temporal second derivative of this function
must be calculated numerically.
The use of analytical measurement equipment for small computers in order to obtain real-time data
is becoming standard practice in laboratories and industries. Moreover, it is now easier to acquire
data quickly in digital format, making use of low cost microcomputers and widely available. File
Applied Mechanics and Materials Vols. 448-453 (2014) pp 1679-1688
© (2014) Trans Tech Publications, Switzerland
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storage and retrieval/exhibition of information are just some of the advantages of digital data
acquisition.
In the process of obtaining and transmitting information, it is common that the signal contain some
distortion because of the mechanical and electrical means. Among the main causes of the distortion,
can be mentioned tracking errors, crosstalk, thermal noise and poor characteristics of pickup
(equipment). If the distortion has random statistical characteristics, it is called noise. Due to
imperfections in the measurement process (signals acquisition) the signal σ (t) tends to be noisy.
This problem also happens in Ozomat, because of some electronic components and due to intrinsic
imperfections of the oxidation process. With the noise in the signal conductivity, the numerical
derivative is markedly impaired. The noise tends to be "amplified" in the chart of the derivative and
this effect is proportional to the derivative order, i.e. to the second derivative the problem is greater
[10, 6]. As a result, the read values need a treatment, in order to obtain the second derivative of the
generated/estimated curve accurately. With the second derivative of the curve, it is found the global
maximum point to determine the induction period. Thus, to measure the oxidative stability it is
needed to obtain the global maximum through the second derivative of the generated curve by the
read resistances (values).
There are a great number of numerical methods that can be used to reduce noise, to increase
resolution of overlapping peaks, optimize measuring strategies, diagnose measurement problems
and decompose complex signals into their component parts. These techniques can often make it
easier some measurements difficult, through of extraction of more information from the available
data. Many of them are based on laborious mathematical procedures, which were not practical
before the advent of computerized instrumentation. As the computers are faster and have become
widely available, the use of the techniques is becoming increasingly common, and therefore, it is
important to understand the characteristics and limitations of each signal smoothing technique.
The operation of removing the noise, which is often necessary to retrieve information or obtain it
accurately, is called filtering (smoothing techniques). It is not so simple to determine how much
noise must be separated from the information contained in the signal. There are cases where a gross
filter has performance similar to a filter extremely complicated and there are cases in which a good
result depends on a well elaborated filter, with some idiosyncrasies [8]. An example of a filtering
operation is showed in the Figure 1.
This way, to accurately use the signals obtained by the Ozomat, it is needed to pass some smoothing
technique at the signal. In this work, four smoothing techniques are compared and a case study is
presented, with some signals collected by Ozomat. This problem can be seen as:
Figure 1: The left half of this signal has a noisy peak, while the right half has a peak after the
execution of an algorithm for smoothing (filtering) [9].
1680 Renewable Energy and Environmental Technology

 Business Problem: deliver filtered datasets of the best way (without significant losses), so
that it is possible to calculate the second derivative of the estimated curve.
 Technical Problem: study and compare techniques for filtering signals and define the best
among them.
As seen, the main aim of this work is determine the better signal smoothing technique, between the
four studied, for subsequent processing of an algorithm for determining the induction period, thus
identifying the oxidative stability of biofuel.
Techniques for Signal Smoothing
As seen, thanks to the increasing use of computer technology for data acquisition, various
techniques are studied and have been used for filtering of various types of signals. This work has
the purpose of compare four techniques: Rectangular, Triangular, Pseudo-Gaussian and Savitzky-
Golay.
Before starting the study with the four techniques mentioned, some studies were read and they
showed different techniques with different approaches to filtering signals. Among the techniques
discussed in these papers, some of them are based on Taylor Series, differentiation, differentiation
with optimizations, recursive implementations of finite impulse response, differentiators for low
frequencies, etc [1, 2, 5, 7, 13 and 14].
The Rectangular or Unweighted Sliding-Average Smooth is the simplest smoothing technique. It
works replacing each point of the signal with the average of m adjacent points, being m a positive
integer usually called as smooth width. For a 3-point smooth width, the formula is:
(1)
In this case, j varies from 2 to n-1 (n is the total number of points in the signal), Sj the jth
point in the
smoothed signal and Yj the jth
point in the original signal. If the noise is "white noise" (evenly
distributed over all frequencies) standard deviation sd, then the standard deviation of the noise
remaining in the signal after one pass of the rectangular smoothing technique (filter) will be
approximately sd divided by the square root of m (m is the smooth width): sd/sqrt(m).
The difference between the rectangular and the triangular filters is that the triangular implements a
weighted smoothing function, i.e., each point of the original signal has a weight. This way,
considering a 5-point smooth width, the formula of the triangular filter is:
(2)
The parameters of this formula are similar to that in the rectangular filter (j now varies from 3 to n-
2). The triangular filter is equivalent to two passes of the rectangular filter with 3-point smooth
width. It is more effective than the rectangular in the reduction of high frequency noise. The smooth
coefficients are symmetrically balanced around the central point.
The Pseudo-Gaussian smoothing technique is equivalent to three passes of the rectangular technique.
This technique has coefficients with features similar to a Gaussian distribution.
Applied Mechanics and Materials Vols. 448-453 1681

The Savitsky-Golay smoothing technique is based on the least-squares fitting of polynomials to
segments of the data. Compared to the three other smoothing techniques mentioned (Rectangular,
Triangular and Pseudo-Gaussian), the Savitsky-Golay is less effective at reducing noise and its
algorithm is more complex. However, it is better at retaining the shape of the original signal, which
is a behavior desirable in many applications of chemical analysis. The general formula of the
Savitsky-Golay technique is [6, 12]:
(3)
The greater the width of the filter (number of signal points used in each iteration), the greater is the
noise reduction and the greater is the possibility of signal distortion due to the operation of
smoothing (filtering). The more points are used for the size of the filter, the lower is the amplitude
of the filtered signal, as shown in Figure 2. If keeping the shape of the peak is more important than
optimizing the signal-noise relation, the Savitzky-Golay method has advantages over the other
techniques, because this filter has the characteristic of reducing the noise while maintaining the
shape and the height of the peak wave [9, 12]. Thanks to this property, some researchers consider
Savitzky-Golay attractive to the use in electrocardiogram processing [12].
Figure 2: The red curves are noisy signals. The three green curvers (both in the left and in the right)
are three smoothed signals with triangular filter of width (from top to bottom): 7, 25 e 51 points.
Experiment to Compare the Techniques
This Section presents how this study was performed, mentioning the hypotheses and what was
performed to judge them, explaining all the process as well the defined metrics to this analyses.
Methodology
To perform this work, some clean signals were generated and to these some noisy signals were
added. This way, the result after the pass of one smoothing technique could be compared to ideal
result, which would be the clean signal. The generated clean signals are: sinusoidal, quadratic, cubic
and exponential.
With these signals (clean and noisy), the four smoothing techniques mentioned were applied to each
case (sinusoidal, quadratic, cubic and exponential). To judge which technique is better, the
following metrics were analyzed:
 Implementation complexity (number and type of arithmetic operations);
 Accuracy in obtaining the results;
 Robustness regarding noise interference.
After determining which of the four signal smoothing techniques is better, according to the
established metrics, the result was used to select a technique and apply it to a signal collected by the
Ozomat (real application). The application of the techniques is accomplished through a library

developed for Matlab, called iSignal [11], which has the four filters implemented (objects of this
paper). Such library receives a signal as input, calculates the filtered signal and generates the
graphic using the smoothing techniques and derivatives up to 4th order.
The elaborated hypotheses are presented in the next subsection. To evaluate the four signal
smoothing techniques cited in this work, some questions were established to facilitate the analysis
of the hypotheses:
Q1. Is there difference between the implementation complexity of the filters Rectangular,
Triangular, Pseudo-Gaussian and Savitzky-Golay?
Q2. Is there difference between the accuracy of the result of applying of the filters rectangular,
triangular, and pseudo-Gaussian Savitzky-Golay?
Q3. Is there difference between the robustness to noise by applying the filters Rectangular,
The independent variables are defined as the following factors:
 Technique used (Rectangular, Triangular, Pseudo-Gaussian or Savitzky-Golay);
 Dataset with signals for which are applied the techniques (4 signals).
The response variables (dependent), according to exposed metrics, are:
 Representative number of the amount of arithmetic operations in accordance with their types
(e.g. division with weight X and multiplication with weight Y; if a technique have four
multiplications and two divisions, the representative value for this metric will be 2X + 4Y);
 Root mean squared error (RMSE) at the end of the application of the technique (how
inaccurate the result becomes);
 Ratio between the filtered signal and noisy signal: signal-noise ratio (SNR).
The required instrumentation for this experiment involves: Ozomat, Personal Computer, Matlab
Software, iSignal Library and some Biofuels Samples.
Hypotheses
The hypotheses that helped to perform the experiment and to define what to investigate for
determining the better technique were the following (with the respective questions):
Q1 - Is there difference between the implementation complexity of the filters Rectangular,
H1-0: There is not difference between the implementation complexity of the filters Rectangular,
Triangular, Pseudo-Gaussian and Savitzky-Golay;
H1-1: There is difference between the implementation complexity of the filters Rectangular,
Triangular, Pseudo-Gaussian and Savitzky-Golay.
Q2 - Is there difference between the accuracy of the result of applying of the filters rectangular,
triangular, and pseudo-Gaussian Savitzky-Golay?
H2-0: There is no difference between the accuracy of the result of applying of the filters
rectangular, triangular, and pseudo-Gaussian Savitzky-Golay;
H2-1: There is difference between the accuracy of the result of applying of the filters rectangular,
triangular, and pseudo-Gaussian Savitzky-Golay.
Q3 - Is there difference between the robustness to noise by applying the filters Rectangular,
H3-0: There is no difference between the robustness to noise by applying the filters Rectangular,
Triangular, Pseudo-Gaussian and Savitzky-Golay;
H3-1: There is difference between the robustness to noise by applying the filters Rectangular,
Triangular, Pseudo-Gaussian and Savitzky-Golay.

For each question, if the null hypothesis is rejected, i.e. the alternative hypothesis is accepted, the
experiment must determine which technique is better according to the respective metrics
(Implementation complexity, Accuracy of the results and Robustness regarding noise interference).
Results and Short Discussion
This Section contains the obtained results according to evaluation of the created hypotheses during
the study. The analysis about the hypotheses, according to the three defined metrics, is discussed.
The clean signals (Figure 3) were generated through the following functions (‘t’ varying from 0 to 4,
step of 0.05, obtaining 81 samples):
 Sinusoidal  f1 = sin(2.π.t);
 Quadratic  f2 = (t – 1).(t – 2);
 Cubic  f3 = t3
– 6t2
+ 11t – 6;
 Exponential  f4 = e(-t)
.sin(3.π).
Figure 3: Clean signals.
After that, some noises were added for each clean signal and the evaluation of the hypotheses was
performed. The noises applied here were of the type Gaussian (they were randomly generated). The
noisy signals (clean signals with noise added) are like showed in Figure 4.
Figure 4: Noisy signals.
The first question answered (Q1) refers to the implementation complexity of the signal smoothing
techniques. To evaluate the implementation complexity of the techniques, the following weights
were considered for each arithmetic operation: Sum - 1, Subtraction - 2, Multiplication - 3, Division
- 4. In addition, it was considered that the width of the filter (technique) to be used is five points
(the width of the filter means the number of points used for a "pass" of it). The formulas of each
technique, considered for obtain this metric, were afore mentioned.

Thus, the following resulting values were obtained for each technique:
 Rectangular filter: 4 sums (weight 1) + 1 division (weight 4), resulting in the value 8 (4x1 +
1x4 = 8);
 Triangular filter: (considered as two passes of the rectangular filter): 4 sums (weight 1) + 3
multiplications (weight 3) + 1 division (weight 4), resulting in the value 17 (4x1 + 3x3 +
1x4 = 17);
 Pseudo-Gaussian (considered as three passes of the rectangular filter): to simplify the
calculations, it was used an approximation by the result of the rectangular filter, i.e., 3 x 8
(result of the rectangular filter) = 24;
 Savitzky-Golay filter: 10 multiplications (weight 3) + 18 sums (weight 1) + 1 division
(weight 4) = 49.
From the above results, it is concluded that the H1-0 is rejected, because the filters do not have the
same implementation complexity. The best filter is the one with lower resulting value, i.e. lower
implementation complexity. Thus, for this metric, the best filter is the rectangular filter.
To answer the other questions, it must be considered the 4 clean signals plotted in the Figure 3. As
already explained, some noise was added to these signals and, after, they were filtered with the 4
smoothing techniques implemented in the iSignal library [11] for Matlab. With the original and
filtered signals it was possible to perform a comparison between these techniques, evaluating, of
this way, the precision and the robustness of them, and analyzing the hypotheses.
The second question answered (Q2) is related to the precision of the techniques. This metric was
evaluated by the calculation of the root-mean-squared errors (or root-mean-squared deviation). The
root-mean-squared error (RMSE) is used to measure the differences between the predicted values
by a model and the really observed values. This kind of measure is an easily interpreted statistic and
is directly interpretable in terms of measurement units, being considered a good measure for
accuracy/precision.
Table 1: RMSE values (evaluation of the smoothing techniques precision).
Average of RMSE values according to different noises, signals and techniques
Signals/Techniques Rectangular Triangular Pseudo-Gaussian Savitzky-Golay
Sinusoidal 0.2779948 0.2156021 0.1969619 0.2932493
Quadratic 0.7434332 0.7476434 0.7682145 0.2954570
Cubic 0.9451742 0.9665742 0.9927753 0.2993203
Exponential 0.2838564 0.2205670 0.1875844 0.2954570
As the RMSE calculated for each case (noisy signal + smoothing technique, varying noise and
smoothing techniques for every signal specified: sinusoidal, quadratic, cubic, exponential) had
different values, the hypothesis H2-0 was rejected. Thus, with H2-1 accepted, it was necessary to
define the best technique with respect to this metric (precision). In this case, the best technique is
the one with the smallest RMSE value.
As can be seen in the Table 1, the lowest RMSE values are in bold and underlined. There is not a
technique that is best for all situations, i.e., for each kind of signal, one technique excels:
 For sinusoidal signals, the best smoothing technique is the Pseudo-Gaussian;
 For quadratic signals, the best smoothing technique is the Savitzky-Golay;
 For cubic signals, the best smoothing technique is the Savitzky-Golay;
 For exponential signals, the best smoothing technique is the Pseudo-Gaussian.
The last question of interest (Q3) raised for this study concerns to the robustness to noise of the
investigated techniques. The robustness of the techniques was measured according to the Signal-
Noise Ratio (SNR). The SNR usually is used to compare the level of a desired signal to the level of

background noise and it is defined as the ratio of signal power to the noise power. Thus, it is a good
measure for determining the robustness to noise.
Table 2: SNR values (evaluation of the smoothing techniques robustness)
Average of SNR values according to different noises, signals and techniques
Signals/Techniques Rectangular Triangular Pseudo-Gaussian Savitzky-Golay
Sinusoidal 0.5724482 0.8507831 1.1481832 0.5057102
Quadratic 1.6299388 2.2044140 2.6967976 1.2793203
Cubic 1.7661211 3.1331958 4.5105400 1.0727437
Exponential 9.1516129 e-32
1.4662886 e-31
1.8284285 e-31
7.7801395 e-32
Through the calculated values, it was concluded that the H3-0 is rejected and then is needed to
determine which of the four techniques is better (H3-1 accepted), considering the robustness. The
Table 2 contains the average of SNR values, for each signal and technique. The higher the SNR
value is, the better is the robustness of the technique. Thus, as can be seen in Table 2, the Pseudo-
Gaussian technique is the best for this metric.
Case study: application of smoothing technique in noisy signal for determination of the
oxidative stability
After the experiment, evaluating each technique according to defined metrics, a signal collected by
the Ozomat was used to verify which technique should show better results for this case, that is a real
need.
The determination of the oxidative stability, as already mentioned in this paper, is given by
calculating the second derivative of the signal, followed by obtaining its maximum point. Therefore,
an ideal signal (clean) was used to determine what would be its maximum of the second derivative,
and then, techniques of this study were applied in the noisy signal, obtained by the Ozomat, for
subsequent determination of the maximum point of the second derivative in this signal. Thus, it was
possible to compare the results of the real signal with the ideal result and determine which
technique presents better behavior. At the graphs below (Figure 5), the Conductivity (x-axis) is
represented in (Ω-m)-1
and the Time (y-axis) is in seconds (s).
Figure 5: Application of the Pseudo-Gaussian smoothing technique in a ‘real’ signal for the
calculation of the oxidative stability.
The point of abrupt growth of the left signal (clean) was found at about 2185s. After that, the
smoothing techniques studied here, together with the second derivative, were applied in the right
signal and the technique which found the better result was the Pseudo-Gaussian, as can be seen in
the Figure 5. Thus, to this case the oxidative stability determined was also 2185s.

Conclusion and Future Work
In this work, a study was made with four signal smoothing techniques, in order to determine the
best of them according to some criteria (metrics). It was noticed that, depending on the metrics
evaluated, the best result for a particular technique depends on the type of signal in which this
technique is applied (e.g. sinusoidal, quadratic, etc.). With these results, it was possible to select the
most suitable technique for filtering the data collected by Ozomat, allowing to establish the correct
value of the oxidative stability by the computational calculation of the induction period.
As a future work, another study can be done investigating other smoothing techniques, different of
the four presented here. Some other questions can also be done, stimulating the thought to new
metrics. These questions can be like:
 What is the technique that allows working with the longest period of sampling without loss
of quality of the result?
 Which technique requires less capacity of data storage?
Thus, this can be performed in the future for a more complete work. Another future work is the
implementation of the better technique, identified here, for the embedded system of the Ozomat.
REFERENCES
[1] AL-ALAOUI, M. A. Novel digital integrator and differentiator. Electronics Letters. Vol. 29,
Issue: 4, Pages: 376-378, 1993.
[2] AL-ALAOUI, M. A. A Class of Second-Order Integrators and Low-Pass Differentiators. IEEE
Transactions On Circuits And Systems I Fundamental Theory And Applications. Vol. 42, Issue: 4,
Pages: 220-223, 1995.
[3] CUNHA, H. do N., MELCHER, E. U. K., VASCONCELOS NETO, W. R., SILVA, F. L. A. J.,
NEFF, F. H. “Determinação da estabilidade oxidativa de óleos e combustíveis utilizando oxidação
acelerada com Ozônio (Patente PI1002057 - Número de depósito),” U.S. Patent PI1002057 –
Number of deposit, 2011.
[4] EN14112, “Fat and Oil Derivatives – Fatty Acid Methyl Esters (FAME) – Determination of
oxidation stability (accelerated oxidation test).” 2003.
[5] KHAN, Ishtiaq Rasool and OHBA, Ryoji. Digital Differentiators Based on Taylor Series. IEICE
TRANS. FUNDAMENTALS - vol. E-82-A - nº 12, December, 1999.
[6] KITAMURA, K.; HOZUMI, K. “Effect of savitzky—golay smoothing on second-derivative
spectra,” Analytica Chimica Acta, vol. 201, pp. 301-304, 1987.
[7] KUMAR, B., DUTTA ROY, S. C. Design of Digital Differentiators for low Frequencies.
Proceedings of the IEEE. Vol. 76, Issue: 3, Pages: 287-289, 1988.
[8] NOHEL, J. A.; SATTINGE, D. H.; ROTA, G. Selected Papers Of Norman Levinson.
Birkhäuser, 1st
Edition, 1997.
[9] O’HAVER, T. Smoothing Algorithms. Available in: Http://Terpconnect.Umd.Edu/~ Toh/Spec
Trum/Smoothing.Html#Algorithms. Accessed in: 05/08/2012a.
[10] O’HAVER, T. “An Introduction to Signal Processing in Chemical Analysis,” 2012. [Online].
Available: Http://Terpconnect.Umd.Edu/~Toh/Spectrum/Differentiation.Html. Accessed in:
25/07/2012b.
[11] O’HAVER, T. iSignal. Available In: Http://Terpconnect.Umd.Edu/~Toh/Spectrum/
Isignal.Html. Accessed in: 25/07/12.
[12] SCHAFER, R. W. “What is a Savitzky-Golay Filter?” Vol. 28 (4), P. 111-117 (2011).
[13] SUNDER, S., SU, Y., ANTONIOU, A., LU, W. S. Design of digital differentiators satisfying
prescribed specifications using optimization techniques. ISCAS, IEEE. CH2692-2/89/0000-1652,
1989.
[14] VAINIO, O., RENFORS, M., SARAMALU, T. Recursive implementation of fir differentiators
with optimum noise attenuation. IEEE TRANSACTIONS ON INSTRUMENTATION AND
MEASUREMENT, VOL. 46, Nº 5, OCTOBER, 1997.

[15] VALADARES, D. C. G.; VITORINO, B. A. F.; NASCIMENTO NETA, M. L.; BATISTA, E.
S.; SANTOS, M. V. D.; NEFF, F. H.; MELCHER, E. U. K.; BARROS, E. N. System for Analysis
of the Biodiesel Quality. In: Rio Oil & Gas Expo and Conference 2012 Proceedings. 2012a, Rio de
Janeiro, RJ, Brazil.
[16] VALADARES, D. C. V, VITORINO, B. A. F., NEFF, F. H., LIMA, A. M. N., MELCHER, E.
U. K. Monitoramento da Qualidade de Biocombustíveis e Medição Automática da Estabilidade
Oxidativa. In: 16º Congresso Internacional de Automação, Sistemas e Instrumentação, Brazil
Automation ISA 2012, 2012b, São Paulo, SP, Brazil.
[17] VITORINO, B. A. F., NEFF, F. H., MELCHER, E. U. K., LIMA, A. M. N. Equipamento para
Medição Automática da Estabilidade Oxidativa do Biodiesel. In: XIX Congresso Brasileiro de
Automática, CBA 2012. Campina Grande, PB, Brazil.

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