=Paper=
{{Paper
|id=Vol-2555/paper15
|storemode=property
|title=Representation of Series and Transforms in engineering subject, using a Web User
Interface for GNU Octave
|pdfUrl=https://ceur-ws.org/Vol-2555/paper15.pdf
|volume=Vol-2555
|authors=Pedro Freddy Huamaní Navarrete
}}
==Representation of Series and Transforms in engineering subject, using a Web User
Interface for GNU Octave==
https://ceur-ws.org/Vol-2555/paper15.pdf
Representation of Series and Transforms in engineering
subject, using a Web User Interface for GNU Octave
Pedro F. Huamaní-Navarrete
Ricardo Palma University, Lima, Perú
phuamani@urp.edu.pe
Abstract. This article shows the experience of using a web user interface (UI
Web) for GNU Octave, in order to represent mathematically and graphically the
Fourier series and transforms that are studied in one of the units of an
introductory subject in the telecommunications area, in the Electronic
Engineering program from Ricardo Palma University (URP), Lima-Peru.
Likewise, we show the development of the programming routines to obtain the
Fourier series coefficients of some periodic signals, as well as the graphical
representations of them in the frequency domain. Also, with the Fourier
Transform, from the discrete point of view, some non-periodic signals were
analyzed. Finally, we show the averages of the evaluations obtained in the
thematic unit of interest, through a trend graph with a positive slope.
Keywords: Web User Interface, Fourier series, Discrete Fourier Transform,
Octave Online.
1 Introduction
Nowadays, computer tools for numerical calculation have become one of the main
supports in science education, and this because many of them grant ease in terms of
2D and 3D graphic representations, animations, logic programming routines,
graphical user interfaces, symbolic operations, numerical operations, and other
features. Likewise, such tools are available for various operating systems, including
those that are freely available as is the case with Linux. In this way, among some of
the most common computer tools that have been used by various universities in the
world in the field of research and development; thus, we have: Matlab, Maple, Scilab,
Mathematica, GNU Octave, etc.; as well as, there are various programming languages
that allow or facilitate the teaching of science in the classroom, particularly in some
engineering programs. So, we have C ++, Java, Python, R, Julia, etc. And, not only
these computational tools can be used from a personal computer, but they are also
possible to use from various portable electronic devices such as Tablets, Cell phones,
iPAD, Laptops, etc., which offers greater versatility for the student allowing him to
simulate, calculate, model, program, graph, among other actions, while moving or
being outside his study center. In most universities that offer engineering programs it
Copyright c 2019 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).
is necessary to teach several science subjects from the first semesters of study, as is
the case with physics, chemistry and mathematics; and, according to the engineering
specialty, it is decided to include more or less of these subjects in the curriculum.
Particularly, in Electronic Engineering program from Ricardo Palma University in
Lima-Peru, according to the 2015-2 Curriculum Plan [1], five math courses, 4 physics
courses and 1 chemistry course are taught, which are dictated in the first two years of
study. In this way, we form a solid basis in the student to face specialized subjects
that require an understanding of this previous theory; such is the case of the subjects
of the area of Process Control and Telecommunications. Specifically, in this last area,
students require knowledge of a very useful mathematical theory to analyze electrical
signals in the frequency domain; for that reason, current curriculum contains the
subject Signals and Systems in the Fifth Academic Semester, and the subject
Telecommunications I in the Sixth Academic Semester. Then, the student continues
with the other subjects until they reach those that are clearly of specialty.
It is like that, the purpose of this article was to represent the Series and Fourier
Transform in the subject Telecommunications I. Thus, we use a User Interface via the
Web for a free access computer tool known as GNU Octave, in order that the student
does not need to go to a computer lab to use this tool. Rather, on the contrary, it
would be enough to remain in the classroom and choose to use a mobile device with
Android or iOS operating system, or as also through a laptop, Apple tablet or iPad.
Whereby, to measure such independence in the use of a personal computer in the
classroom, it is complemented by the average scores obtained in the evaluation of the
learning unit related to Fourier Theory, the results being satisfactory compared to the
academic semesters of previous years.
1.1 GNU Octave
GNU Octave is a scientific programming language that has a powerful math-oriented
syntax, with integrated plotting and visualization tools. In addition, it is a free
distribution software that runs on GNU / Linux, macOS, BSD (Berkeley Software
Distribution) and Windows. Moreover, likewise, it is compatible with many Matlab
digital computing software scripts [2]. It is also known as free Matlab equivalent and
is part of the GNU operating system software packages. Likewise, in March 2019, the
publication of the GNU Octave version 5.1.0 was announced, which is available to be
downloaded from the official link.
1.2 Web User Interface
Web user interface is a digital and robust platform, accessed directly from the web or
internet, allowing direct and easy interaction with the user. Specifically, web user
interface of this article emphasizes that corresponding to the GNU Octave scientific
programming language and its name is Octave Online.
Further, we use this interface by thousands of students, educators and researchers
around the world to study machine learning, control systems, numerical methods, and
much more [3]. Likewise, the main feature of this web user interface is that it can be
accessed directly after an immediate scan in the Google search engine. For it, you
must type the phrase octave online, and immediately a list of links related to it is
received; but clicking on the first search result allows us to enter this interface to be
able to use it freely. Then, figure 1 shows a screenshot of the Web User Interface
obtained after your Google search.
Fig. 1. Screen capture of the Web User Interface for GNU Octave programming language,
made from the Google search engine.
In the upper right, from the previous figure, we observe the menu option; and, when
you click on it, the path to access through a gmail account is displayed, which allows
access to more tools. For example, upload files, create new files, and refresh files,
among others.
2 Methodology used with Web UI
This section describes the methodology used with the Web UI, to represent the Series
and Fourier Transform in a course of the URP Electronic Engineering program. For
this, below are the main characteristics of this subject, as well as the procedure used
in the classroom, and the respective simulation examples performed.
2.1 Course of Telecommunications I
The subject of Telecommunications I belongs to the Sixth academic semester of the
Program of Electronic Engineering of the URP. Likewise, according to the 2015-2
curriculum, it has 6 hours per week of which 4 are used to teach the theoretical and
practical part in a conventional classroom, while the other 2 hours are used for the
development of experimental laboratory guides in the corresponding laboratory. In the
next table, we show the name of each thematic unit of this subject, with the number of
sessions and academic hours to cover your classroom dictation as well as the
development of laboratory experiences.
Table 1. Thematic Units of Telecommunications I course.
Unit
Thematic Unit Name Sessions Academic hours
number
1 Communications systems. 4 12 hours
Linear Systems and Frequency
2 6 18 hours
Representation.
Amplitude Modulation and
3 8 24 hours
Demodulation.
4 Angular Modulation and Demodulation. 10 30 hours
TOTAL: 28 84 hours
The topic of Series and Fourier Transform belongs to the second thematic unit of the
subject Telecommunications I, and it takes place in three classroom sessions using a
fraction of hours of the total corresponding to that unit. In this way, the need to learn,
understand and use this Fourier Theory it is essential because in subsequent subjects,
the student must master the concepts related to the frequency domain. So, that in this
way it is possible to perform the frequency analysis of the electrical signals that are
transmitted and / or received, in order to use it in audio and video communications.
2.2 Temporary representation of periodic and non-periodic signals.
For the temporary representation of the periodic signals, in the Octave Online, two
variables are required; one temporary and the other for the amplitude. Examples of
periodic signals are square wave, sawtooth, triangular, or some other arbitrary signal
that shows periodicity. Then, in equations (2), (3) y (4), the mathematical expressions
of four periodic signals are shown [4], [5]. Then, in figures 2 and 3, we present their
respective time graphs obtained with lines of code developed in the Octave Online.
+1 , for: 0 < t 0.5*T
(1)
-1 , for: 0.5*T < t T
(4 / T) t - 1, for: 0 < t 0.5*T
(2)
- (4 / T ) t + 3, for: 0.5*T < t T
- 4, for: 0 < t T/3
(3)
0, for: T/3 < t 2*T/3
4, for: 2*T/3 < t T
- (4 / T) t + 2 , for: 0 < t 0.25*T
(4 / T) t , for: 0.25*T < t 0.5*T
(4)
1 , for: 0.5*T < t 0.75*T
0 , for: 0.5*T < t T
On the other hand, in the case of non-periodic signals, two examples were
established where one is generated mathematically with the temporal variable to
square. Moreover, we obtained the other by reading an audio file with WAV
extension corresponding to a fraction of voice signal. See figure 4.
2.3 Frequency representation of periodic and non-periodic signals.
For the frequency representation of the periodic signals, in the Octave Online, Fourier
Series Theory is required to determine the coefficients a 0, an and bn, that will allow to
represent the periodic signal with a sum of sinusoidal functions, with different
frequencies and amplitudes. Next, the mathematical representation of the Fourier
Series is shown as well as the expressions for the calculation of the three coefficients
(see equation 5). For this reason, we decide to use the Octave Online complemented
with functions that allow developing a numerical integral in a literal way.
(5)
In this way, for frequency representation; first, the Fourier Series coefficients had to
be determined in the case of the four periodic signals. This was obtained with support
from the INT function, which was responsible for developing the literal integral to
later evaluate it in each range. We obtained the coefficients, then, we proceeded with
a programming based on the syntax of the FOR to proceed with a finite sum of
sinusoidal signals. Then, the left side of Figure 5 shows the result of obtaining the
Fourier Series coefficients for the signal of equation 1, while on the right side we
show the result of a sum of 100 sinusoidal functions. In the same way, in the figure 6,
on the right side we show the result of a sum of 20 sinusoidal functions for equations
3 and 4.
Fig. 2. Screen capture of the programming code developed in Octave Online for the graphic
representation. Left: equation (1) signal. Right: equation (2) signal.
Fig. 3. Screen capture of the programming code developed in Octave Online for the graphic
representation. Left: equation (3) signal. Right: equation (4) signal.
Fig. 4. Screen capture of the programming code in Octave Online for the graphic representation
of two non-periodic signals. Left: temporal variable squared. Right: voice fraction.
Fig. 5. Screen capture of the programming code in Octave Online. Left: obtaining the Fourier
Series coefficients. Right: graph with sum of sinusoidal functions.
On the other hand, in the case of the frequency representation of a non-periodic
signal, the Fourier Continuous Transform is the most indicated. Nevertheless,
considering that non-periodic signals are digital because they have been represented
on a computer, it was decided to use the Discrete Fourier Transform. For this, the FFT
function of the Octave Online was used, with its correspond parameters. Then, the
mathematical expression used, and the programming statement used in the Octave
Online are shown. See figure 7.
Fig. 6. Screen capture of the Octave Online. Left: Graph with sum of sinusoidal functions of
equation 3. Right: Graph with sum of sinusoidal functions of equation 4.
(6)
,
Fig. 7. Screen capture of the programming code in Octave Online to obtain Fourier Transform.
Left: temporal signal squared. Right: fraction voice signal.
2.4 Evaluation of students with the Fourier Theory
The evaluation of the students regarding the Fourier Theory, it was carried out in the
first qualified practice of the subject Telecommunications I. We always do this
evaluation in the third or fourth week of classes and we developed in two different
ways. Thus, on some occasions, the evaluation is done in a traditional way in the
classroom, being one of the questions obtaining the Fourier Series coefficients. While
on other occasions the approach to homework is chosen, where students are motivated
to use scientific computing software to determine the Fourier Series coefficients, then
evaluate them and graph the sum of sinusoidal signals. However, Ricardo Palma
University has an updated license of Matlab scientific computing software, but this
only is use in the computer labs of the university itself. Therefore, we force students
to use free software to develop their simulation tasks.
3 Results and conclusions
The use of the Octave Online web interface has presented favorable results regarding
his willingness to be employed in the classroom, as it was done in the works [6], [7],
[8], [9] y [10]. Whereby, it has not been necessary to have a computer lab to run the
simulations and expand the knowledge of the Fourier Theory. In this way, Table 2
represents the average of the first evaluated practice that corresponds to the topic of
interest; we observe that there is an increase in the semester 2019-1, compared to
previous semesters. Well, this confirms that the use of this interface began during this
period and has led to a better student performance in terms of evaluation. Similarly,
with the information obtained in the last semesters, we represented a trend graph in
Figure 8. In addition, Table 2 shows that in some semesters, the rating was higher,
and this is because the evaluations were not uniform; on the contrary, we used two
different methodologies. They were explained in the previous section.
Table 2. Average of practice 1 for the last 8 academic cycles.
Item Academic Semester Practice N° 1 Evaluation
1 Semester 2019-1 15.4444
2 Semester 2018-2 13.0000
3 Semester 2018-1 14.0000
4 Semester 2017-2 13.2000
5 Semester 2017-1 14.3750
6 Semester 2016-2 15.6429
7 Semester 2016-1 13.1667
8 Semester 2015-2 14.4286
Fig. 8. Trend graph with positive slope.
Acknowledgments. Special thanks to the School of Electronic Engineering of the
Ricardo Palma University, and to the students who studied Telecommunications I,
without them the analysis and preparation of this article would not have been
possible.
References
1. Sílabo de Telecomunicaciones I - Plan 2006-2, Facultad de Ingeniería, Universidad Ricardo
Palma [Available] http://v-beta.urp.edu.pe/pdf/id/5087/n/ce-0601
2. Octave Online. [Available] https://octave-online.net/
3. GNU Octave 5.1.0 Released, March 2019, [Available]
https://www.gnu.org/software/octave/news/release/2019/03/01/octave-5.1-released.html
4. A. Oppenheim, A. Willsky and H. Nawab. Señales y Sistemas. Segunda Edición. Editorial
Prentice Hall. 1998. 990 pp.
5. Lathi, B. Introducción a la Teoría y Sistemas de Comunicación. México: Editorial Limusa.
2001.
6. A. Costa, M. Loureiro and L. Reis, “Courseware sere: Technical and didactic evaluation
made by students”, in 5th Iberian Conference on Infromation Systems and Technologies,
España, pp. 1-9, 2010.
7. J. Ramírez and M. Romero, “Scilab as a Tool to Increase Learning in Courses of
Communication Systems”, in 2008 Electronics, Robotics and Automotive Mechanics
Conference (CERMA), México, October 2008.
8. L. Wenjiang, D. Nanping and F. Tongshun, “Application of Scilab in teaching of
engineering numerical computations”, in 2009 IEEE International Workshop on Open-
source Software for Scientific Computation, Guiyang, China, September 2009.
9. I. de Lessa, G. de Carneiro, M. Monteiro and F. Brito, “A Multiple View Interactive
Environment to Support MATLAB and GNU/Octave Program Comprehension”, in 2015
12th International Conference on Information Technology - New Generations, Las Vegas,
USA, April 2015.
10. I. de Lessa, G. Carneiro, M. Monteiro, F. Brito, “A Concern Visualization Approach for
Improving MATLAB and Octave Program Comprehension”, in 2015 29th Brazilian
Symposium on Software Engineering, Belo Horizonte, Brasil, September 2015.