Spectral Algorithms for Signal Generation as Learning-Methodical Tool for Engineer Preparation

Spectral Algorithms for Signal Generation as Learning-Methodical Tool for Engineer Preparation

Vladimir V. Syuzev (Bauman Moscow State Technical University, Russia), Elena V. Smirnova (Bauman Moscow State Technical University, Russia), Kirill Kucherov (Bauman Moscow State Technical University, Russia), Vladimir Gurenko (Bauman Moscow State Technical University, Russia) and Gurgen Khachatrian (American University of Armenia, Armenia)
Copyright: © 2019 |Pages: 19
DOI: 10.4018/978-1-5225-3395-5.ch023

Abstract

In this chapter, a spectral method of deterministic signals simulation is proposed. The target is to solve the teaching methodological problem of individual tasks creation for students: future engineers in the field of real-time control systems' development and research. The tasks are related to the correlation theory. The method of simulation algorithms tuning with the help of specified spectrally correlation of signal characteristics and their parameters in the harmonic Fourier and Hartley basis is presented. To expand the set of task's variants for the independent student self-preparation the task of signals simulation has been formulated mathematically and solved in arbitrary complex and real systems of orthogonal basic functions. The requirements have been underlined on how teacher can teach basic functions for the practical applications. During such kind of decision task, the student will be able to counts the multiplicity, precision, and computational complexity of the resulting spectral simulation algorithms.
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Introduction

This paper proposes Science-Based Approach in Engineer’s Preparation which is a continuation of Project-Based Approach. Students took part in a research project which been supported by Ministry of Education and Science of Russian Federation (Project Contract ID 2.7782.2017/BC). The project is concern to simulation algorithms, which use spectral representation of signal in different orthogonal bases. Such an approach allows students to produce simulation algorithms, which are differ in accuracy and computation complexity due to the proper basis function systems choice. The approach provides the multivariate tasks for the student’s individual work. Moreover, the independent research on the variety of spectral representations will expand the scope of learner’s knowledge and his skills in analog and digital signal spectral processing - theoretically and in practice. The results of the students work give statistical material for further ideas of the scientists.

From the large number of known base systems the most attractive ones to meet different authors’ goals are parametrical bases containing changing parameters in the structure of their functions. They affect their properties. Examples of such bases systems are complex exponential functions, Vilenkin – Chrestenson functions, the generalized Hartley functions. The control over their properties is achieved by using variation of different bases.

In this paper the deterministic signals are under consideration only in the framework of the correlation wide sphere of practical applications because they are useful components of input signal processing in different control and management systems. The variation of such signal’s frequency characteristics provides an extension for many options in simulation algorithms, which are helpful for student’s individual task’s creation from the side of teacher too.

The authors of the chapter develop an enrolled course named “Digital Signal Processing” (DSP) supported by industry enterprises working in the field of automation.

First part of the chapter is about how teacher could create variants of tasks for the individual student’s work. The authors paid attention to the mathematical description of tasks assigned to students (see the Appendix) for performing laboratory work with the aim that teacher who carries on similar DSP course could use this mathematical device to create their own versions of tasks. The main emphasis in the paper is made precisely on the fact that this is a methodical material for conducting new form laboratory works, while each student or each group of students investigates new mathematical calculations and creates new solutions.

Second part of the chapter is about software environment which student use for his/her individual research work. An example of student’s research work is given. The explanation is given about how student’s engagement ensured and promoted.

Third part concerns to students’ experiences feedbacks in their research of the fast algorithms of signal’s transformation, which confirms the interactive and motivated science based approach to engineer’s preparation.

Fourth part contains some students’ feedbacks.

The Conclusion is dedicated to further development of the individual task’s variants using different theoretical bases.

Key Terms in this Chapter

Fast Transformation (FT) Algorithms: A computational procedure using fast spectral transformations in order to save computational resources, for example, fast Fourier transform (FFT).

Science-Based Approach in Engineer Preparation: New trend in future engineer preparation when students do their homework as a practical research on of theoretical problem given by teacher.

Spectral Method for Engineering and Scientific Computing Applications: Actual modern course in engineer preparation curricula.

Independent Study: Is a form of education offered by many high schools, colleges, and other educational institutions. It is sometimes referred to as directed study, and is an educational activity undertaken by an individual with little to no supervision.

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