A New Experiment-Based Way to Introduce Fourier Transform and Time Domain–Frequency Domain Duality

Morente, Juan A.; Salinas, Alfonso; Toledo‐Redondo, Sergio; Fornieles-Callejón, Jesus; Méndez, Alfredo; Portí, J.A.

doi:10.1109/te.2013.2246164

Cited by 7 publications

(4 citation statements)

References 16 publications

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“…The proposal of this work is novel and original due to the way of introducing the Fourier Transform using the oscillatory or periodic movement [22]; this being one of the best known phenomenon in nature or mechanics; and with which it is possible to apply and explain the Fourier Transform. Most of the reviewed bibliography introduces the Fourier transform by studying signals and generally analyzing a certain physical phenomenon, [24][25][26][27][28]. With the proposal presented in this article, it is possible to introduce the concept of the Fourier transform by experimentally observing on a screen the graphic behavior of the oscillatory movement in the temporal domain as well as in the frequency domain, as explained in Sec.…”

Section: Discussionmentioning

confidence: 99%

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Introduction to the Fourier transform studying the oscillations of a pendulum

Reyes

Forgach

2023

Rev. Mex. Fis. E

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Students of physics, engineering and related majors; generally, do not know the usefulness and applications of transforming a signal from the time domain to the frequency domain. The mathematics that makes possible this transformation is well known to senior students of the majors, but vaguely applied in teaching laboratories. The main phenomena that could provide us with frequency information, the pendulum and the spring, are minimized by focusing only on obtaining the mathematics dictated in books. The pendulum is the most studied physical system in teaching laboratories from precollege up to college levels; this phenomenon is analyzed mathematically in most of the related literature in the area of Physics and Engineering. It is an introduction to the wave phenomenon. However, teaching paradigms, focus on the plain demonstration that periods are invariant to suspended masses, if and only if the oscillation is within angles not greater than 10 degrees from their normal. The use of technologies, computational and electronic, also focuses on the demonstration of such assertion. In the present work, a mechanical-electrical system was designed that allows to observe, in real time, on the screen of an oscilloscope, the swinging behavior of a pendulum. This system makes evident that the swing movement of a pendulum can be described by a sine function, but also with this same system, and with the help of a digital oscilloscope, it is possible to simultaneously observe the signal generated in the temporal domain and in the frequency domain. This innovation not just breaks the paradigms of teaching but also promotes an alternative to valuable observations promotes understanding.

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Section: Discussionmentioning

confidence: 99%

“…The latter is possible thanks to Joseph Fourier [4,[24][25][26][27][28][29]; who developed a tool capable of observing the signal, or signals, that give a certain appearance to a signal observed in the time domain. This tool is better known as the Fourier Transform.…”

Section: Time Domain or Frequency Domainmentioning

confidence: 99%

Introduction to the Fourier transform studying the oscillations of a pendulum

Reyes

Forgach

2023

Rev. Mex. Fis. E

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“…According to the duality between frequency and time [25], the correlation function in the frequency domain can be defined as…”

Section: Caf Analysis For Single-hop Baseband Signalmentioning

confidence: 99%

TDOA/FDOA estimation algorithm of frequency‐hopping signals based on CAF coherent integration

Ouyang

Yang

et al. 2020

IET Communications

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“…In ref. , the fundamentals of the Fourier transform (FT) and the time domain–frequency domain duality concept in the framework of PBL (Problem‐Based Learning) are introduced. In ref.…”

Section: Related Workmentioning

confidence: 99%

An interactive approach for illustrating a proof of the sampling theorem using MATHEMATICA

Guerrero¹

2018

Comp Applic In Engineering

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Learning methods in engineering education should evolve to take advantage of the progress of technology. Despite being one of the most important theorems of engineering, at undergraduate level the foundations of sampling theorem are usually oversimplified, whereas at graduate level its proof is frequently presented in the context of a rigorous mathematical framework. This paper presents an interactive approach to illustrate an amenable proof of the sampling theorem through example. Apart from its practical value as a learning tool, the proof captures some mathematical subtleties that can help to understand some more advanced concepts. The goal of this work is to show that learning the sampling theorem through an interactive example of its mathematical proof can be an enjoyable and insightful experience.

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A New Experiment-Based Way to Introduce Fourier Transform and Time Domain–Frequency Domain Duality

Cited by 7 publications

References 16 publications

Introduction to the Fourier transform studying the oscillations of a pendulum

Introduction to the Fourier transform studying the oscillations of a pendulum

TDOA/FDOA estimation algorithm of frequency‐hopping signals based on CAF coherent integration

An interactive approach for illustrating a proof of the sampling theorem using MATHEMATICA

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