id: 06439623
dt: j
an: 2015d.00913
au: Oliveira, Margarida; Nápoles, Suzana; Oliveira, Sérgio
ti: Fourier analysis: graphical animation and analysis of experimental data
with Excel.
so: Spreadsheets Educ. 5, No. 2, 18 p., electronic only (2012).
py: 2012
pu: Bond University, Faculty of Business, Gold Coast, Queensland
la: EN
cc: M50 N50 I30 I70 U70
ut: Fourier series; Fourier analysis; approach; university teaching;
engineering; spreadsheets; visualisation; graphical representations;
movie clips in spreadsheets; spectral analysis; experimental data;
trigonometric functions; sinusoidal waves; geometric interpretation of
parameters; approximation; discrete Fourier transform; continuous
Fourier transform; mean values; integral calculus; Fourier integrals;
Laplace transform; decomposition of accelerograms into sinusoidal
waves; experimental data
ci:
li: http://epublications.bond.edu.au/ejsie/vol5/iss2/2/
ab: Summary: According to Fourier formulation, any function that can be
represented in a graph may be approximated by the “sum" of infinite
sinusoidal functions (Fourier series), termed as “waves". The adopted
approach is accessible to students of the first years of university
studies, in which the emphasis is put on the understanding of
mathematical concepts through illustrative graphic representations, the
students being encouraged to prepare animated Excel-based computational
modules (VBA-Visual Basic for Applications). Reference is made to the
part played by both trigonometric and complex representations of
Fourier series in the concept of discrete Fourier transform. Its
connection with the continuous Fourier transform is demonstrated and a
brief mention is made of the generalization leading to Laplace
transform. As application, the example presented refers to the analysis
of vibrations measured on engineering structures: horizontal
accelerations of a one-storey building deriving from environment noise.
This example is integrated in the curriculum of the discipline
“Matemática Aplicada à Engenharia Civil" (Mathematics Applied to
Civil Engineering), lectured at ISEL (Instituto Superior de Engenharia
de Lisboa). In this discipline, the students have the possibility of
performing measurements using an accelerometer and a data acquisition
system, which, when connected to a PC, make it possible to record the
accelerations measured in a file format recognizable by Excel.
rv: