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MAE107 – Dynamic Systems Laboratory
Spring 2010
Lab Report #8
Introduction
In this lab we have studied systems and signals in the frequency domain by numerically
calculating the Fourier Series of some periodic signals and measuring the frequency
response of a torsional system using the relationship between the Fourier Series of the
input and output signals.
The Fourier series reconstruction of a continuous time
periodic signal, denoted
u
FS
,
is
where
are the Fourier series coefficients associated with u(t) and can by calculated as
follows
Since we sample the signals, though, they must be passed through an
antialias
filter to remove those frequencies outside of the Nyquist band, where .
The periodic,
continuoustime, but bandlimited signals, can then be perfectly represented by a
periodic sequence of samples.
The periodic sequence of samples can be analyzed with
discretetime Fourier series in order to determine the Fourier series components of the
original continuoustime signal within the Nyquist band.
The
fft
command in MATLAB
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 Spring '06
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