Basic Fourier Series Academic Resource Center
Workshop for BME
by: Neha Bansal
Agenda
• Fourier Series • Trigonometric Fourier Series • Compact Trigonometric Fourier Series • Examples
o Square Waves o Sawtooth Waves
• References
Fourier Series • A periodic function f(t) can be represented by an
infinite sum of sine and/or cosine functions that are harmonically related. That is, the frequency of any trigonometric term in the infinite series is an integral multiple, or harmonic, of the fundamental frequency of the periodic function.
Trigonometric Fourier Series • Given f(t) is periodic, f(t) can be represented as
follows:
where n is the integer sequence 1,2,3, ... , a0, an, and bn are called the Fourier coefficients, and are calculated from f(t), 0 = 2 /To is the fundamental frequency
Compact Trigonometric Fourier Series
Exponential Fourier Series
Example: Square wave
Let us consider a sawtooth wave
For convenience, we shall shift our interval from to . In this interval
we have simply f(t)=t. Using Eqs. of Fourier series, we have
Example: Sawtooth Wave
Example: Sawtooth wave
So, the expansion of f(t) reads
(7.15) .
References
• WikiBooks Resources: o http://en.wikibooks.org/wiki/Signals_and_Systems/Fourier
_Series • Wolfram MathWorld Fourier Series:
o http://mathworld.wolfram.com/FourierSeries.html • ARC Website:
o iit.edu/arc • BME Schedule
o http://iit.edu/arc/tutoring_schedule/biomedical_engineering.shtml
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