Basic Fourier Series Academic Resource Center Workshop for BME by: - - PowerPoint PPT Presentation

Basic Fourier Series

Academic Resource Center Workshop for BME by: Neha Bansal

Agenda

• Fourier Series
• Trigonometric Fourier Series
• Compact Trigonometric Fourier Series
• Examples
• Square Waves
• 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

• f 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:
• http://en.wikibooks.org/wiki/Signals_and_Systems/Fourier

_Series

• Wolfram MathWorld Fourier Series:
• http://mathworld.wolfram.com/FourierSeries.html
• ARC Website:
• iit.edu/arc
• BME Schedule
• http://iit.edu/arc/tutoring_schedule/biomedical_engineerin

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