# Signals and Systems Using MATLAB

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## The Fourier Series

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### What is in this chapter?

Eigenfunctions and LTI systems

Properties of Fourier Series

Complex and trigonometric Fourier Series

Line spectrum: distribution of power over frequency

Response of LTI systems to periodic signals Laplace and Fourier Series

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Eigenfunctions revisited

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21 Application in

communications

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input sinusoid ss output sinusoid of same frequency

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input

output magnitude and phase at

harmonic frequency

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### What have we accomplished?

Connection of Laplace and Fourier transforms Response of LTI systems to periodic signals

Extension of Fourier representation for aperiodic signals

Unification of spectral theory for periodic and aperiodic signals

### Where do we go from here?

Sinusoidal representation of periodic signals Eigenfunction property of LTI systems

Convolution and frequency response of LTI systems

Connection of Fourier series and Laplace transform Inverse time frequency relation

Referências

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