Signals and SystemsUsing MATLAB

Luis F. Chaparro

Chapter 4 - Frequency Analysis

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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Application in communicatio

ns

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input sinusoid ss output sinusoidof 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