Signals and Systems

Using MATLAB

Luis F. Chaparro

Chapter 5 - Frequency Analysis

The Fourier Transform

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What is in this chapter?

From Fourier series to Fourier transform

Spectral representation of periodic and aperiodic signals

Existence of Fourier transform

Fourier and Laplace transforms

Modulation and signal transmission

Time frequency relations and Fourier transform

Convolution and Filtering

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Full-wave

rectifier

Low-pass

filter

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What have we accomplished?

Convolution and Filtering

Application of Laplace analysis and transient response

Application of Fourier analysis and steady state response

Where do we go from here?

Unification of frequency representation of periodic and aperiodic signals

Duality in time and frequency

Frequency response of LTI systems

Connection of Fourier series and Laplace transform

Inverse time frequency relation

Application of time-frequency relation in sampling theory

Filter design