11. Continuous-Time Fourier Transform

In previous chapters, our presentation of the spectrum was limited to sinusoids and periodic signals. Now we want to develop a completely general definition of the frequency spectrum that will apply to any signal x(t). Armed with this powerful tool, we will be able to:
  1. define a precise notion of bandwidth for a signal,
  2. explain the inner workings of modern communication systems which are able to transmit many signals at one time by sharing the available bandwidth, and
  3. define filtering operations that are needed to separate signals in such frequency-shared systems.
There are many other applications of the Fourier transform, so it is safe to say that Fourier analysis provides the rigorous language needed to define and design modern engineering systems.

Demos
CLTI Demo CLTIDemo is a program that illustrates the relationship between the input and output of a continous-time linear time-invariant (LTI) filter when the input is a sinusoidal function. The user is allowed to control the parameters of both the input sinusoid and the filter.
Fourier Series This MATLAB demo reconstructs a square, triangle, or sawtooth waveform, using a given number of Fourier Series coefficients.

Labs

No labs for this chapter.

Examples

Exercises

Homework


McClellan, Schafer, and Yoder, Signal Processing First, ISBN 0-13-065562-7.
Prentice Hall, Upper Saddle River, NJ 07458. © 2003 Pearson Education, Inc.