Chapter 9

The Fourier Transform for Continuous-Time Signals and Systems

In This Chapter

Checking out the world of Fourier transform for aperiodic signals

Getting familiar with Fourier transforms in the limit

Working with LTI systems in the frequency domain and the frequency response

The Fourier transform (FT) is the gateway to the frequency domain — the “home, sweet home” of the frequency spectrum for signals and the frequency response for systems — for all your signals and systems analysis. In the time domain, the independent variable is time, t; in the frequency domain, the independent variable is frequency, f, in hertz or via a variable change in radians per second.

When you take signals and systems to the frequency domain, you not only get a frequency domain view of each, but you also have the ability to perform joint math operations. The most significant is multiplication of frequency-domain quantities — the spectrum of a signal and the frequency response of a linear time-invariant (LTI) system, for example.

Consider this: The FT convolution theorem says that multiplication ...

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