ELEC 320

Prof. Rich Kozick

Fall, 1998

Prof. Rich Kozick

Fall, 1998

Date Assigned: Monday, November 2, 1998 Date Due: Wednesday, November 4, 1998

**Reading:** Chapter 4, Sections 4.3 and 4.4.

**Lab:** Please decide on a lab project by November 5 and 10
so that we can begin working on them.

**Problems:**

- 1.
- Please study Example 4.7 in the text on pages 166-167.
Do your best to write down all of the steps required to show that
the Fourier transform of a rectangular pulse is a ``sinc'' function.
This is one of the
*most important*Fourier transform pairs to understand - it arises in many applications. You do not have to submit anything for this item. - 2.
- Find the Fourier transform of the functions and
using the
*definition*of the Fourier transform, not the table. In other words, compute the integral that defines the Fourier transform for these time functions. (Hint: Recall the ``sifting'' property of impulse functions.) - 3.
- Sketch , , and .Label the amplitude at
*t*=0 and the zero-crossing points. - 4.
- Sketch .Find the inverse Fourier transform
*x*(*t*) using the tables, and sketch*x*(*t*). - 5.
- What is the Fourier transform of ? Sketch the 2-sided amplitude spectrum.