ELEC 320
Prof. Rich Kozick
Fall, 1997

EE 205: Homework Assignment 19

Date Assigned: 		 Friday, October 24, 1997 
Date Due: 		 Monday, October 27, 1997

Reading: Chapter 4, Sections 4.3 to 4.6.

Problems:

1.

Find the Fourier transform of the functions $\delta(t)$ and $\delta(t-1)$ using the definition of the Fourier transform, not the table. (Hint: Recall the ``sifting'' property of impulse functions.)

2.

Sketch ${\rm sinc}(10t)$, ${\rm sinc}(t/10)$, and ${\rm sinc}(\pi t)$.Label the amplitude at t=0 and the zero-crossing points.

3.

Sketch $X(\omega) = {\rm sinc}\left( \frac{1000 \omega}{\pi} \right)$.Find the inverse Fourier transform x(t) using the tables, and sketch x(t).

4.

What is the Fourier transform of $\cos(2 \pi 1000 t)$? Sketch the 2-sided amplitude spectrum.