ELEC 470, Spring 1998
Prof. Rich Kozick

## Homework 3

Date Assigned: Wednesday, January 28, 1998
Date Due: Nothing to hand in

1. Reading: Continue reading Chapter 2. We will use the Fast Fourier Transform described in Section 2.15 as a tool, but we will not discuss the details of the algorithm itself. Sections 2.10-2.13 might be rough in your first reading, but we will discuss them in class, probably on Friday and next week.

Please do the following problems for Friday, January 30. We will discuss the solutions in class.

2. Suppose a time signal g(t) has Fourier transform G(f) = 3 rect(f/20). A new signal y(t) is formed as follows:
y(t) = g(t) * 2 * cos(2 pi 100 t)
(a) What is the time signal g(t) ?
(b) Sketch the spectrum Y(f) of y(t).

3. Sketch the Fourier transform of g(t) = 12 cos (2 pi 10^6 t).

4. Suppose that a signal has Fourier transform G(f) = 3 * delta(f - 10).
(a) Sketch G(f).
(b) What is the inverse Fourier transform g(t)? Is g(t) real-valued?

5. Please work on Project 1.
Thank you.