Date Assigned: Wednesday, January 28, 1998 Date Due: Nothing to hand in
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.
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).
Sketch the Fourier transform of
g(t) = 12 cos (2 pi 10^6 t).
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?