ECE 512 Homework Assignment #2
1. Time Shifting and Scaling – Given the signal in Lathi Figure P1.2–1, sketch the following:
(a) f(t–2), (b) 3f (t+4), (c) 0.5f(–0.5t), (d) f(2t+9), and (e) 4f(5–t/3)
2. Unit Step and Impulse Functions – Solve Lathi problem 1.4–2(b). For the signal x2(t) (assuming each of these quantities exists) and sketch
them on separate axes. Show all of your work.
3. Impulse Functions – Solve Lathi problems 1.4–5(a)(d)(e), 1.4–6(c)(d)(e), 1.4–8, and 1.4–9.
Show all of your work.
4. Even/Odd Signal Components – Solve Lathi problems 1.5–1, 1.5–2, and 1.5–3(a).
MATLAB – Roots of Unity & the Complex Plane
The purpose of this exercise is to facilitate learning in the following areas:
Increased familiarity with the MATLAB environment
Angular spacing on the unit circle in the complex plane
Mapping between Cartesian and polar representations on a two-dimensional grid
Periodicity in the complex plane
Create a MATLAB script called XXX_hw2.m (where ‘XXX’ is your initials) that calculates and
plots the roots of unity in the complex plane for n = 12. Represent these roots as red “+’s.” Next,
draw the outline of the unit circle with a blue dashed line, then add a meaningful title and axis labels
to your plot. Use ‘axis equal’ with your plot to get the proper aspect ratio, and remember that
‘hold on’ will allow you to add new points and curves to the existing figure.
To practice thinking about conversions between Cartesian complex number representations (a + jb)
and polar representations (rej ), add another curve to the existing figure (see the next page) based on
the following background.
When you were young, you may have played with a game called a Spirograph. In this game, you
have two geared disks, each of which contains holes in which you can insert an ink pen. You are encouraged to play
around with this applet in order to become familiar with the process.
These patterns are described mathematically by a pair of parametric equations:
a(t) = (R+r)cos(t) + p*cos((R+r)t/r)
b(t) = (R+r)sin(t) + p*sin((R+r)t/r)