EE103L Visualizing signal in Matlab
Assignment 2

1. For the following function:
g(t) = 3π sin(8πt + 1.3)cos(4πt − 0.8)e
sin(12πt)
create an m-file that plots the function within the window t ∈ [−1,1] in a 3-by-1
subplot with steps of t equal to 0.1, 0.01, and 0.001. What is the period of this
signal?

2. For the following function

x(t) =
−2 t + 10, t ∈ [−5,5)
10, t ∈ [5,10)
0, elsewhere
⎧
⎨
⎪⎪
⎩
⎪
⎪

create an m-file that plots the function x(t) within the window t ∈[−10,15] . Also create
a separate figure that has 4 sublpots in 2-by-2 arrangement with the following signals:
(a) x(t+2)
(b) x(t-3)
(c) x(-t)
(d) -3x(-t+4)

3. Consider the signal x(t) = te
−0.15t, − 20 ≤ t ≤ 20 . Plot
(a) The signal x(t)
(b) The even decomposition xe(t) of x(t)
(c) The odd decomposition xo(t) of x(t)
(d) The signal y(t)=xe(t)+xo(t)

4. For the signal g(x) in problem 1, calculate the energy of the signal in the window
t ∈ [0.25,0.75]. Also calculate the power of the signal.

5. Suppose N different musicians in an orchestra are trying to play a pure tone, a sinusoid
of frequency 160 Hz. Assume the N players while trying to play the pure tone (160 Hz)
end up playing tones separated by Δ Hz, so the overall sound they produced is:

y(t) = 10 cos(2πfit)
i=1
N
∑
where the fi are the frequencies from 159 to 161 Hz. Generate the signal y(t), 0 ≤
t ≤ 200 sec considering that each musician is playing a unique frequency. First
assume the number of musicians to be N = 51 with Δ= 0.04 Hz, and then N=101
with Δ= 0.02 Hz. Plot y(t) for the two cases on the same figure.





















































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