1. For the following function:
2. For the following function
⎧ −2t+10, x(t)= ⎪10,
t∈[−5,5) t∈[5,10) elsewhere
⎪ 0, ⎩
EE103L
Visualizing signal in Matlab
Assignment 2
g(t) = 3π sin(8πt + 1.3)cos(4πt − 0.8)esin(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?
⎨
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:
∑N
i
y(t) = wherethefiarethefrequenciesfrom159to161Hz. Generatethesignaly(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.
i=1
10cos(2πft)