SIGNALS and SYSTEMS HOMEWORK-8
The Continuous-Time Fourier Transform
1) Consider a casual LTI system with frequency response
𝐻(𝑗𝑤)=1
𝑗𝑤 +2
For a particular input 𝑥(𝑡) this system is observed to produce the output
𝑦(𝑡)= 𝑒−3𝑡𝑢(𝑡)−𝑒−4𝑡𝑢(𝑡).
Determine 𝑥(𝑡). (15 P)
2) Consider the signal
𝑥0(𝑡)={𝑒−2𝑡, 0 ≤ 𝑡 ≤ 1
0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
Determine the Fourier transform of each of the signals shown in Figure-1. You should be able to do
this by explicitly evaluating only transform of 𝑥0(𝑡) and then using properties of the Fourier
transform. (40 P)
3) Find the Fourier transforms of the following signals. (45 P)
a)
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