Download - Solutions HW1

7/21/2019 Solutions HW1

http://slidepdf.com/reader/full/solutions-hw1 1/3

Solutions Homework 1

Problem 1

As discussed in our lectures, for a Gaussian pulse the time bandwidth product is given by:

∆∆ = 0.44

At the input the pulse duration Δ = 10 × 10−

Therefore the spectral bandwidth of the pulse is given by:

∆ = 0.44 10 × 10−

⇒ ∆ = 4.4× 10

= ⁄

=

⇒ ∆ =

∆

∆ = 3.53×10 = 0.353

We know that Δ = 10 , = 20/. and = 3

The pulse stretching is given by:

= × Δ ×

= (3×0.353×10−9 × 20) = 2.12×10−

∆ = ∆ + = √ 100+21.2

∆ = 23.44 = 2.344 × 10−

Let time difference between pulses = Δt

From our definition of acceptable time delay between pulses ∆ ≥ 2∆

⟹ ∆ = 4.688 × 10−

Maximum Transmission Frequency (Bits/Sec) = 1 4.688×10− = 21.3/

If instead a different source is used, then

∆ = 2 × 10−9

= × Δ × = 1.2 × 10−

∆ = ∆ + = 1.204×10−

∆ = 2∆ = 2.408 × 10−

Maximum Transmission Frequency (Bits/Sec) = 1 2.408×10− = 4.15/



Problem 2

Problem 3