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# 通信原理代写｜SYSC 3503 Communication Theory II Assignment #1

1. For the sequence of bits 11010, sketch the transmitted analogue signal if each of the following line codes are used:

(a) unipolar NRZ
(b) polar NRZ
(c) unipolar RZ
(d) bipolar RZ
(e) Manchester coding

2. If X is a Bernoulli random variable with parameter ρ (that is, PrfX = 1g = ρ and PrfX = 0g = 1 − ρ), prove that
the mean of X is ρ and the variance is ρ(1 − ρ).

3. If {Xi|i < {1; 2; :::; N}} is a set of Bernoulli random variables, each with parameter ρ, and then Y is a binomial random variable with parameters (N; ρ). Prove that the mean of Y is Nρ and the variance is
Nρ(1 − ρ).

4. For the signals s0(t), s1(t), and s2(t) shown below:

(a) Use the Gram-Schmidt orthogonalization procedure to find a set of basis signals. Sketch the basis signals.

(b) Express s0(t), s1(t), and s2(t) as linear combinations of the basis signals.

(c) Show s0(t), s1(t), and s2(t) on a signal space diagram. 5. For the data signals s0(t), s1(t), s2(t), and s3(t) shown below:

(a) Find and sketch a set of orthonormal basis signals that can be used to represent the data signals.

(b) Express the data signals as linear combinations of the basis signals.

(c) Carefully plot the data signals in a signal space diagram.

(d) What is the average transmitted energy, if each signal is equally likely to be transmitted? 