这是一个加拿大的通信理论作业代写

1. Suppose the normalized pulse shape, hT (t), shown below, is used to generate the pulse train

where fvng are the transmitted symbols, with each vn selected independently from f−1; +1g with equal probability.
Note that this line coding technique is known as polar return-to-zero (RZ).

(a) Find the Fourier transform of hT (t).
(b) Find a simple mathematical expression for the power spectral density of v(t).
(c) Sketch the PSD of v(t).

2. Suppose the normalized pulse shape, hT (t), shown below, is used to generate the pulse train

where fvng are the transmitted symbols, with each vn selected independently from f−1; +1g with equal probability.
Note that this line coding technique is known as Manchester coding.

(a) Find the Fourier transform of hT (t).
(b) Find a simple mathematical expression for the power spectral density of v(t).
(c) Sketch the PSD of v(t).

3. Suppose the normalized pulse shape, hT (t), shown below, is used to generate the pulse train

where fvng are the transmitted symbols, with each vn selected independently from f−1; +1g with equal probability.
The pulse train is then used to modulate the amplitude of a sinusoidal carrier wave, giving the transmitted bandpass
signal

where fc is the carrier frequency.

(a) Find a simple mathematical expression for the power spectral density of vc(t).
(b) Sketch the PSD of vc(t), assuming fc = 5=T.
(c) What is the null-to-null bandwidth of the signal?
(d) What is the 3dB bandwidth of the signal?