Consider a QAM communication system that employs raised cosine pulse shapingat the transmitter and a carrier frequency of 2GHz. In this problem you will answer various questionsabout the relationships between symbol rates and bandwidths. Hint: Refer to Lecture 4 slides.1) Suppose that the symbol rate is 1 Megasymbol per second and that the raised cosine pulse shapehas 50 percent excess bandwidth. What is the baseband absolute bandwidth?2) Suppose that the symbol rate is 1 megasymbol per second and that the raised cosine has 50 percentexcess bandwidth. What is the passband absolute bandwidth?3) Suppose that the absolute bandwidth of a signal is 1MHz at baseband. What is the best symbolrate that can be achieved with a raised cosine pulse? Choose any raised cosine pulse rolloff factor(e.g., 0.2, 0.3...)4) Suppose that the absolute bandwidth of your modulated signal is 3MHz at baseband with an excessbandwidth of 25 percent. What is the Nyquist frequency? What is the Nyquist rate

1. Suppose that the symbol rate is 1 Megasymbol per second and that the raised cosine pulse shape has 50 percent excess bandwidth. What is the baseband absolute bandwidth?

The baseband absolute bandwidth of a raised cosine pulse shape is given by the formula:

B = (1 + α) * Rs

where α is the excess bandwidth (also known as the roll-off factor) and Rs is the symbol rate. Substituting the given values gives:

B = (1 + 0.5) * 1 MHz = 1.5 MHz

2. Suppose that the symbol rate is 1 megasymbol per second and that the raised cosine has 50 percent excess bandwidth. What is the passband absolute bandwidth?

The passband absolute bandwidth for a QAM system is twice the baseband absolute bandwidth. Therefore, the passband absolute bandwidth is:

Bp = 2 * B = 2 * 1.5 MHz = 3 MHz

3. Suppose that the absolute bandwidth of a signal is 1MHz at baseband. What is the best symbol rate that can be achieved with a raised cosine pulse?

The symbol rate for a raised cosine pulse shape is given by the formula:

Rs = B / (1 + α)

To achieve the best symbol rate, we want to minimize the excess bandwidth α. Let's choose α = 0.2 as an example. Substituting these values gives:

Rs = 1 MHz / (1 + 0.2) = 0.83 Megasymbols per second

4. Suppose that the absolute bandwidth of your modulated signal is 3MHz at baseband with an excess bandwidth of 25 percent. What is the Nyquist frequency? What is the Nyquist rate?

The Nyquist frequency is equal to the baseband absolute bandwidth, which is 3 MHz in this case.

The Nyquist rate is twice the Nyquist frequency, which is:

Nyquist rate = 2 * Nyquist frequency = 2 * 3 MHz = 6 Megasamples per second