(b) Consider a QPSK system having a bit rate

Table of Contents

Symbol Rate Calculation: The symbol rate is determined by the bit rate and the number of bits per symbol in QPSK modulation.
Nyquist Bandwidth Formula: The minimum bandwidth required for a signal without intersymbol interference (ISI) is given by the symbol rate. A raised cosine filter expands this bandwidth.
Raised Cosine Filter Bandwidth: The bandwidth of a signal filtered with a raised cosine filter is a function of the symbol rate and the roll-off factor.
No Alternative Approach Needed: The provided information directly leads to a single, straightforward calculation.

In QPSK (Quadrature Phase Shift Keying), each symbol represents two bits. Therefore, the symbol rate (Rs) is half the bit rate (Rb).

Rs = Rb / 2 = 9600 bps / 2 = 4800 symbols/second

The bandwidth (B) of a signal filtered by a raised cosine filter is given by:

B = Rs * (1 + α) / 2

where Rs is the symbol rate and α is the roll-off factor.

Substituting the values:

B = 4800 symbols/second * (1 + 0.35) / 2 = 4800 * 1.35 / 2 = 3240 Hz

The bandwidth required by the QPSK signal using a raised cosine filter with a roll-off factor of 0.35 is 3240 Hz.

Key Points: Understanding the relationship between bit rate, symbol rate, and bandwidth in digital modulation schemes is crucial. The raised cosine filter is commonly used to minimize ISI.
Potential Challenges: Incorrectly calculating the symbol rate from the bit rate is a common mistake. Forgetting to account for the roll-off factor in the bandwidth calculation is another potential error.