If the bit rate for a 8-QAM signal is 1500 bps, the bandwidth in Hertz is equal to __________.Group of answer choices30001500500750

Break Down the Problem

1. Identify the key parameters: bit rate for an 8-QAM signal is given as 1500 bps.
2. Determine the relationship between bandwidth and bit rate for QAM signaling.

Relevant Concepts

3. For an $M$-QAM signaling scheme, the relation between the bit rate $R$ and the bandwidth $B$ is given by:

$B = \frac{R}{\log_2(M)}$

where $M$ is the number of symbols. For 8-QAM, $M = 8$.

Analysis and Detail

4. Calculate $\log_2(8)$:

$\log_2(8) = 3 \quad \text{(because \( 8 = 2^3 \))}$

5. Substitute the parameters into the bandwidth formula:

$B = \frac{1500}{\log_2(8)} = \frac{1500}{3} = 500 \text{ Hz}$

Verify and Summarize

6. The calculation shows that the bandwidth required for an 8-QAM signal with a bit rate of 1500 bps is indeed 500 Hz. This verification confirms that all calculations are correct.

Final Answer

The bandwidth in Hertz is equal to 500 Hz.