Let's solve both questions step by step: --- ### **iv) What is the figure of merit for a single-tone FM modulation receiver when the modulation index is β = 4?** #### **Step 1: Figure of Merit for FM** The figure of merit for FM (compared to AM) is given by: \[ \text{Figure of merit} = 1 + \beta^2 \] #### **Step 2: Substitute β = 4** \[ \text{Figure of merit} = 1 + (4)^2 = 1 + 16 = 17 \] But notice none of the options are 17, so let's check the standard definition for a single-tone FM signal: For a single-tone FM, the improvement in SNR (figure of merit) at the output is: \[ \text{Improvement Factor} = \frac{3}{2} \beta^2 \] So, let's use this formula: \[ \text{Improvement Factor} = \frac{3}{2} \times (4)^2 = \frac{3}{2} \times 16 = 24 \] **So the answer is:** > **c. 24** --- ### **v) In a single-tone FM signal, the threshold appears at the carrier signal to noise ratio of about** #### **Step 1: FM Threshold Effect** The threshold effect in FM occurs when the carrier-to-noise ratio (CNR) is about **12 dB**. #### **Step 2: Choose the Correct Option** > **b. 12 dB** --- ## **Final Answers:** **iv) c. 24** **v) b. 12 dB** Let me know if you need further explanation!