A square wave of the modulating signal is shown in the figure. The carrier wave is given by $$C(t) = 5 \sin(8\pi t)$$ Volt. The modulation index is

We need to determine the modulation index of an amplitude modulated (AM) signal based on the provided modulating signal's graph and the carrier wave equation.

1. Identify the System Parameters

• Carrier Wave Equation: $$C(t) = 5 \sin(8\pi t)\text{ Volt}$$

  From the standard carrier form $$C(t) = A_c \sin(\omega_c t)$$, the peak amplitude of the carrier wave is:

  $$A_c = 5\text{ V}$$
• Modulating Signal Graph ($$m(t)$$):

  Looking at the provided square wave graph, the maximum positive peak reaches a value of $$1\text{ V}$$. Thus, the peak amplitude of the modulating signal is:

  $$A_m = 1\text{ V}$$

2. Calculate the Modulation Index ($\mu$)

The modulation index ($$\mu$$) for an amplitude modulated wave is defined as the ratio of the peak amplitude of the modulating signal to the peak amplitude of the carrier wave:

$$\mu = \frac{A_m}{A_c}$$

Substituting our identified parameters into the formula:

$$\mu = \frac{1}{5} = 0.2$$

Conclusion

The modulation index of the signal is 0.2