Modulation Index:

The modulation index of a frequency modulation (FM) signal is a measure of the amount of frequency deviation produced by the modulating signal. It represents the ratio of the peak frequency deviation to the modulating frequency. Mathematically, the modulation index (μ) can be calculated as:

μ = Δf / fm

where Δf is the peak frequency deviation and fm is the modulating frequency.

Given Parameters:
- Carrier swing (Δf): 100 kHz
- Modulating frequency (fm): 8 kHz

Calculating the Modulation Index:
Using the given values, we can calculate the modulation index as follows:

μ = Δf / fm
= 100 kHz / 8 kHz
= 12.5

Explanation:
The modulation index of the FM signal is 12.5.

Interpretation:
The modulation index represents the amount of frequency deviation in relation to the modulating frequency. In this case, for every peak of the modulating signal, the frequency of the carrier swings by 100 kHz. Therefore, the modulation index of 12.5 indicates that the carrier frequency swings 12.5 times the frequency of the modulating signal.

Importance of Modulation Index:
The modulation index is an important parameter in FM as it determines the bandwidth occupied by the FM signal. A higher modulation index results in a wider bandwidth, which can affect the overall efficiency and quality of the transmitted signal.

Conclusion:
The modulation index of an FM signal with a carrier swing of 100 kHz and a modulating frequency of 8 kHz is 12.5.