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Answer :
Final Answer:
For an FM system with a modulation index K = 190 , the frequency deviation [tex]\( \Delta f \)[/tex] is directly proportional to the amplitude of the message signal m(t) . To find [tex]\( \Delta f \),[/tex] we use the formula[tex]\( \Delta f = K \cdot m(t) \),[/tex] where K is the modulation index. By plotting the frequency deviation [tex]\( \Delta f \)[/tex]against time t , we can visualize how the carrier frequency varies due to the modulation by the message signal m(t) .
Explanation:
In frequency modulation (FM), the frequency of the carrier signal is modulated by the message signal m(t) . The extent of this modulation is determined by the modulation index K , which represents the ratio of the maximum frequency deviation to the frequency of the message signal. In this case, the modulation index is K = 190 .
To find the frequency deviation, we multiply the modulation index K by the amplitude of the message signal m(t) . This gives us the instantaneous change in frequency from the carrier frequency. Plotting the frequency deviation against time allows us to visualize how the carrier frequency varies over time due to the modulation by the message signal.
Understanding the relationship between the modulation index, message signal, and frequency deviation is crucial in FM systems design and analysis. By manipulating the modulation index and the characteristics of the message signal, engineers can control the frequency spectrum of the modulated signal, enabling various applications in telecommunications, broadcasting, and signal processing.
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