Question

The modulating signal and the carrier wave at a point are represented by m(t)= 0.5cos10³t and c(t) = 1cos10⁷trespectively. Find value of modulation index, upper band and lower band frequency?

Answer 1

$$\begin{gathered} Thefrequencyofmodulatingsignal=\frac{{10}^3}{\omega }and \\ thefrequencyofcarrierwavesignal=\frac{{10}^7}{\omega } \\ ModulationIndex=\frac{frequencydeviation}{modulatingfrequency}=\frac{\frac{{10}^7}{\omega }-\frac{{10}^3}{\omega }}{\frac{{10}^3}{\omega }}9999 \\ Upperbandfrequency=f_c+f_m=\frac{{10}^7}{\omega }+\frac{{10}^3}{\omega }=10001\times \frac{{10}^3}{\omega } \\ andlowerbandfrequency=\frac{{10}^7}{\omega }-\frac{{10}^3}{\omega }=9999\times \frac{{10}^3}{\omega } \end{gathered}$$