Problem 4: You are given a message signal that is a cosine with a frequency of 1 kHz. This message signal is used in producing an FM signal that has a center frequency of 10.7 MHz. A. What is the index of modulation, B, that will produce an FM signal with a Bandwidth of 6.8 kHz as given by Carson's Rule? 5 Points B. Using this value of , what is the Frequency Deviation, Af? 5 Points C. Write the equation for the FM signal with an average power of 1000 W. 5 Points D. Write the Fourier Series expression for the FM signal. 5 Points E. Sketch the Magnitude of the Spectrum of the FM Signal. 5 Points Table 1: Bessel Functions of the First Kind, J.(B) J J B 0.0 .2 .6 1.00 .99 .96 .91 .85 .77 .67 .57 .46 .10 .20 .29 .37 .44 .SO .54 .01 1.0 .02 .04 .08 .11 .16 .21 26 .31 -02 .03 05 .57 .07 .01 .8 .58 .58 .10 .13 2.0 .35 .56 40 .02 .03 .05 .06 .08 .52 .47 .43 .46 .01 .02 .02 .4 .6 .8 3.0 .22 .11 .00 - 10 -19 - 26 -32 - 36 -39 .20 .24 27 .31 03 .49 .34 .26 .18 .10 .4 .6 .8 .47 .04 .06 .07 .09 .13 .16 .19 .22 .25 .37 .40 .42 .01 .02 .02 .03 .04 -40 .01 .01 4.0 -.40 .02 -38 .36 .31 .02 -07 -.14 -20 -26 -.30 .28 .31 .34 .36 .38 .13 .16 .18 21 .23 25 .18 .12 .03 OS .06 .08 .09 .11 .43 .42 .40 .6 .8 -30 .03 .01 .01 -24 .04 5.0 .2 -33 36 Os -18 -11 --04 .03 .09 .05 -02 -.09 -15 -20 .26 .29 .31 -35 -33 -31 .39 .40 .40 .39 .38 .33 .28 .23 .17 .13 .15 .18 20 .22 .07 .08 .09 .11 .02 .02 .03 .04 GOS .6 .01 .02 .35 Problem 4: You are given a message signal that is a cosine with a frequency of 1 kHz. This message signal is used in producing an FM signal that has a center frequency of 10.7 MHz. A. What is the index of modulation, B, that will produce an FM signal with a Bandwidth of 6.8 kHz as given by Carson's Rule? 5 Points B. Using this value of , what is the Frequency Deviation, Af? 5 Points C. Write the equation for the FM signal with an average power of 1000 W. 5 Points D. Write the Fourier Series expression for the FM signal. 5 Points E. Sketch the Magnitude of the Spectrum of the FM Signal. 5 Points Table 1: Bessel Functions of the First Kind, J.(B) J J B 0.0 .2 .6 1.00 .99 .96 .91 .85 .77 .67 .57 .46 .10 .20 .29 .37 .44 .SO .54 .01 1.0 .02 .04 .08 .11 .16 .21 26 .31 -02 .03 05 .57 .07 .01 .8 .58 .58 .10 .13 2.0 .35 .56 40 .02 .03 .05 .06 .08 .52 .47 .43 .46 .01 .02 .02 .4 .6 .8 3.0 .22 .11 .00 - 10 -19 - 26 -32 - 36 -39 .20 .24 27 .31 03 .49 .34 .26 .18 .10 .4 .6 .8 .47 .04 .06 .07 .09 .13 .16 .19 .22 .25 .37 .40 .42 .01 .02 .02 .03 .04 -40 .01 .01 4.0 -.40 .02 -38 .36 .31 .02 -07 -.14 -20 -26 -.30 .28 .31 .34 .36 .38 .13 .16 .18 21 .23 25 .18 .12 .03 OS .06 .08 .09 .11 .43 .42 .40 .6 .8 -30 .03 .01 .01 -24 .04 5.0 .2 -33 36 Os -18 -11 --04 .03 .09 .05 -02 -.09 -15 -20 .26 .29 .31 -35 -33 -31 .39 .40 .40 .39 .38 .33 .28 .23 .17 .13 .15 .18 20 .22 .07 .08 .09 .11 .02 .02 .03 .04 GOS .6 .01 .02 .35
