sin a sin = [cos(a - B)- cos(a +)] sin(a+) = sin a cos cos a sin cos a cos = [ sin a cos = cos(a-B)+cos(a+B)] [sin(a B) + sin(a+) ] sin a sin cos(a ) = cos a cos cos (2 ft /4)= [cos(2 ft) = sin(2 ft)]/2 cos' a = -sina, sin' a = cos a |FT[cos (2n fet + 0)] = |FT[sin(2n fet + 0)]] = // [ 8( - fc) + 8( + c)] TABLE A6.5 Table of Bessel functions alx 0. 1 2 0.9385 0.7652 0.2239 0.2423 0.4401 0.5767 0.0306 0.1149 0.3528 0.0016 0.0196 0.0002 0.0025 0.1289 0.0340 0.0002 0.0070 0.0012 0.0002 0 1 2 3 4 S 6 7 8 9 10 11 12 13 14 - - 3 4 1. Consider a triangle message signal m(t) = = 4t-2, if 0t1 6-4t, if 1t2, whose pulse width is 0, else T = 2 second and bandwidth is approximately W = 2 = 1 Hz. We modulate it over the carrier c(t) = cos(2720t) using FM modulation with frequency sensitivity factor kf = 1.5. (a) Write down the FM signal waveform expression s(t) (no need to calculate integration) and sketch the time-domain waveform. (b) Write down the instantaneous frequency fi(t) and sketch it. (b) Calculate this FM signal's bandwidth BT.