sin a sin = [cos(a - B)- cos(a +)] sin(a+) = sin a cos cos...

 

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sin a sin ß= [cos(a - B)- cos(a +ß)] sin(a+ß) = sin a cos ß cos a sin ß cos a cos = [ sin a cos = cos(a-B)+cos(a+B)] [sin(a− B) + sin(a+ß) ] sin a sin ß cos(a ± ß) = cos a cos cos (2π ft ±π/4)= [cos(2π ft) = sin(2π ft)]/√2 cos' a = -sina, sin' a = cos a |FT[cos (2n fet + 0)] = |FT[sin(2n fet + 0)]] = // [ 8(ƒ - fc) + 8(ƒ + ƒc)] 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 <-0.2601 0.3391 0.4861 -0.3971 0.1506 0.1717 -0.0660 <-0.2767 0.2346 0.3641 <-0.2429 <-0.11.30 0.3091 0.4302 0.1148 -0.3911 0.1320 0.2811 0.3576 <-0.1054 0.0430 0.1321 0.3621 0.1858 0.0114 0.0491 0.2458 0.3376 0.1296 0.3206 0.0040 0.0565 0.2235 0.0009 0.0212 0.1263 0.0070 0.0609 0.0020 0.0256 0.1131 0.0025 0.0152 acons 0.0001 0.0002 0.0005 0.0001 0.0096 0.0634 0.0033 0.0290 0.0010 0.0120 8 10 <-0.2459 0.0435 0.2546 0.0584 -0.2196 -0.2341 -0.0145 0.2167 0.3179 0.2919 0.2075 12 0.0477 <-0.2234 -0.0849 0.1951 0.1825 -0.0735 <-0.2437 P -0.1703 200 0.0451 Pe 0.2304 P 0.3005 0.2704 0.1953 01201 0.0650 1. Consider a triangle message signal m(t) = = 4t-2, if 0≤t≤1 6-4t, if 1≤t≤2, 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. sin a sin ß= [cos(a - B)- cos(a +ß)] sin(a+ß) = sin a cos ß cos a sin ß cos a cos = [ sin a cos = cos(a-B)+cos(a+B)] [sin(a− B) + sin(a+ß) ] sin a sin ß cos(a ± ß) = cos a cos cos (2π ft ±π/4)= [cos(2π ft) = sin(2π ft)]/√2 cos' a = -sina, sin' a = cos a |FT[cos (2n fet + 0)] = |FT[sin(2n fet + 0)]] = // [ 8(ƒ - fc) + 8(ƒ + ƒc)] 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 <-0.2601 0.3391 0.4861 -0.3971 0.1506 0.1717 -0.0660 <-0.2767 0.2346 0.3641 <-0.2429 <-0.11.30 0.3091 0.4302 0.1148 -0.3911 0.1320 0.2811 0.3576 <-0.1054 0.0430 0.1321 0.3621 0.1858 0.0114 0.0491 0.2458 0.3376 0.1296 0.3206 0.0040 0.0565 0.2235 0.0009 0.0212 0.1263 0.0070 0.0609 0.0020 0.0256 0.1131 0.0025 0.0152 acons 0.0001 0.0002 0.0005 0.0001 0.0096 0.0634 0.0033 0.0290 0.0010 0.0120 8 10 <-0.2459 0.0435 0.2546 0.0584 -0.2196 -0.2341 -0.0145 0.2167 0.3179 0.2919 0.2075 12 0.0477 <-0.2234 -0.0849 0.1951 0.1825 -0.0735 <-0.2437 P -0.1703 200 0.0451 Pe 0.2304 P 0.3005 0.2704 0.1953 01201 0.0650 1. Consider a triangle message signal m(t) = = 4t-2, if 0≤t≤1 6-4t, if 1≤t≤2, 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.

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