angle modulation

Question 1

angle modulation signal can be written:

Answer 1

u(t) = Accos(2pifct + fi(t)),
where fc denotes carrier frequency
fi(t) - a time caring phase

Question 2

instantaneous frequency of the signal

Answer 2

fi(t) = fc + 1/2*pi *d/dt(fi(t))

Question 3

phase

Answer 3

fi(t) = kp*m(t), where m(t) is message signal
fi(t) = 2*pi*kf*integral of m(t) dt

Question 4

the maximum phase and frequency deviation are given:

Answer 4

ΔΦmax = kp*max[|m(t)|]
Δfmax = kf*max[|max(t)|]

Question 5

modulation index for general nonsinudoidal signal m(t)

Answer 5

Bp = kp*max[|m(t)|].= ΔΦmax
Bf = kf*max[|m(t)|]/W = Δfmax/W

Question 6

modulated signal using Euler’s relation

Answer 6

u(t) = Re(Ace^(j2pifct)e^(jBsin(2pifm*t)

Question 7

Bessel function of the first kind of order n which is denoted by Jn(B)

Answer 7

Jn(B) = 1/2piintegral from 0 to 2pi of e^(j(Bsinu - nu)) du
where u = 2pifmt

Question 8

modulated signal with bezel function in place

Answer 8

u(t) = Re(Acsum(Jn(B)e^(j2pifmt)e^(j2pifc*t))

= sum(AcJn(B)cos(2pi(fc + nfm)t)

Question 9

approximation of Bessel function for small B

Answer 9

Jn(B) = B^n/(2^n*n!)

Question 10

effective bandwidth of angle modulated signal which contains at least 98% of the signal power is given

Answer 10

Be = 2(B+1)fm
B - modulation index
Fm - frequency of message signal

Question 11

Carson rule

Answer 11

Be = 2(B + 1)W