Amplitude modulation Flashcards
power content of the analog signal denoted by m(t) which is lowpass signal with bandwidth W -> M(f)=0 for |f| > W
Pm = lim (as T goes to inf) 1/T * ∫ from -T/2 to T/2 of |m(t)|^2 dt
how the message signal m(t) is transmitted through the channel
it is impressed on a carrier signal of the form c(t) = Accos(2pift + fi)
amplitude modulation
the message signal is impressed on the amplitude of the carrier signal - this results in a sinusoidal signal whose amplitude is a function of the message signal m(t)
double sideband surpassed carrier AM
DSB-SC AM is obtained by multiplying the message signal m(t) with the carrier signal -> u(t) = m(t)*u(t)
spectrum of DSB-SC AM
is obtained by taking Fourier transform of u(t) -> U(f) = Ac/2*[M(f - fc) + M(f + fc)]
upper and lower sideband of U(f)
upper sideband is in the f band |f| > fc and lower for |f| < fc
why it is called DSB-SC am
it is called double-sideband since it contains upper and lower sidebands, it also doesn’t contain a carrier component -> all transmitted power is in modulating signal that’s why is called suppressed carrier signal
power content of DSB-SC AM signal
Pu = lim T->INF ∫ u^2(t) dt = lim T -> inf ∫ Ac^2m^2(t)cos^2(2pifc*t)dt = Ac^2 / 2 * Pm
conventional amplitude modulation
it consists of a large carrier component in addition to the DSB am signal -> u(t) = Ac[1+m(t)]cos(2pifct)
sometimes m(t) is expressed as:
m(t) = a*mn(t) where
mn(t) = m(t)/max|m(t)|
spectrum of conventional am signal
U(f) = Ac*a/2 [Mn(f-fc) + Mn(f+fc)] + Ac/2[δ(f-fc) + δ(f+fc)]
power for the conventional am signal
power of message signal: Pm= lim integral [1+amn(t)]dt
Pm = 1 + a^2Pmn
Pu = Ac^2/2 + Ac^2/2a^2*Pmn
envelope detector
the combination of rectifier and the lowpass filter
