University:
Massachusetts Institute of Technology
Course:
16.01 | Unified Engineering I, II, III, & IV
Academic year:

2023
Views:

479

Pages:

6
Author:

limeja9tu

LECTURE S23 Incoherent Demodulation of AM-DSB/SC In practice we Know the frequency, but not the phase, of the carrier. So we really have [Diagram: A block diagram is shown. An input signal 'y(t)' is multiplied by 'cos(ωct+θ)'. The product is then passed through a low-pass filter 'L(jw)'. Finally, a multiplier '2' is applied to the output, resulting in 'x(t)'.] Then g(t) = cos(ωct + θ) y(t) = [cos(ωct) cos(ωct + θ) x(t) ] = [1/2 cosθ + 1/2 cos(2ωct + θ)] x(t) | | | | |low frequency| high frequency| Therefore, after filtering: x^(t) = (cosθ) x(t) In practice, phase varies with time: x^(t) = cos(θ(t)) ⋅ x(t) Signal fades in and out with time! Without some means to estimate the phase of the carrier, AM-DSB/SC is not very practical. ⇒ We need to transmit information about the phase. AM Double Sideband with Carrier (AM-DSB/WC) To allow the receiver to determine the phase, add some carrier to the signal: [Diagram: A block diagram is shown. An input signal 'x(t)' is multiplied by 'cos(ωct)'. The product is then added to a carrier signal 'A cos(ωct)'. The final output is 'y(t) = [x(t) + A] cos(ωct)' ] w(t) = cos(ωct) The Fourier Transform of y(t) is Y(jw) = 1/2 X(j(ω-ωc)) + 1/2 X(j(ω+ωc)) πA [δ(ω-ωc) + δ(ω+ωc)] [Graph: A plot of the magnitude of Y(jw) is shown. Two peaks are visible at frequencies ωc-ωb and ωc+ωb, representing the sidebands. Two vertical lines at ωc indicate the presence of the carrier signal.] Two sidebands with carrier This is the type of AM used on commercial AM stations.