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While sitting in ELEC 241 class, he falls asleep during a critical time when an AM receiver is being described.The received signal has the form $r(t)=A(1+m(t))\cos (2\pi {f}_{c}t+\phi )$ where the phase $\phi $ is unknown. The message signal is $m(t)$ ; it has a bandwidth of $W$ Hz and a magnitude less than 1( $\left|m(t)\right|< 1$ ). The phase $\phi $ is unknown. The instructor drew a diagram for a receiver on the board; Sammy slept through the description of what the unknownsystems where.
Sid Richardson college decides to set up its own AM radio station KSRR. The resident electrical engineerdecides that she can choose any carrier frequency and message bandwidth for the station. A rival college decides to jam its transmissions by transmitting a high-power signal thatinterferes with radios that try to receive KSRR. The jamming signal $\mathrm{jam}(t)$ is what is known as a sawtooth wave (depicted in [link] ) having a period known to KSRR's engineer.
A stereophonic signal consists of a "left" signal $l(t)$ and a "right" signal $r(t)$ that conveys sounds coming from an orchestra's left andright sides, respectively. To transmit these two signals simultaneously, the transmitter first forms thesum signal ${s}_{+}(t)=l(t)+r(t)$ and the difference signal ${s}_{-}(t)=l(t)-r(t)$ . Then, the transmitter amplitude-modulates the differencesignal with a sinusoid having frequency $2W$ , where $W$ is the bandwidth of the left and right signals. The sum signal and the modulated difference signal are added,the sum amplitude-modulated to the radio station's carrier frequency ${f}_{c}$ , and transmitted. Assume the spectra of the left and right signals are as shown .
A clever engineer has submitted a patent for a new method for transmitting two signals simultaneously in the same transmission bandwidth as commercial AM radio. As shown , her approach is to modulate the positive portion of the carrier with onesignal and the negative portion with a second.
In detail the two message signals ${m}_{1}(t)$ and ${m}_{2}(t)$ are bandlimited to $W$ Hz and have maximal amplitudes equal to 1. The carrier has a frequency ${f}_{c}$ much greater than $W$ . The transmitted signal $x(t)$ is given by $$x(t)=\begin{cases}A(1+a{m}_{1}(t))\sin (2\pi {f}_{c}t) & \text{if $\sin (2\pi {f}_{c}t)\ge 0$}\\ A(1+a{m}_{2}(t))\sin (2\pi {f}_{c}t) & \text{if $\sin (2\pi {f}_{c}t)< 0$}\end{cases}$$ In all cases, $0< a< 1$ . The plot shows the transmitted signal when the messagesare sinusoids: ${m}_{1}(t)=\sin (2\pi {f}_{m}t)$ and ${m}_{2}(t)=\sin (2\pi \times 2{f}_{m}t)$ where $2{f}_{m}< W$ . You, as the patent examiner, must determine whether thescheme meets its claims and is useful.An ELEC 241 student has the bright idea of using a square wave instead of a sinusoid as an AM carrier. Thetransmitted signal would have the form $$x(t)=A(1+m(t)){\mathrm{sq}}_{T}(t)$$ where the message signal $m(t)$ would be amplitude-limited: $\left|m(t)\right|< 1$
An amplitude-modulated secret message $m(t)$ has the following form. $$r(t)=A(1+m(t))\cos (2\pi ({f}_{c}+{f}_{0})t)$$ The message signal has a bandwidth of $W$ Hz and a magnitude less than 1 ( $\left|m(t)\right|< 1$ ). The idea is to offset the carrier frequency by ${f}_{0}$ Hz from standard radio carrier frequencies. Thus,"off-the-shelf" coherent demodulators would assume the carrier frequency has ${f}_{c}$ Hz. Here, ${f}_{0}< W$ .
An excited inventor announces the discovery of a way of using analog technology to render musicunlistenable without knowing the secret recovery method. The idea is to modulate the bandlimited message $m(t)$ by a special periodic signal $s(t)$ that is zero during half of its period, which renders the message unlistenable and superficially, atleast, unrecoverable ( [link] ).
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