An introduction to frequency and amplitude modulation.
Especially for wireless channels, like commercial radio and
television, but also for wireline systems like cable television,an analog message signal must be
modulated : The
transmitted signal's spectrum occurs at much higher frequenciesthan those occupied by the signal.
We use analog communication techniques for analog message
signals, like music, speech, and television. Transmission andreception of analog signals using analog results in an
inherently noisy received signal (assuming the channel addsnoise, which it almost certainly does).
The key idea of modulation is to affect the amplitude, frequency
or phase of what is known as the
carrier sinusoid. Frequency modulation (FM) and less frequently used
phase modulation (PM) are not discussed here; we focus onamplitude modulation (AM). The amplitude modulated message
signal has the form
where
is the
carrier frequency and
the
carrier amplitude . Also, the signal's
amplitude is assumed to be less than one:
. From our previous exposure to amplitude modulation
(see the
Fourier Transform example ), we know that the
transmitted signal's spectrum occupies the frequency range
, assuming the signal's bandwidth is
Hz (see the
figure ). The carrier
frequency is usually much larger than the signal's highestfrequency:
, which means that the transmitter antenna and carrier
frequency are chosen jointly during the design process.
The AM coherent receiver along with the spectra of key
signals is shown for the case of a triangular-shaped signalspectrum. The dashed line indicates the white noise level. Note that
the filters' characteristics — cutoff frequency andcenter frequency for the bandpass filter — must be match to
the modulation and message parameters.
Ignoring the attenuation and noise introduced by the channel for
the moment, reception of an amplitude modulated signal is quiteeasy (see
[link] ).
The so-called
coherent receiver multiplies the
input signal by a sinusoid and lowpass-filters the result (
[link] ).
Because of our trigonometric identities, we know that
At this point, the message signal is multiplied by a constant
and a sinusoid at twice the carrier frequency. Multiplication bythe constant term returns the message signal to baseband (where
we want it to be!) while multiplication by the double-frequencyterm yields a very high frequency signal. The lowpass filter
removes this high-frequency signal, leaving only the basebandsignal. Thus, the received signal is
This derivation relies solely on the time domain; derive the
same result in the frequency domain. You won't need thetrigonometric identity with this approach.
The signal-related portion of the transmitted spectrum is
given by
.
Multiplying at the receiver by the carrier shifts thisspectrum to
and to
, and scales the result by half.
The signal components centered at twice the carrier frequency
are removed by the lowpass filter, while the baseband signal
emerges.
Because it is so easy to remove the constant term by electrical
means—we insert a capacitor in series with the receiver'soutput—we typically ignore it and concentrate on the signal
portion of the receiver's output when calculatingsignal-to-noise ratio.
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
