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
What are the factors that affect demand for a commodity
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
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Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
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