<< Chapter < Page Chapter >> Page >
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
x t A c 1 m t 2 f c t
where f c is the carrier frequency and A c the carrier amplitude . Also, the signal's amplitude is assumed to be less than one: m t 1 . From our previous exposure to amplitude modulation (see the Fourier Transform example ), we know that the transmitted signal's spectrum occupies the frequency range f c W f c W , assuming the signal's bandwidth is W Hz (see the figure ). The carrier frequency is usually much larger than the signal's highestfrequency: f c W , 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] ).

m ^ t LPF x t 2 f c t LPF A c 1 m t 2 f c t 2
Because of our trigonometric identities, we know that
2 f c t 2 1 2 1 2 2 f c t
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
m ^ t A c 2 1 m t

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 X f 1 2 M f f c 1 2 M f f c . Multiplying at the receiver by the carrier shifts thisspectrum to f c and to f c , and scales the result by half.

1 2 X f f c 1 2 X f f c 1 4 M f 2 f c M f 1 4 M f 2 f c M f 1 4 M f 2 f c 1 2 M f 1 4 M f 2 f c
The signal components centered at twice the carrier frequency are removed by the lowpass filter, while the baseband signal M f emerges.

Got questions? Get instant answers now!

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 does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of electrical engineering i' conversation and receive update notifications?

Ask