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{{Modulation techniques}}
 
'''Phase modulation''' ('''PM''') is a [[modulation]] pattern that encodes [[information]] as variations in the [[instantaneous phase]] of a [[carrier wave]].
 
Unlike [[frequency modulation]] (FM), phase modulation is not widely used for transmitting [[radio]] waves. This is because PM requires more complex receiving hardware, and there can be ambiguity problems in determining whether, for example, the [[Signal (electrical engineering)|signal]] has changed [[Phase (waves)|phase]] by +180° or -180°.
 
PM is used in [[digital synthesizer]]s, such as the [[Casio CZ synthesizers]],{{how|date=July 2013}} and to implement [[Frequency modulation synthesis|FM synthesis]] in such digital synthesizers as the [[Yamaha DX7]].
 
==Theory==
PM changes the phase angle of the complex envelope in direct proportion to the message signal.
 
Suppose that the signal to be sent (called the modulating or message signal) is <math>m(t)</math> and the carrier onto which the signal is to be modulated is
:<math>c(t) = A_c\sin\left(\omega_\mathrm{c}t + \phi_\mathrm{c}\right).</math>
Annotated:
:carrier(time) = (carrier amplitude)*sin(carrier frequency*time + phase shift)
 
This makes the modulated signal
:<math>y(t) = A_c\sin\left(\omega_\mathrm{c}t + m(t) + \phi_\mathrm{c}\right).</math>
This shows how <math>m(t)</math> modulates the phase - the greater m(t) is at a point in time, the greater the phase shift of the modulated signal at that point. It can also be viewed as a change of the frequency of the carrier signal, and phase modulation can thus be considered a special case of FM in which the carrier frequency modulation is given by the time [[derivative]] of the phase modulation.
 
The mathematics of the [[spectral density|spectral]] behavior reveals that there are two regions of particular interest:
*For small [[amplitude]] signals, PM is similar to [[amplitude modulation]] (AM) and exhibits its unfortunate doubling of [[baseband]] [[bandwidth (signal processing)|bandwidth]] and poor efficiency.
*For a single large [[sinusoidal]] signal, PM is similar to FM, and its bandwidth is approximately
::<math>2\left(h + 1\right)f_\mathrm{M}</math>,
:where <math>f_\mathrm{M} = \omega_\mathrm{m}/2\pi</math> and <math>h</math> is the modulation index defined below. This is also known as [[Carson bandwidth rule|Carson's Rule]] for PM.
 
==Modulation index==
As with other [[modulation index|modulation indices]], this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to the variations in the phase of the carrier signal:
:<math> h\, = \Delta \theta\,</math>,
where <math>\Delta \theta</math> is the peak phase deviation. Compare to the modulation index for [[frequency modulation#Modulation index|frequency modulation]].
<!-- in anolog communication . phase modulation how to change phase of carrier with accordance modulating signal-->
<!-- the above text makes no sense. I do not understand why it is there.-->
 
==See also==
* [[Angle modulation]]
* [[Automatic frequency control]]
* [[Modulation]] for a list of other modulation techniques
* [[Phase-shift keying]] (PSK), the digital version of PM
* [[Polar modulation]]
* [[Electro-optic modulator]] for Pockel's Effect phase modulation for applying sidebands to a monochromatic wave
 
{{DEFAULTSORT:Phase Modulation}}
[[Category:Radio modulation modes]]

Revision as of 16:32, 18 February 2014

A Wine Lover's Weekly Manual To $10 Wines - A Mexican Petite Syrah

Link Schwartz California is a dichotomy, surf tradition on a single hand and higher end residing on the other. Soothing in California has been turned into an artwork you just have to knowledge.

Jesus Christ claimed that he was 'God' in flesh. He arrived to earth to offer forgiveness for sin to all who would receive him and believe. He additional mentioned...

The offer is having to pay a lower month-to-month payment with no getting to enhance your fascination prices. As a rule, a good 2%25 off from your common mortgage desire will make california refinance a far better option. Link Schwartz is nevertheless the best area to be and lower fascination rates could entice you get it. A lot of lenders with appealing fascination charges will be vying for your enterprise. Be vigilant, though, if you want to have a profitable refinance program.

I guess a tiny airplane crashed in Florida today at 11:15 a.m. or so ET, someplace in the location of Fort Lauderdale. The Broward County sheriff's office and the FAA are all more than the scene. I guess it lower a home in fifty percent and started a fireplace. So considerably, no 1 looks to know at this time regardless of whether or not the house experienced dwelling folks within. Why don't we look up who owns the residence and uncover out if individuals folks ended up on getaway or at function when this took place? Sounds like a no-brainer to me.

For those people in the Boston area, I guess it's not protected to day folks off Craigslist any more. A killer, supposedly a young, clear-reduce blond man is in search of victims via ads for therapeutic massage providers posted on Craigslist. 3 girls essential a masseuse. Sadly, two girls were robbed and the third was murdered. Word to the smart, don't inquire for a masseuse on the web. Go to a massage parlor. Feel about how vulnerable you are when you get off your clothes, lie on your back again and feel so peaceful. It may not be cheap, but you certainly wouldn't have to give up as much as individuals three victims did.

It took just seven times to get all my worldly possessions loaded up in my motorhome, all my obligations taken treatment of, and I was off to see what this region retains. I was cost-free. Free of charge to snooze in. Free to get up early and view the sunrise. Totally free to continue to be up late and howl at the moon. Free of charge to lay all around for times on end. Fish, hike, read through textbooks, daydream. I was free of charge. Or, so I imagined. I lived that way for a pair of several years prior to truth slapped me in the encounter.

Dakota Club, GP and Nationwide are variants of training course. These a few layouts are street classes with GP and National incorporating some portion of the high-banked tri-oval in their layouts. These three layouts are exciting, about one mile in length give or just take, and supply the driver lots of problems. Only the Club structure has no elevation alter throughout all the different layouts.

Yummi Bears has been rated as America's #1 Children's Vitamin, and for great cause. This dietary complement for little ones comes in an all-normal watermelon taste and appears just like the gummy bear's candy you would find in your neighborhood grocery shop. Kid's don't realize this Yummi Bear is in fact great for them and consider their mother and father are permitting them have candy for breakfast.

3) Of the more mature inhabitants with prolonged-time period treatment requirements in the local community, about thirty%twenty five (one.five million men and women) have significant extended-expression treatment demands (a few or a lot more ADL restrictions). Of these, about twenty five%twenty five are eighty five and more mature Link Schwartz and 70%25 report they are in truthful to inadequate wellness. The Henry J. Kaiser Basis. Long-expression Care: Medicaid's part and challenges [Publication #2172]. Washington, DC: Writer, 1999.

Through the world wide web you can get heap electrical carts. The carts are bought in various websites. buy a auto from a reputable dealer to get value for money. The carts don't come low-cost as they are high priced. There are a lot of reliable sellers on line. Verify the reliability of a business prior to you buy a cart from them. Decide up carts with warrant durations so that they can be replaced in case of split downs. Electric carts are ideal to be employed as they are eco pleasant. To prevent any sort of pollution pick electric carts over Link Schwartz gas carts.

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