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# Answer to Question #190546 in Electrical Engineering for Faiq

Question #190546

When a frequency offset exists the complex envelope of the received signal will be rotating due to this frequency offset, i.e.,

where  is the existing frequency offset. Get the Matlab ﬁle angmodex1.m and angmodex3.m from the class web page. In these ﬁles a PM transmitter (for a sinusoid message signal) and receiver is implemented. If the carrier frequency offset is set to 10 Hz (in the Matlab code deltaf = 10) the demodulator implemented in the m-ﬁle still works pretty well with this frequency offset. Explain why. Note, at higher frequency offsets (e.g., 100 Hz) the performance suffers noticeable distortion. Extra credit will be given if you can ﬁgure out a method to eliminate this distortion.

1
2021-05-10T02:42:35-0400

In radio engineering, a frequency offset is an intentional slight shift of broadcast radio frequency (RF), to reduce interference with other transmitters.

The most important problem encountered in broadcasting via terrestrial transmitters is the interference from other broadcasters. In principle, each broadcaster has a different radio frequency (planned by the public authority) in a common reception area to avoid interference from each other. However, still, there are two problems: spurious radiation of adjacent channels and fringe reception.

Fringe reception is unintended reception under certain weather conditions. The exceptionally long-range reception means that the receiver may be tuned to more than one transmitter (transmitting at the same frequency) at the same time. These transmitters may transmit programs of different broadcasters as well as the programs of the same broadcaster. In analogue transmission, even the transmitters transmitting the very same program interfere with each other because of phase differences of the incoming signal, but in digital transmission, the transmitters transmitting the same program in the same channel may reinforce each other.

The shift in RF

In order to reduce the interference from the fringe area transmitters transmitting in the same channels, a method named frequency offset is often used. By this method, a slightly shifted RF is assigned for a transmitter that may experience interference from other transmitters.

In TV transmission, the shifted RF is calculated by the formula;

"f_{os}=f_{ch}+\\frac{f_L*p}{12}"

"f_{os}"  is the offset RF,

"{\\displaystyle f_{ch}}"  is the standard channel frequency,

"{\\displaystyle p}"  is an integer such that "{\\displaystyle -12<p<0} or {\\displaystyle 0>p>12}"

"{\\displaystyle f_{L}}"  is the line frequency. ( 15625 Hz. for 625-line systems, 15750 Hz. for System M and System J and 20475 Hz. for system E)

Precision offset is the same as frequency offset, except that in this case, the offset frequency is produced by a cesium controlled oscillator.

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