how to make barcodes in excel 2011 The bandwidth ofperiodic and nonperiodic composite signals in Software

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The bandwidth ofperiodic and nonperiodic composite signals
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Amplitude
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5000 Bandwidth = 5000 - 1000 = 4000 Hz
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a Bandwidth of a periodic signal
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b Bandwidth of a nonperiodic signal
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DATA AND SIGNALS
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Example 310
If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth Draw the spectrum, assuming all components have a maximum amplitude of 10 V
Solution
Letfh be the highest frequency, fl the lowest frequency, and B the bandwidth Then B =fh -
it = 900 -
100 = 800 Hz
The spectrum has only five spikes, at 100, 300, 500, 700, and 900 Hz (see Figure 313)
The bandwidthfor Example 310
Amplitude
10+-----]
Frequency
Bandwidth = 900 - 100 = 800 Hz
Example 311
A periodic signal has a bandwidth of 20 Hz The highest frequency is 60 Hz What is the lowest frequency Draw the spectrum if the signal contains all frequencies of the same amplitude
Solution
Letfh be the highest frequency,fz the lowest frequency, and B the bandwidth Then
B =fh -
fz :::::}
20 =60 -
ft =60 - 20 =40 Hz
The spectrum contains all integer frequencies We show this by a series of spikes (see Figure 314)
The bandwidth for Example 311
4041 42
Bandwidth = 60 - 40 = 20 Hz
Frequency (Hz)
Example 312
A nonperiodic composite signal has a bandwidth of 200 kHz, with a middle frequency of 140 kHz and peak amplitude of 20 V The two extreme frequencies have an amplitude of 0 Draw the frequency domain of the signal
SECT/ON 33
DIGITAL SIGNALS
Solution
The lowest frequency must be at 40 kHz and the highest at 240 kHz Figure 315 shows the frequency domain and the bandwidth
The bandwidth for Example 312
Amplitude
40 kHz
140kHz
240 kHz
Frequency
Example 3 J3
An example of a nonperiodic composite signal is the signal propagated by an AM radio station, In
the United States, each AM radio station is assigned a lO-kHz bandwidth The total bandwidth dedicated to AM radio ranges from 530 to 1700 kHz We will show the rationale behind this lO-kHz bandwidth in 5
Example 3 J4
Another example of a nonperiodic composite signal is the signal propagated by an FM radio station In the United States, each FM radio station is assigned a 200-kHz bandwidth The total bandwidth dedicated to FM radio ranges from 88 to 108 MHz We will show the rationale behind this 200-kHz bandwidth in 5
Example 3/5
Another example of a nonperiodic composite signal is the signal received by an old-fashioned analog black-and-white TV A TV screen is made up of pixels (picture elements) with each pixel being either white or black The screen is scanned 30 times per second (Scanning is actually 60 times per second, but odd lines are scanned in one round and even lines in the next and then interleaved) If we assume a resolution of 525 x 700 (525 vertical lines and 700 horizontal lines), which is a ratio of 3: 4, we have 367,500 pixels per screen If we scan the screen 30 times per second, this is 367,500 x 30 = 11,025,000 pixels per second The worst-case scenario is alternating black and white pixels In this case, we need to represent one color by the minimum amplitude and the other color by the maximum amplitude We can send 2 pixels per cycle Therefore, we need 11,025,000/2 = 5,512,500 cycles per second, or Hz The bandwidth needed is 55124 MHz This worst-case scenario has such a low probability of occurrence that the assumption is that we need only 70 percent of this bandwidth, which is 385 MHz Since audio and synchronization signals are also needed, a 4-MHz bandwidth has been set aside for each black and white TV channel An analog color TV channel has a 6-MHz bandwidth
DIGITAL SIGNALS
In addition to being represented by an analog signal, information can also be represented by a digital signal For example, a I can be encoded as a positive voltage and a 0 as zero voltage A digital signal can have more than two levels In this case, we can
DATA AND SIGNALS
send more than 1 bit for each level Figure 316 shows two signals, one with two levels and the other with four Figure 316
Two digital signals: one with two signal levels and the other with four signal levels
Amplitude
8 bits sent in I s, Bit rate = 8 bps
1 Levell
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Tim e
a A digital signal with two levels
Amplitude
"1 I 6 b"Its sent III s, Bit rate = 16 bps
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b A digital signal with four levels
We send 1 bit per level in part a of the figure and 2 bits per level in part b of the figure In general, if a signal has L levels, each level needs log2L bits
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