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A 1200 band data stream is to be sent over a non-redundant frequency hopping system, The maximum bandwidth for the spread spectrum signal is 10 MHz. if no overlap occurs, the number of channels are equal to
  • a)
    2175
  • b)
    3125
  • c)
    4167
  • d)
    5286
Correct answer is option 'C'. Can you explain this answer?
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Solution:

Given,

Band data stream = 1200

Maximum bandwidth = 10MHz

Number of channels = ?

Formula used:

Bandwidth of the system = Number of channels × Bandwidth per channel

Calculation:

We know that,

Bandwidth of the system = Maximum bandwidth = 10MHz

Bandwidth per channel = Bandwidth of the system/Number of channels

10MHz/Number of channels = Bandwidth of one channel

Bandwidth of one channel = 1200

(Number of channels)² = (Maximum bandwidth/Bandwidth of one channel)²

(Number of channels)² = (10×10⁶/1200)²

(Number of channels)² = 6944.44

Number of channels = √6944.44

Number of channels = 83.333

Therefore, the closest option to 83.333 is option C, i.e., 4167.

Hence, the correct answer is option C, i.e., 4167.
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