Question
Download Solution PDFGiven below are two statements :
Statement I : A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.
Statement II : The side band frequencies are 1002 kHz and 998 kHz.
In the light of the above statements, choose the correct answer from the options given below :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- Bandwidth is defined as the difference between the upper and lower frequencies in continuous bands of frequencies and the formulation of bandwidth frequency is written as;
Bandwidth = 2 fm
here we have fm is the modulation frequency or a signal frequency.
- The side frequencies are written as;
(fc + fm) and (fc - fm)
Here we have fm is the modulation frequency or a signal frequency, fc is the carrier frequency.
EXPLANATION:
The statement " I " said that a speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.
As we know, Bandwidth = 2fm -----(1)
Given: Modulation frequency,fm = 2 kHz
Now, on putting the value in equation (1) we have;
Bandwidth = 2×2
⇒ Bandwidth = 4 kHz
Therefore, the statement " I " is correct.
The statement "II" said that the sideband frequencies are 1002 kHz and 998 kHz.
The side frequencies are written as;
Given: (fc + fm) = 1002 kHz
and (fc - fm) = 998 kHz.
Now, (fc + fm) = 1002 kHz
⇒(fc + fm) = 1000 + 2 = 1002 kHz
and (fc - fm) = 1000 - 2 = 998 kHz
Therefore, statement "II" is correct.
Hence, option 1) is the correct answer.
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