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UPRVUNL AE EC 2016 Official Paper

Option 4 : 2 kHz

ST 1: Logical reasoning

5333

20 Questions
20 Marks
20 Mins

__Concept:__

WBFM is given as:

\(WBFM\;\left( t \right) = {A_c}\;\mathop \sum \limits_{n = - \infty }^\infty {J_n}\left( \beta \right)\cos 2\pi \left( {{f_c} + n{f_m}} \right)t\;\;;\;\;\beta > 1\)

Actual BW of WBFM is ∞ so to Bandlimit WBFM signal all of its significant lower-order sidebands retained and higher-order insignificant sidebands should be eliminated.

__Calculation:__

BW = 32 KHz

Given FM system has 8 sidebands (significant) i.e. 8 sidebands on the positive side of frequency & 8 sidebands on the negative side of the frequency

So, It has sidebands up to order ‘8’.

According to carson rule:

Significant sideband upto order of (β + 1) has B.W

BW = (β + 1) 2f_{m}

So,

32 = 8 × 2 f_{m}

f_{m} = 2 kHz