How many minimum number of samples are required to exactly describe the following signal?

x(t) = 10 cos(6πt) + 4 sin(8πt)

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UPSC IES Electrical 2022 Prelims Official Paper
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  1. 4 samples per second
  2. 6 samples per second
  3. 8 samples per second
  4. 2 samples per second

Answer (Detailed Solution Below)

Option 3 : 8 samples per second
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Detailed Solution

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Sampling Theorem:

 A continuous-time signal can be represented in its samples and can be recovered back when sampling frequency (fs)is greater than or equal to twice the highest frequency component of the message signal (fm).

The sampling frequency is given by:

\(f_s=2\times max(f_{m1},f_{m2})\)

Calculation:

Given, x(t) = 10 cos(6πt) + 4 sin(8πt)

6π = 2πfm1

fm1 = 3 Hz

8π = 2πfm2

fm2 = 4 Hz

\(f_s=2\times max(3,4)\)

fs = 8 Hz

fs = 8 samples per second

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