Question

The fundamental period of the signal X (t) = 10 cos^2(10 πt) is __________

(a) 0.2

(b) 0.1

(c) 0.5

(d) No fundamental period exists

I have been asked this question in class test.

I'm obligated to ask this question of Periodic and Non-Periodic Signals in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Correct choice is (b) 0.1

Explanation: X (t) = 10 cos^2 (10 πt)

Since, cos 2t = 2cos^2 t – 1

Or, cos^2 t = \(\frac{1+cos⁡2t}{2}\)

∴ X (t) = 5 + 5 cos 20πt

Now, Y (t) = cos 20πt

Fundamental period of the signal is = \(\frac{2π}{20π} = \frac{1}{10}\) = 0.1.