Question

Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)

Answer 1

The above given signal are periodic and explained below image.

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W2 = 5 Crational) a) alt) = Cosst + Sin 25t W, = 5 rad /sec ,- 25 radisec. if wza rational value 21 sec 27 w it is periodic We's irrational (52, n..), it is Non-periodic It is a periodic, fundamental frequency = 5 vad/sec. fundamental time period 2 x (t)= sin(91+1)+ sin(6t-2) + cos(394) W3 = 39, heyet e 23 crational) so periodic. H.C.F of 9,6,39 fundamental frequency = 3 rad /sec fundamental time period() = W, 9, 3L9, 6.39 3 ² 13 27 sec.

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