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Which of the following cannot be the Fourier series of a periodic signal?(a) x(t) = 2Cost + 4Cos7t(b) x(t) = 2Cosπt + 4Cos7t(c) x(t) = Cost + 0.7(d) x(t) = 2Cost + 4Sin7tThe question was asked at a job interview.Origin of the question is AM Wave Representation topic in portion Amplitude Modulation of Analog Communications

Answer»

The correct answer is (c) x(t) = COST + 0.7

For EXPLANATION I would say: x(t) = Cost + 0.7does not FOLLOW Dirchlet’s conditions. FOURIER series of a periodic signal will only be applicable if it satisifies Dirchlet’s conditions firstly. Dirichlet integral states that a finite NUMBER should have finite number of discontinuities and also have finite number of extrema. x(t) doesn’t satisfy any of the criteria, whereas other options satisfy Dirchlet’s conditions. Thus, x(t) = Cost + 0.7, cannot be the Fourier series of a periodic signal.


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