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Is the sum of discrete time periodic signals periodic?

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in Signals and Systems by (1.2m points)
Is the sum of discrete time periodic signals periodic?

(a) No, they are not

(b) Yes they are

(c) Depends on the signal

(d) Not periodic if their ratio is not rational

This question was addressed to me during a job interview.

I would like to ask this question from Periodic Signals topic in portion Fourier Series of Signals and Systems

1 Answer

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by (42.1k points)
The correct option is (b) Yes they are

The best explanation: The sum of discrete time periodic signals always periodic because the period ratios N/N are always rational.

For the continuous time, it depends on the ratio.

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