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How can we generate a periodic signal from a periodic signal itself?

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in Signals and Systems by (1.2m points)
How can we generate a periodic signal from a periodic signal itself?

(a) By extending a  signal with duration T

(b) Cannot be extended

(c) By extending the periodic signal’s amplitude

(d) By extending the sugar with duration 2π

The question was posed to me in my homework.

This question is from Periodic Signals topic in portion Fourier Series of Signals and Systems

1 Answer

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by (42.1k points)
Correct option is (a) By extending a  signal with duration T

The explanation: A periodic signal x(t) can be generated by a periodic extension of any segment of x of duration T( the period).

As a result, we can generate x(t) from any segment x(t) having a duration of one period by replacing this segment and reproduction thereof end to end ad infinitum on either side.

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