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Signal and systems miscellaneous

Signals and Systems

  1. A square wave is defined by
    x(t) =
    A; 0 < t < T0/2
    – A; T0/2 < t < T0

    It is periodically extended outside this interval. What is the general coefficient an in the Fourier expansion of the wave?
    1. 0
    2. 2A(1 – cos nπ)
    3. 2A(1 + cos nπ)
    4. 2A(1 – cos nπ)
      [(n + 1)π]
Correct Option: A

Given that

x(t) =
A; 0 < t < T0/2
– A; T0/2 < t < T0

where T0 is the fundamental period. If we plot this periodic square wave.

From the wave, it is clear that wave is an odd function, therefore an = 0.
Hence, alternative (A) is the correct choice.



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