Check each true statement and leave blank each false statement. A periodic odd f

Question

Check each true statement and leave blank each false statement. A periodic odd function satisfies the following conditions: {x(t) = x(t + T) x(t) = -x (-t)} for all t and a specified positive constant T The sum of any two sinusoids must be periodic. A periodic even function satisfies the following conditions: {x(t) = x(t - T) x(t) = x(t)} for all t and a specified positive constant T The Fourier Transform and its inverse are linear operations. Any Laplace Transform x(s) can be transformed into a Fourier Transform by the substitution s = j omega.

Explanation / Answer

1) False for odd signal it is x(-t) = x(t)

2) False only if the frequencies of individual sinusoids are rationally related their sum is periodic

3) True periodic signal is x(t+mT) where m is any integer

4) These are non-linear False

5) True

4)

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