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Signal and systems miscellaneous

Signals and Systems

  1. If x(t) is given by figure shown below

    Then its Fourier transform is—
    1. None of these
Correct Option: B

X(t) =
δ(t – kT)
k = – ∞

To determine the Fourier transform of this signal, we first compute its Fourier series coefficients, defined by

ak = t/2δ(t) e–jkω0t dt
-t/2

where,
ω0 =
T

ak =
1
T

The Fourier transform of given function is a linear combination of impulses equally spaced in frequency, i.e.
X(jω) =
2π ak.δ(ω – kω0)
k = – ∞

or
X(jω) =
2π.(1/T){δω – k(2π/1)}
k = – ∞

or
X(jω) = (2π/T)
δ{ω -(2πk/1)}
k = – ∞

→ As shown below

Hence, alternative (B) is the correct choice.



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