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ZOH Impulse Response FT

Ask
Zero Order Hold system has an impulse response given by
u(t)- u(t-T)
The Fourier transform of the system is
(a)\frac{[1-e^{j\omega T}]}{ j\omega }
(b)\frac{[1-e^-j\omega T]}{j\omega}
(c)\frac{[1+e^j\omega T]}{j\omega}
(d) none of these

Answer is ( b )
Concept
Lets understand an additional concept (may not be useful to solve the question ) of the Zero Order Hold impulse response graphically:


Laplace Transform of u(t) \rightarrow \frac{1}{s} 
u(t-T) \rightarrow \frac{e^{-Ts}}{s}

Thus , u(t) - u(t-T) 
\implies \frac{1}{s} - \frac{e^{-Ts}}{s}
\implies \frac{1-e^{-Ts}}{s}

For Fourier Transform ,  s = j\omega
 u(t) - u(t-T) =   \frac{1-e^{-T j\omega}}{j\omega}

http://nptel.ac.in/courses/108103008/4


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