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