For the data given in Q. 146 if X(jω) satisfies the constraints

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For the data given in Q. 146 if X(j_ω) satisfies the constraints required, then the pass band gain A of the ideal low pass filter needed to recover x(t) from c(t) x(t) is—

1. 1
2. 2
3. 4
4. 8

Correct Option: C

From the sampling theorem the Fourier transform of Y (j_ω) of the signal Y(t) = x(t)·c(t) consists of shifted replica of X (j_ω). The replica of X (j_ω) centered around ω = 0 is scaled by Δ/T, where Δ is the width of each pulse c(t). The LPF needs to have a passband gain of

T	=	10⁻³	= 4
Δ		0.25 × 10⁻⁴