GATE 2025 EE – Question 61

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 2 marks · Numerical answer

An ideal low pass filter has frequency response given by

$$H(j\omega)=\begin{cases}1,&|\omega|\le200\pi\\0,&\text{otherwise}\end{cases}$$

Let $h(t)$ be its time domain representation. Then $h(0)=$ _____ (round off to the nearest integer).

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Correct answer: 200

Explanation

$h(0)=\dfrac1{2\pi}\int_{-\infty}^{\infty}H(j\omega)\,d\omega=\dfrac{400\pi}{2\pi}=200$.