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GATE 2022 EE – Question 11

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 1 mark · Multiple choice

The transfer function of a real system, $H(s)$, is given as:

$$H(s)=\frac{As+B}{s^2+Cs+D},$$

where $A,B,C$ and $D$ are positive constants. This system cannot operate as

  1. low pass filter.
  2. high pass filter.
  3. band pass filter.
  4. an integrator.

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Show answer and explanation

Correct answer: (B) high pass filter.

Explanation

As $s\to\infty$ the gain tends to $\frac{A}{s}\to0$, so the system cannot pass high frequencies and cannot be a high pass filter. With $B\ne0$ it passes DC (low pass), it can peak at a mid frequency (band pass) and can behave like an integrator over a range of frequencies.