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GATE 2020 IN – Question 15

Signals and Systems · Signals and linear time-invariant systems: Periodic, aperiodic and impulse signals, continuous-time and discrete-time systems, transfer function, LTI systems, impulse response, frequency response, pulse transfer function, convolution, correlation · 1 mark · Multiple choice

A differentiator has a transfer function whose

  1. Phase increases linearly with frequency.
  2. Magnitude remains constant.
  3. Magnitude increases linearly with frequency.
  4. Magnitude decreases linearly with frequency.

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Show answer and explanation

Correct answer: (C) Magnitude increases linearly with frequency.

Explanation

An ideal differentiator has $H(s)=Ks$, so $H(j\omega)=jK\omega$. Its magnitude is $|K|\omega$, linear in frequency, while its phase is constant at +90° for positive K. Therefore C describes the transfer function.

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