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GATE 2015 EC – Question 32

Communications · Analog Communications · 1 mark · Multiple choice

A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size $\Delta$ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

  1. $\frac{1}{2\pi}$
  2. $\frac{1}{\pi}$
  3. $\frac{2}{\pi}$
  4. $\pi$

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Correct answer: (A) $\frac{1}{2\pi}$

Explanation

To avoid slope overload, the signal slope $A\omega$ must not exceed $\Delta f_s$. So $A \leq \frac{\Delta f_s}{2\pi f_m} = \frac{0.1 \times 20000}{2\pi \times 2000} = \frac{1}{2\pi}$.