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A sinusoidal signal of $2$ kHz frequency is applied to a delta modulator. The sampling rate and step-size $\Delta$ of the data 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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