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A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits.


If the bits $0$ and $1$ are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is

  1. $64 \; \mathrm{kHz}$
  2. $32 \; \mathrm{kHz}$
  3. $8 \; \mathrm{kHz}$
  4. $4 \; \mathrm{kHz}$
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