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The image below shows the formula for the bandwidth of pulse code modulation (PCM.) There are two questions I want to ask:

Bandwidth of the PCM signal waveform is bounded by \$ B_{PCM} = \frac{1}{2}(R) =\frac{1}{2}(nf_s) \$

R is the bitrate and since this is a square wave, the fundamental frequency will be the frequency of the square wave itself (according to Fourier transform, I think.)

Why does R needs to be halved? (I thought it must be R itself since that is the fundamental frequency.)

For one using a rectangular pulse with polar NRZ line codes = \$ B_{PCM} = R = nf_s \$ (first null bandwidth)

Why in this case does the bandwidth become R itself just because the coding technique is polar NRZ?

enter image description here

JRE
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hontou_
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1 Answers1

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If your bit rate is 1000 bits per second, when the bits are changing at the maximum rate (10101010 etc.) it is effectively a square wave of 500 Hz. That's where the divide by 2 comes in.

Andy aka
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  • Okay I got now that part, thanks! How about polar NRZ not needing divided by 2? – hontou_ Nov 20 '21 at 14:38
  • Might it be referring to something like Manchester encoding. There's probably not enough info contained in your extract in tour question so I can't tell. – Andy aka Nov 20 '21 at 14:49
  • @hontou_ if we're done here then maybe you should accept this answer or ask for more clarification in a comment. – Andy aka May 28 '22 at 13:59