A 4 kHz (voice-band) noiseless channel is PCM sampled once every 125 microseconds (i.e., 8000 samples/s). If standard telephony coding with 8 bits per sample is used (as in CCITT 2.048 Mb/s systems), what is the resulting bit rate for that single channel?

Difficulty: Medium

Correct Answer: 64 Kbps

Explanation:


Introduction:
Telephony Pulse Code Modulation (PCM) encodes analog voice (nominal 300–3400 Hz) by sampling and quantization. The classic public network standard samples at 8000 samples/s (every 125 microseconds) and uses 8 bits per sample, yielding a familiar channel bit rate. This question tests your ability to connect sampling parameters to bit rate, and to recognize the relationship to CCITT (now ITU-T) 2.048 Mb/s E1 framing.


Given Data / Assumptions:

  • Channel bandwidth: approximately 4 kHz voice-band.
  • Sampling period: 125 microseconds => sampling rate = 8000 samples/s.
  • Quantization: 8 bits per sample (A-law or μ-law companding in practice).
  • Ideal noiseless channel assumed for rate calculation.


Concept / Approach:
Bit rate for PCM = samples per second * bits per sample. For a single encoded voice channel, this is independent of framing overhead; framing becomes relevant when multiplexing many channels (e.g., 32 time slots in an E1 line at 2.048 Mb/s).


Step-by-Step Solution:

1) Compute sampling rate: 1 / 125 microseconds = 8000 samples/s.2) Multiply by bits per sample: 8000 * 8 = 64,000 bits/s.3) Express in kbps: 64,000 bits/s = 64 Kbps.4) Recognize link to E1: 32 * 64 Kbps = 2.048 Mbps (one time slot for framing/signal depending on system).


Verification / Alternative check:
Nyquist sampling for a ~3.4 kHz voice passband leads to a standard 8 kHz sampling rate, which aligns with the 64 Kbps channel rate widely used in telephony.


Why Other Options Are Wrong:

  • 500 Kbps: far too high for a single PCM voice channel.
  • 32 Kbps: would require 4 bits per sample or sub-PCM compression.
  • 8 Kbps: characteristic of low-rate vocoders, not standard PCM.
  • 16 Kbps: typical of ADPCM profiles, not 8-bit PCM.


Common Pitfalls:
Confusing the single-channel rate (64 Kbps) with the aggregate E1 rate (2.048 Mb/s); mixing PCM with ADPCM/vocoder assumptions.


Final Answer:
64 Kbps.

More Questions from Networking

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion