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?

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:

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.