PCM block diagram; T1 signaling rate and frame

Functional block diagram of PCM

Pulse code modulation (PCM) turns an analog signal into a stream of binary code words by sampling, quantising and encoding it.

 TRANSMITTER
 m(t)->[LPF]->[Sampler]->[Quantizer]->[Encoder]->
                                     PCM bits
 CHANNEL with REGENERATIVE REPEATERS
 ->[Equalizer]->[Decision/Timing]->[Regenerate]->
 RECEIVER
 ->[Regenerator]->[Decoder]->[Reconstruction LPF]->m'(t)

• Anti-aliasing LPF: limits the message to $W$ Hz.
• Sampler: takes samples at $f_s \ge 2W$ (8 kHz for speech).
• Quantiser: rounds each sample to one of $L = 2^n$ levels (with companding for speech).
• Encoder: turns each level into an $n$-bit code word, then a line code is applied.
• Regenerative repeaters: reshape and retime the pulses along the line, so noise does not build up.
• Receiver: the regenerator cleans the pulses, the decoder turns code words back into PAM samples, and the LPF rebuilds $m(t)$.

Signalling rate of T1

T1 sends 24 voice channels, each sampled at 8 kHz with 8 bits per sample, plus 1 framing bit per frame.

$$\begin{aligned} \text{Bits per frame} &= 24 \times 8 + 1 = 193\ \text{bits} \\ \text{Frames per second} &= f_s = 8000\ \text{frames/s} \\ R_b &= 193 \times 8000 = 1\,544\,000\ \text{b/s} = 1.544\ \text{Mb/s} \end{aligned}$$

Answer: T1 signalling rate = 1.544 Mb/s (frame of 193 bits every 125 µs).

T1 frame diagram

|<--------- one frame = 125 us = 193 bits --------->|
+---+--------+--------+--------+-------+--------+
| F |  Ch 1  |  Ch 2  |  Ch 3  |  ...  | Ch 24  |
+---+--------+--------+--------+-------+--------+
 1 bit  8 bits  8 bits  8 bits           8 bits
 F = framing bit (pattern spread over 12 frames)