Figure 5 – Stages at the forming of a group signal
Н. Н. Моисеев. Универсум. Информация. Общество. — М.: «Устойчивый мир», 2001. — 199 с.
Н. Н. Моисеев. Математика ставит эксперимент. — М.: «Наука», 1979. — 223 с.
T ch – channel time slot (channel interval),
T clk – clock interval,
m – quantity of bits of PCM code.
Continuous signal is converted to a sequence of samples (individual PAM signal) (Fig 5 a).
Further individual PAM signals of all sources combined into a group PAM signal (Fig 5 b).
After that, the group PAM signal is coded by the PCM coder (Fig 5 c).
Now give a definition of the main parameters of the transmission cycle (frame).
PAM signal transmission frame on duration is equal to the discrete sampling period. It consists of:
- Pulses of channels 1, 2,…N;
- Service pulses.
On a following time interval an arrangement of pulses is similarly 1, 2,…N and service pulses. This periodically repeating information structure consisting of information and service pulses is called as a transmission frame (cycle). Sometimes the transmission cycle is called as a time spectrum.
As channel time slot (channel interval) is called the time interval between samples of the adjacent channels. An equation for calculation is:
T ch= T frame/ N ch
Clock interval is time of transmission of one (binary) digit. A calculation formula is:
T clk= T ch/ m = T frame/(m * N ch)
Clock frequency f clkin DTS is called the quantity of clock intervals per a time unit (1 second). For the ADE at fulfillment of conditions T frame= T s and f frame= f s we obtain the formula for a clock frequency (clock rate):
f clk= f s* m * N ch
where f s is a sampling frequency (f s=8 kHz);
N ch – quantity of channel intervals (N ch= N vbc for the approximate calculation or N ch= N vbc+ N serv for accurate calculation).
Transmission bit rate B is called the quantity of the binary symbols which are transmitted during unit time interval (1 second).
The DTS frequency band Δ f PCM is called a frequency band which contains a basic power part (>90%) of binary signal.
The next equality is carried out for DTS:
f clk= B = Δ f PCM=
Hz bit/s Hz
kHz kbit/s kHz
MHz Mbit/s MHz
Consider the principle of formation of the DTS frame for the example PCM-30
PCM-30 line signal (primary digital bit stream (PDB or PDS or E1)) is organized into the multiframes (MF) and every multiframe consists of 16 frames (F). Each PCM-30 frame consists of 32 channel time slots (TS) with numbers 0, 1,…31. Each channel time slot consists of eight bits.
Figure 6 – Frame of PCM-30
30 TS are informational and serve for transmission of sampled signal by means of PCM code combinations. Two others (TS-0 and TS-16) serve for transmission of service information.
Every even frame contains the frame alignment signal (FAS) in the TS-0 (0011011). In odd frames transmitted the alarm FAS.
First bit in TS-0 of all frames transmits the signal of discrete information (DI).
All others TS (with the exception of TS-16) transmits PCM code combinations (or organized into the data channels E0 with bitrate 64 kbps in each).
TS-16 contains the signaling bits (with Command and Interaction Signals, CIS) for two voice channels. For CIS transmission of all 30 information (voice) channels are necessary 30/2=15 frames, and so frames are organized into the multiframes from 16 frames each.
Multiframes alignment signal (MFAS) is transmitted (0000 codeword) in frame-0.
Frames 1…15 contain the CIS of 30 voice channels.
Figure 7 – Structure of PCM-30 TS-16
Let's calculate the PCM-30 frame basic characteristics.
As it is said earlier the frame frequency is determined by the sampling frequency and frame period is determined by the sampling period:
T frame= T s=125μs,
f frame= f s=8 kHz.
Based on of these values are determined every other frame parameters.
Multiframe duration is:
T MF= T frame* N frame=125*10-6*16=2 ms.
Multiframe frequency is:
f MF= f frame /N frame=8*103/16=0.5 kHz.
Channel time slot duration is:
T TS= T frame/ N ch=125*10-6/32=3.9 μs.
Channel frequency is:
f TS= f frame *N ch=8*103*32=256 kHz.
Clock interval duration is:
T clk= T frame/(N ch*m)=125*10-6/(32*8)=488 ns.
Clock frequency is:
f clk= f frame *N ch*m=8*103*32*8=2048 kHz.
Transmission bit rate and frequency band of the group signal is equal clock frequency:
B =2048 kbps and Δ f PCM=2048 kHz.
FAS frequency is:
F FAS= f frame /2 =8*103/2=4 kHz.
Transmission bit rate through the channel DI:
BDI = f frame*mDI=8*103*1=8 kbps.
Maximum rate of the one CIS channel:
B1CIS = f frame*m1CIS=8*103*4=32 kbps.