Why has the pulse code modulation sampling time been set at 125 microseconds?

Answer 1

It goes as follows:

As per the Nyquist-Shannon sampling theorem :

Suppose the highest frequency component, in hertz, for a given analog signal is fmax. According to the Nyquist Theorem, the sampling rate must be at least

2fmax, or twice the highest analog frequency component. The sampling in an analog-to-digital converter is actuated by a pulse generator (clock). If the

sampling rate is less than 2fmax, some of the highest frequency components in the analog input signal will not be correctly represented in the digitized

output. When such a digital signal is converted back to analog form by a digital-to-analog converter, false frequency components appear that were not in the

original analog signal. This undesirable condition is a form of distortion called aliasing.

Now The Max frequency in analog signal of Human speech is found in between 0 to 3.5 Khz, so round about they've they considered it as 4 Khz ,

Now to sample this analog Signal , as per the Nyquist criteria we've to use Double the Sampling Frequency so that'll come around 8 Khz...More precisely that

means 8000 samples per second ! Now apply simple Unitary method i.e

8000 samples in 1 Second

1 Sample in 1/8000 second & i.e 125 micro Seconds !

Hence between every 2 sample you'll find Time Gap of 125 micro seconds, For you being a Human , The 125 micro second can be very small duration , but for

Today's multiplexers (working at Clocking speed of Ghz !)...This can be Huge Waiting Period...& Being a Hard working Machine :-) they don't like to wait IDLE

Just for your another sample.....Rather in that Period they want to do some other work .....Now what other work they can do ?

Just transfer the voice sample of some other People !!!! :-)

Now for How many People they can work ? This depends upon the Individual capacity of each Mux (Multiplexer) !, If its a E1 line Mux then it can transfer

samples of 32 People in 125 micro second & then again come back for your Next coming Sample ! & in this way Non stop the Whole Process goes On & On !

This is Called TIME DIVISION MULTIPLEXING !...i.e The Mux has allocated a Fixed time for collecting your voice sample & machines are not like Human (Keep

their commitment for tine & don't create delay) they work strictly in Fixed time slots allocated for each person & do this Repeatedly without fail.

Similarly STM1 line Mux can serve 2016(63 E1s) People in the same 125 micro second, STM4 Line Mux can 8064, Wheras STM16 can 32256 !!! Thanks to High speed

CLK Generators & Optical Backbone Technology...Same line can be used by so many people at the the same time !

Now every Single sample in terms of data means 8 bits (Reason : we use 0-256 as a scale for measuring the length of Frequency sample, & to represent 256 (The

Max value) in binary (11111111) requires atleast 8 bits ). So 8 bits for 1 Sample & Total of 8000 Samples Per second Means it gives you a Speed of :

8000*8 = 64000 Bits per second = 64Kbps ! for 1 Time Slot. Pretty Clear Now ?

So for your understanding you can visualise the Data flowing on E1 as follows (I am explaining here for E1 , the same way you can correlate with High speed

Mux lines like STM):

As soon as E1 will come IN SERVICE ..... The 8 bit sequence of "ZEROs' & 'ONES' that denotes 1 of your Voice Sample will be Trasferred via Applying Voltage

on Line (To Represent 1) & No Voltage (To represent 0) . After this till the time you'll produce another Voice Sample The MUX is Free to do the Job of some

other Person (or Serve another Time slot) & after Serving as many People it can serve, it'll come back again for taking YOUR NEXT Voice Sample 8 Bits & this

goes On & On ....at a Very High Speed.

So at Physical Level on E1 Line you'll always see Voltage Applied or Voltage OFF wrt the Data bit pattern ...But their Timing & Perception at Higher

Level/Layer will Create the Entire Complex & Bigger Picture !

At Physical Level E1 line means 4 wires or 2 pair of wires, One Pair (TX & RX) for sending Voltage Signal from A to B & another Pair (TX & RX) for sending

Voltage Signals from B to A. During IDLE Period Frame Format is Generally all 1s i.e 11111111 or 01111110 (Flag Pattern).

Anybody who would've taste of working in Telecom Companies must be knowing about Loop, Loop simply means Shorting TX & RX of Each PAIR so that Whatever TX will sent , the same will be returned back to sender via RX .....CONFIRMING Continuity of Physical Path till the Point from where Loop has been Given. This is the way though which Transmission Engineer isolate the point of Fault...Whenever any Media Goes down.

OK so Now your question is What is this Flag 01111110 (Flag Pattern), Huh ?

Well Recall - Earlier I told you that in 125 micro second E1 MUX can work for 32 People, Actually I was Only Partially True by saying that ! ..In Reality it serves Not for 32 People but Only 30 People , Then where does 2 Times slots has been utilised ? Well 1 for "Synchronisation"

(use 0th Time slot) & another for "Signaling" (Normally we use 16th but its not mandatory , you may use any other too !).

To understand Signaling ...it is just a Control data for whatever Data/Payload we're sending on the line.

And coming back to Synchronisation....you might be thinking why at all its reqd, well Let's consider about the Time when Equipments (MUX Both Trans &

Recieve) were Powered Down, You've gone to the Data Center & Turned them ON , Let's say First you've turned on TX Mux ....Now what will happen ? Its Simple

...the Mux will start sending 8 Bit Signals on towards the other side MUX on the E1 Line (It can be all 1s , 11111111 If No data or it can be according to

Sampled Data pattern in case Data is Present),

& Then you've started Recieving side MUX:

After that the Recieving side MUX who was sleeping with "Sweet Dreams" has all of sudden started getting lot of ZERO's & ONE's !!! Literally Fired from the

other side..........Now Here the Big Million Dollar Question Comes....That how it will understand from where to Start Counting bits (So that it can have an

idea that these 1st bits are from One particular Customer/Subscriber & don't do the mixing of bits of 2 different subscribers & messing everything into a

Jargon !!!), How it can come to know which is the First Time Slot & which is the Last ?

Well Here Flag Byte (01111110) or Synchronisation Time Slot comes to Rescue !, The Moment reciever will get First Flag Byte (01111110), it will treat it as

0th Time Slot & after that It'll consider 1st to 31st Time slot as Payload/Subcriber's Data (Obviously Among these 1st to 31st Time slot in One or Two Time

Slot your Signaling will also be Present!) & again when it recives another Flag Byte (01111110) then it'll get an idea that Another Cycle is Just Begining !

& In this way I've to keep Reading & Reading ....till the Time I am Alive ! (Powered UP) :-)

Now again there may be Good Question coming from your side :

What if any Data sample in a Subscriber's Payload can Match Flag Byte Pattern (01111110), Well, Yes ..certainly it can be Possible as Data Sample can have

any Value Possible value between 0 to 256, So Definitely the Flag Byte (01111110 in Binary) value 126 (in Decimals) comes in between this range...So its very

much possible Situation. To Fix this issue : There's a Soln from Standards Forming Body as follows:

"Since the flag sequence could appear in user data, such sequences must be modified during transmission to keep the receiver from detecting a false frame

delimiter. The receiver must also detect when this has occurred so that the original data stream can be restored before it is passed to higher layer

protocols. This can be done using bit stuffing, in which a "0" is added after the occurrence of every "11111" in the data. The receiver, when detects these

"11111" in the data, removes a "0" added by the transmitter." (This may be Bit hard for you to Understand, Realize, Visualise but think Hard with Calm for

sometime & you'll Understand this as i did !).