0 1 2 3 t x(t) pulse code modulation (pcm) consider the analog signal x(t)

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x(t)

Pulse Code Modulation (PCM)

Consider the analog Signal x(t).

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x[n]


The signal is first sampled

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Sample n


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And Hold n


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Assign Closest Level

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Each quantization level corresponds to a unique combination of bits. The analog signal is transmitted/ stored as a stream of bits and reconstructed when required.

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Each quantization level corresponds to a unique combination of bits. The analog signal is transmitted/ stored as a stream of bits and reconstructed when required.

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x(t) Original Signal


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x~(t)Quantized Signal

It is quite apparent that the quantized signal is not exactly the same as the original analog signal. There is a fair degree of quantization error here. However; as the number of quantization levels is increased the quantization error is reduced and the quantized signal gets closer and closer to the original signal


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x~(t)Quantized Signal

It is quite apparent that the quantized signal is not exactly the same as the original analog signal. There is a fair degree of quantization error here. However; as the number of quantization levels is increased the quantization error is reduced and the quantized signal gets closer and closer to the original signal


PCM System Block Diagram

Sample & Hold Comparator

Ramp Generator

Binary Counter

Parallel to Serial Converter

All pulses have same height and width.

f(t)

PCM of Speech Signals (very-important)

• Most of the significant spectral components of speech signals are contained in the range 300-3400 Hz

• Nyquist Rate = 2x3400 = 6.8 kHz

• Practical Sampling Rate fs= 8 kHz (WHY..???)

• Number of quantization levels = 256 Number of Bits/Sample n = 8 (log2256 )

Data Rate = nfs = 8x8000 = 64 kbps

PCM of Speech Signals (very-important)

• Bandwidth Requirement

Communication theory tells us that we can transmit errorfree at most two pieces of information per second per hertz bandwidth (lathi pg. 260)

Therefore the minimum required bandwidth for transmission of a PCM speech signal BWmin = 64/2 = 32 kHz

Recall that for analog techniques such as AM, FM etc the bandwidth of the order of 4 kHz, 8 kHz etc.

We may require more bandwidth but the signal is now digital and we now have the ability to manipulate, store, regenerate the data. (see advantages of Digital Communication pg 263 of lathi)

PCM Based TDM Systems• PCM is widely used in transmission of speech signals in fixed line telephone

system.

• In this lecture we shall briefly explore an example PCM, the T1 carrier system which was developed at Bell labs in the US. And is still in use today in the US and Japan.

• A similar scheme called the E1 is used in Europe and Pakistan.

• These schemes are used to multiplex the speech from multiple subscribers and transmit them to their destinations over a common “Time Shared” channel. Hence the name time division multiplexing (TDM).

PCM Based TDM Systems• The sampling rate used for voice = 8000 samples/sec

Therefore, Sampling Interval = 1/8000 = 125µs

– This means that the time between two consecutive samples (from the same source) is 125µs. TDM systems exploit this fact and utilize this interval to sample signals from other subscribers. In T1 systems the signals from 24 subscribers is sampled in 125µs.

– The samples are quantized and then converted into a bitstream for transmission over the channel.

PCM Based TDM Systems

125µs


Sample 1

Channel 1


Sample 1 1

Channel 1 2


Sample 1 1 1

Channel 1 2 3


Sample 1 1 1 1

Channel 1 2 3 4


Sample 1 1 1 1 --- --- --- --- --- --- --- --- 1

Channel 1 2 3 4 --- --- --- --- --- --- --- --- 24

Time for sample 2


125µs

Sample 1 1 1 1 --- --- --- --- --- --- --- --- 1 2

Channel 1 2 3 4 --- --- --- --- --- --- --- --- 24 1

Time for sample 2


125µs

Sample 1 1 1 1 --- --- --- --- --- --- --- --- 1 2

Channel 1 2 3 4 --- --- --- --- --- --- --- --- 24 1

1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1

Every sample is represented by one of the 256 quantization levels that is closest to it. This corresponds to 8 bits (log2256) bits to transmit one sample.

PCM Based TDM Systems• As mentioned previously, sampling rate used for voice = 8000 samples/sec• Every sample is represented by 8 bits• Therefore,

Data rate of 1 voice channel = 8x8000 = 64kbps

• In the T1 system 24 voice channels are multiplexed in timetherefore,

Data rate of a T1 stream should be = 24x64kbps = 1.536 Mbps

However, the actual data rate = 1.544Mbps The extra 8000 bps (1.544-1.536=.008Mbps) result from the overhead bits

which are inserted alongside the data (details ahead).


• The T1 carrier system multiplexes binary codewords corresponding to samples of each of the 24 channels in a sequence. A segment containing one codeword (corresponding to one sample) from each of the 24 channels is called a FRAME.

• Each frame has 24x8 = 192 data bits and takes 125µs.

• At the receiver it is also necessary to know where a frame starts in order to separate information bits correctly. For this purpose, a Framing bit is added at the beginning of each frame.

Therefore, Total number of bits/ frame = 193

PCM Based TDM SystemsT1 Frame Format

• Along with voice data, frames should also contain: Framing bits and Signaling bits.

• Framing Bits: Indicate start of frames.

• Signaling Bits: Contain control information such as Routing Information, On-Hook/ off-Hook signals, Alarm signals etc.

• Lets see how the T1 frame caters for these needs. We’ll have a look at the frame structure of older T1 schemes first.


Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2Channel-1

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-1 Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)

1 Framing Bit at start of each frame


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)

7 bits to represent each sample. Note this is the old T1 scheme and is now obsolete.


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)

1 bit in each channel reserved for signalling. This means a total of 24 bits/ frame for signalling.


• T1 newer version:

24 signalling bits/ frame is just too much and that many bits are not required for voice data signalling.

This why a modification was introduced.

The newer version uses 8 bits to represent every sample. However, the total number of bits in each frame remains the same i.e, 193 bits/frame.

• Does this mean that the signalling bits are eliminated..????

• If so then how is the signalling information conveyed..????


• T1 newer version:

Actually the signalling bits are not eliminated altogether. Instead the number of signalling bits in a ‘collection of frames’ is reduced.

In the newer version, signalling bits are included in every 6th frame.

This is done by replacing the Least Significant Bit (LSB) of every sample by a signalling bit. Therefore, some amount of information in every 6th sample is sacrificed for signalling. However, since only the LSB is removed there is no noticeable loss in voice quality.


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8F .... 1 2 3 4 5 6 7 8

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)

The LSB of all the samples in frames 1, 7, 13, etc is replaced by signalling bits.


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

Frame-1(125µs)

Frame-2(125µs)

Frame-3(125µs)

Frame-4(125µs)

Frame-5(125µs)

Frame-6(125µs)

Frame-7(125µs)

Frame-8(125µs)

Frame-9(125µs)

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 SF .... 1 2 3 4 5 6 7 S


1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 S 1 2 3 4 5 6 7 S

Channel-24Channel-2

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Channel-24

All other frames use 8 bits/sample. This technique in which signalling information is sent in every 6th frame is called Robbed-Bit- Signalling.

Frames 1, 7, 13......

All Frames except 1, 7, 13......


• Frame Synchronization in T1:

– It was mentioned in the previous slides that 1 Framing bit indicates the start of each frame. How is this framing bit different from any of the other bits that arrive before or after it..?????

– One framing bit alone doesn't signify much. However, a collection of framing bits can be used to check the beginning of a collection of frames.

– The receiver accumulates the framing bits of a collection of 12 frames and checks whether these 12 framing bits are the same as a pre-decided pattern (100011011100).

– If the framing bits are exactly the same as this pattern then the transmitter and receiver are in frame Synchronization and the samples can be easily extracted from the frames.

– What happens when the framing bits do not match the pre-decided pattern….???


• Loss of Frame Synchronization in T1:

– When frame synchronization is lost in T1, the receiver immediately send an LFA alarm, indicating loss of frame synchronization, to the transmitter.

– Without disconnecting the calls the transmitter redirects the data and sends it via an alternate route, and also tries to regain frame synchronization with the receiving party by send some fixed pattern.

– Since it takes 12 frames to realize that frame synchronization is lost, it means that at-least 12 voice samples from all the effected 24 channels will be lost. However, this is not noticed by the subscribers because this is still a very small time frame

12 x 125µs = 1.5ms of conversation is lost.

0 1 2 3 t x(t) pulse code modulation (pcm) consider the analog signal x(t)

Documents

original analog signal

analog signal xt

number of quantization

pcm speech signal bwmin

transmission of speech

ftpcm of speech signals

kbpspcm of speech signals

analog techniques