Time Division Multiplexing

1. Time Division Multiplexing Time Division Multiplexingallows multiple devices to communicate over the same circuit by assigning time slots for each device on the line.

5. TDM HIERARCHY T1 CARRIER SYSTEM Accommodate 24 voice channels each frame 24 words -125µs – 1sync bit each word - 8-bits sampling rate – 8 KHz duration of each bit= 0.647 µs transmission rate1.544 Mbps S1 1.544 Mb/s S2 T1 1 First level multiplexer T2 1 S24 Second level multiplexer 2 6.312 Mb/s 44.736 Mb/s 3 2 Third level multiplexer T3 4 1 274.176 Mb/s 7 T4 Fourth level multiplexer T2 system – combination of 4 T1 system T3 system – combination of 7 T2 system T4 system – combination of 6 T3 system 2 6

6. Bandwidth-Noise Tradeoff • Continuous wave modulation like FM and analog pulse modulation like PPM have Figure of merit propotional to square of transmission bandwidth. • Digital pulse modulation like PCM provides better tradeoff than square law. • In PCM , sampling does discrete time representation of message signal and quantization does discrete amplitude representation of message signal . • By representing message signal as coded binary pulses PCM provides better trade off between bandwidth and noise.

9. Quantization

11. In non uniform quantization the step size increase as the separation from origin increase. Weak passage voice signals which occur frequently are favored than rarely occuring voice signals with high amplitude .

13. Non uniform quantization is equivalent to applying compressed base band signal to uniform quantizer

15. DERIVATION-SNR OF UNIFORM QUANTIZER

16. DERIVATION-SNR OF UNIFORM QUANTIZER

17. DERIVATION-SNR OF UNIFORM QUANTIZER

18. DERIVATION-SNR OF UNIFORM QUANTIZER

21. Quantization

22. Quantization

24. Regenerative repeaters are present at sufficiently close spacing along the transmission route to control the effect of distortion and noise

26. Error Threshold

27. VIRTUES, LIMITATIONS & MODIFICATIONS OF PCM

28. Differential Pulse Code Modulation(DPCM) transmitter m[n] – unquantized input sample m^[n] – predicted value e[n] – prediction error (or) difference between unquantized input sample and prediction of it q[n] – quantization error mq[n] – prediction filter output

29. Differential Pulse Code Modulation(DPCM) transmitter

30. Differential Pulse Code Modulation (DPCM) • Differential Pulse Code Modulation (DPCM) is a procedure of converting an analog into a digital signal in which an analog signal is sampled and then the difference between the actual sample value and its predicted value (predicted value is based on previous sample or samples) is quantized and then encoded forming a digital value. • DPCM code words represent differences between samples unlike PCM where code words represented a sample value. EKT343-Principles of Communication Engineering

31. Differential Pulse Code Modulation (DPCM) • It often happens that in the analogical signals, which are coded in PCM (voices, images, etc), that many next samples show the same quantization level; as a consequence there is the transmission of many equal PCM codes and this is redundant for the reception signal reconstruction. • The DPCM coding exploits this redundancy between adjacent samples. • DPCM requires fewer bits than the standard PCM. EKT343-Principles of Communication Engineering

32. Differential Pulse Code Modulation (DPCM) Can save bandwidth by not sending all samples. * Send true samples occasionally. * In between, send only change from previous value. * Change values can be sent using a fewer number of bits than true samples.Examples (CCITT standards) * 32 k bits / s (4-bit quantization and 8 k samples /s) for 3.2kHz * 64 k bits / s (4-bit quantization and 16 k samples /s) for 7 kHz

33. How it works – the background • We know the signal up to a certain time • Use prediction to estimate future values • Signal sampled at fs= 1/Ts; sampled sequence – {m[n]}, where samples are Ts seconds apart • Input signal to the quantizer – difference between the unquantized input signal m(t) and its prediction: prediction of the input sample Digital Communication Systems 2012 R.Sokullu

34. Predicted value – achieved by linear prediction filter whose input is the quantized version of the input sample m[n]. • The difference e[n] is the prediction error (what we expect and what actually happens) • By encoding the quantizer output we actually create a variation of PCM called differential PCM (DPCM). Digital Communication Systems 2012 R.Sokullu

35. Receiver side • decoder – constructs the quantized error signal • quantized version of the input is recovered by using the same prediction filter as at the tx • if there is no channel noise – encoded input to the decoder is identical to the transmitter output • then the receiver output will be equal to mq[n] (differs from m[n] by q[n] caused by quantizing the prediction error e[n]) Digital Communication Systems 2012 R.Sokullu

36. Differential Pulse Code Modulation(DPCM) Receiver

39. PROCESSING GAIN

40. PROCESSING GAIN

42. Delta Modulation

43. Delta Modulation (DM) • A single-bit PCM code to achieve digital transmission of analog. Use only 1 bit either logic ‘1’ or ‘0’. • Logic ‘0’ is transmitted if current sample is smaller than the previous sample • Logic ‘1’ is transmitted if current sample is larger than the previous sample EKT343-Principles of Communication Engineering

44. Cont’d… EKT343-Principles of Communication Engineering

46. DELTA MODULATION SYSTEM

47. Cont’d... • Analog input is approximated by a staircase function • Move up or down one level () at each sample interval (by one quantization level at each sampling time)  output of DM is a single bit. • Binary behavior • Function moves up or down at each sample interval • In DM the quantization levels are represented by two symbols: 0 for - and 1 for +. In fact the coding process is performed on eq. • The main advantage of DM is its simplicity. EKT343-Principles of Communication Engineering

48. Delta Modulation - Example EKT343-Principles of Communication Engineering