1. Digital Multiplexing 1- Pulse Code Modulation 2- Plesiochronous Digital Hierarchy 3- Synchronous Digital Hierarchy

2. Pulse Code Modulation The first stage of multiplexing requires the conversion of a voice or modem signal into a digital pulse steam and is the same for PDH or SDH, this process is called the pulse code modulation. Pulse code modulation is simply a Analogue to digital conversion process.

3. Sampling One of the first step in the conversion of an analogue signal into a digital one, is the process of sampling. Sampling is the process of measuring amplitude values at equal intervals of time. Sampling rate for periodic sampling is the number of samples per unit time. Shannon’s Sampling Criterion.

4. PCM cont------- Within one 125 µs sampling period, samples of several telephone channels can be sequentially accommodated, This process is called time division multiplexing (TDM). In 24 – Channel PCM system, samples of 24 telephone channels are available for transmission in each sampling period. The samples signal contains all the information of the about the source signal, provided fs is greater than 2B. If this condition is not satisfied then it results in the loss of information about original source signal, called “ Aliasing distortion’

5. Quantization Quantization is a process by which an analogue sample is classified into one of a number of adjacent quantizing intervals. Quantized value: A sample whose amplitude falls anywhere within a particular interval is represented by a single value called the quantized value. Quantized value: A sample whose amplitude falls anywhere within a particular interval is represented by a single value called the quantized value. At the receiver the reconstructed sample is equal to the quantized sample. The reconstructed sample is almost always slightly different from the actual sample value, but the discrepancy is less as the chosen number of quantization values increases. Quantizing usually involves encoding as well. A quantization interval is limited by two decision values at the extremities of the quantizing interval.

7. Uniform Quantizing This is quantizing in which the quantizing intervals are of equal size. PAM signal In both the North American and European PCM systems, the codeword has eight bits. The first bit (the most significant bit) gives the polarity of the PAM signal, and the next 7 bits denote the magnitude. Transmission of code word means that 2^8 = 256 quatizing intervals are used.

8. Quantization Noise The difference between the input signal and quantized output signal is called the quantizing noise. Quantizing noise can be reduced by increasing the number of quantizing steps, but this would amount to increasing the number of bits in the code word designating the amplitude information. An increase in the number of bits per word can be accommodated only by reducing the the number of multiplexed channels. By using the binary code word, the number of amplitude levels that can be encoded with n bits in 2^n.

9. Cont------- The recovered analogue signal-to-quantization noise power ratio is found to be approximately 6n dB, where n the number of bits in the PCM word. Therefore using uniform quantization, the PCM system S/N in decibels varies linearly with the no. of bits in the word, and therefore with the bandwidth. In contrast, the frequency modulation (FM) system the S/N in decibels varies with the logarithm of bandwidth as show in table indicates the approximate S/N that can be achieved, depending on the number of bits in the code word.

10. Quantization Detail S.no No of bits/code Number of Quantizing s steps, 2^n S/N,dB 1712842 2825648 310102460 412409672

11. Cont----- A system transmitting speech signals must be able to accommodate signals of about 60 dB. To achieve this with uniform quantization, the number of bits per code word should be at least 10 (1024) quantization steps. To conserve bandwidth, 8 bit code words are used, but the quantizing steps are not equal and this non- uniform quantization improves the dynamic range.

12. Non uniform quantization With uniform quantization, the quantization distortion for signals with small amplitude is greater than that for signal with larger amplitudes. Also in telephony, the probability of the presence of smaller amplitudes is much greater than that of larger amplitudes. Low signal levels must therefore be amplified more than the stronger signal to achieve a reasonably constant S/N. This is done by passing the speech signal through a non linear amplifier so that its dynamic range is compressed at the transmitting end prior to being uniformly quantized.

13. Cont------- The reconstructed signal is expanded at the receiving end (hence the term companded) by passing the signal through a device having an inverse characteristic of the compressor. In PCM, this is effectively the same as making the quantization steps wider for higher – level signals and narrower for lower – level signals. By this process, the signal to quantization distortion ratio is nearly independent of the signal level. Because the ear’s response to sound is proportional to the logarithm of the sound amplitude, the compression curve use by all equipment manufacturers have an approximate logarithmic characteristic.

14. µ-Law In North America and Japan the µ- Law characteristics is used for companding. Y = sgn (x) [ln (1+µx)/ln (1+ µ) where where x = input amplitude x = input amplitude sgn (x) = the polarity of x sgn (x) = the polarity of x µ = amount of compression and is chosen to be 255 µ = amount of compression and is chosen to be 255

15. A-LAW Another compander characteristics use in Europe and many other parts of the country including Pakistan, the A-Law curve.According to ITU-T recommendation G.711, this is defined by equations: Y = (1+ ln Ax)/ (1+ln A) for 1/A <x<1 Y = Ax/1+lnA for 0<x<1/A Where “x” = normalized input level. Where “x” = normalized input level. Y = normalized quantized steps Y = normalized quantized steps ln = natural logarithm ln = natural logarithm A = amount of compression an is chosen to be 87.6. A = amount of compression an is chosen to be 87.6.

16. Cont-------- For µ = 255 and A= 87.6, the A-law curve is almost indistinguishable from the µ-Law. In practice the logarithmic curve of the A-law compander is approximately by a 13- linear – segment compander circuit. The compressed signal at the transmitting end, when combined with the expanded signal at the receiving end is therefore a good reconstruction of the transmitter signal, for a small amount of quantization noise.

17. The µ-law and A-law compander Xtics A-Law µ-Law 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

18. Cont------- Voice Compressor Sampler Quantizer and coder DecoderExpander Voice

19. a - compressor inIn out b- expanderC- result out Compressor + Expansion = Linear Result in out

20. ADAPTIVE DIFFERENTIAL PCM ITU –T (G,726) allows a reduction of the transmitted bit rate to 32 kb/s while preserving audio quality. For a given transmitted bit rate, the no. of voice channels transmitted can be doubled. The technique that was developed for reducing the sampling rate to 32 kb/s was called adaptive differential PCM (ADPCM).

21. ADPCM Principle When successive samples are quantized, because of the gradual nature of the variation of the source signal, a lot of redundant information is transmitted. For example when a sine wave signal is quantized, the successive sample quantization amplitudes near the peak of the sine wave vary only a small amount from one to the next. So instead of transmitting the long digital word for each sample, the small digital word indicating the difference between on sample amplitude to the next. This more efficient method of quantization is the essence of differential PCM, and lead to lower bit rate per channel than the original method

22. ADPCM CIRCUIT The inclusion of an adaptive predictor circuit for tracking the trend of the of the sampled signal and statistically predicting its future amplitude provides further transmission efficiency, resulting in an even lower bit rate per channel.

23. Cont-------- The companded (log PCM) is linearized and difference signal is formed by subtracting a previous estimate created from an earlier input. Every 125µs, the difference signal is 4- bit coded in the 16- level adaptive quantizer to produce the 32-kb/s output. The inverse adaptive quantizer forms part of the feedback loop, in which a quantized difference signal is added to the signal estimate as part of the adaptive prediction process. Fig show the ADPCM decoder, which simply performs the inverse process to revert the signal to a 64- Kb/s companded PCM output.

24. Cont------- The encoder contains the decoder circuit. ADPCM codec effectively introduces a doubling of the companding process, so that it can operate on the linear signal.

25. ADPCM SYSTEMS ITU-T G.728 describes the 16-kb/s speech encoder using a lower delay code excited linear predictor (LD-CELP) And ITU-T,G.729 describes an 8kbits/s speech encoder using an advanced code-excited linear predictor (ACELP). Various CELPs techniques used to code speech signals down to 4.8 kb/s, for example the IS-54 North American cellular system 7.95 kb/s speech coder uses vector –sum excited linear predictive coding (VSELP).Rapid quality deterioration is experienced below this rate.

26. Future of coding It is highly probable that bit rates less than 1 Kb/s will be used in future cellular system.