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# 1 PCM & Encoding

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A general overview of signal encoding
You will learn why to use digital encoding, how signal is transmitted and received and how analog signals are converted to digital
Some digital encoding methods

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### 1 PCM & Encoding

1. 1. Introduction A general overview of signal encoding You will learn why to use digital encoding, how signal is transmitted and received and how analog signals are converted to digital Some digital encoding methods
2. 2. OverviewConversion to digital signal from a analog is composed of 4 main stages Analog signal is filtered by LPF and then sampled w.r.t time ‘T’. LPF:  Low Pass Filter, a filter that eliminates the high frequencies of the input signal. The samples are distributed over infinite set of values are converted to final set if M values. Called quantization. Each of these M values are converted binary representation. PAM encoding composed of 3 stages.
3. 3. Why PCM method? A digital representation of an analog signal where the magnitude of the signal is sampled regularly at uniform intervals, then quantized to a series of symbols in a numeric (usually binary) code. Answer is the advantages over digitizing. Part of them is also available in analog systems , but cost is higher and performance is usually worse.
4. 4. PCM Error correction Retransmit the damaged data again (as in TCP) Encryption Encrypted easily advantage in business/military purpose Compression Compress data take less memory Storage Retrieval of data using cheaper peripherals devices Transmission Repeater for long distance to reduce noise and regeneration Line encoding PCM signal is not ready to be transmitted requires line encoding Some formal technique are used to represent data, and narrow B/W
5. 5. Analog => Digital Passing the Analog signal through a LPF and sampling it. Transferring the sampled signal through a quantizer. Converting the quantized value to a binary representation. Sampling and quantization of a signal (red) for 4-bit PCM
6. 6. LPF and Sampling Nyquest theorem, an Analog signal can be reconstructed from a sequence of samples if the sampling rate is, at least, twice as the highest frequency of the signal. The LPF must come before the sampling. Filtering the frequencies higher then the sampling rate, removing the phenomenon called Aliasing. Sampling rate help in calculating the time period of each sample Ts= 1/fs. Which defines the samples over an infinite set of values, which is a big problem when it comes to transmission. What to do then >>>???? We need to Quantize the data
7. 7. Quantization Confine the infinite set to finite set of values, defined by letter M which is an exponential function M = 2n It can be easily derived from the above table that this quantizer has 8 levels (M=8). The quantizer used here is a linear quantizer. Speech contain lower frequencies then higher therefore we use more quantization levels then higher X, the input voltage [Volt] Output voltage [Volt] X >= 6 7 6 > X >= 4 5 4 > X >= 2 3 2 > X >= 0 1 0 > X >= -2 -1 -2 > X >= -4 -3 -4 > X >= -6 -5 -6 > X -7
8. 8. sampling When you sample the wave with an analog-to-digital converter, you have control over two variables: The sampling rate - Controls how many samples are taken per second The sampling precision - Controls how many different gradations (quantization levels) are possible when taking the sample
9. 9. sampling A/D Conversion D/A Conversion Higher rate sampling
10. 10. Binary conversion Last stage of PCM is the conversion of the value of quantization to binary representation. We used M=8 => the number of bits needed for binary representation is n=3. We can use any desired representation, such as octal or hexadecimal.* The binary representation designating each quantization level should be also considered.
11. 11. Gray codes Gray code can be very useful here. In Gray code, every two neighboring words are different in only one bit. Thus a error caused due to additive noise will cause only a minor shift to neighboring frequencies Decreasing the impact of the error occurred significantly. Quantizer output voltage [Volt] PCM output [binary representation] 7 110 5 111 3 101 1 100 -1 000 -3 001 -5 011 -7 010
12. 12. Problems still exist with PCM Quantization noise  The difference between the original samples to their quantized values is called Quantization noise. This noise will appear at the reconstruction of the Analog signal. Bandwidth  Each sample is represented by n bits, therefore the required bandwidth is multiplied a factor of, at least, n ISI (Inter-symbol Interference)  Each binary representation of the samples, will be transformed at the end to some shape, usually a pulse, called a symbol. It is very likely that neighboring symbols will interfere each other, thus adding difficulties to the reconstruction of the analog signal.
13. 13. Encodings Digital data, digital signals How to represent bits (codes) Analog data, digital signals How to represent voltages (sampling)
14. 14. Digital/Digital Encoding Issue in comparing various techniques: Signal spectrum  High freq-big b/w, no dc – Better isolation Signal synchronization capability Signal error detecting capability Signal interference and noise immunity Cost and complexity
15. 15. More A – D modulation Pulse Amplitude Modulation (PAM) Delta Modulation (DM) Quantizing noise Slope-overload noise Differential Pulse code Modulation (DPAM)
16. 16. NRZ-L: Non Return to Zero Level Zero is represented as no voltage, and one by high voltage level. First, it has a DC component, meaning that its average voltage is not 0 but some positive constant. Second, it has the inability to carry synchronization information. Again, if we have a series of ones, we won’t be able to know how many we got.
17. 17. Polar NRZ-L: Polar Non Return to Zero Level Zero is represented as negative voltage level, and one by positive voltage level. This code is similar to the previous one. It handles the DC component issue, meaning the average voltage level is 0. It still has the synchronization problem.
18. 18. NRZ-I: Non Return to Zero Inverted Transition on one only. Like Polar NRZ no change in voltage in the case of zeroes sequence and no carry of synchronization information. This code doesn’t handle the DC component (average is not 0).
19. 19. Bipolar (Multilevel Binary encoding) No voltage on zero, the first one is a positive voltage, the second one is a negative voltage, and the voltage values of subsequent ones alternate. Here the problem of DC component (average not 0) was solved by introducing negative voltage level. The code is not sensitive for polarity but we can lose synchronization on a long sequence of zeroes.
20. 20. Manchester (Biphase encoding) Zero is represented as a transition from high to low voltage level in the middle of the bit, while one is represented by the transition from low to high. Good for timing as we have a transition every cycle, fully self synchronizing. Used on 10 Mb/s Ethernet
21. 21. Differential Manchester (Biphase) Always a transition in the middle of a bit, transition at the beginning only for zero. As in the regular Manchester code, fully self synchronizing Another advantage here, polarity is not significant. The drawback of this line code is the same as for the previous one, double bandwidth.
22. 22. Scrambling Techniques For long distance applications, the encoding schemes that are normally used are known as scrambling tech. Applied in case of bipolar AMI (Alternate mark inversion) Solve problem of long strings of ‘0’  B8ZS- bipolar 8 zero substitution HDB3- high density Bipolar 3 zeros
23. 23. 4B/5B Insert extra bits to break up runs 4 bit vales sent as 5 bit codeword Codeword have <2 leading 0 and <3 trailing 0; 16 of 32 used (other for ctrl) Transmittied using NRZI 80% efficiency Used by FDDI and 100 Mb/s ethernet
24. 24. Complete communication system A basic block diagram of a complete communication system for analog signals.
25. 25. Receiver Modulation taking the input bits (called Baseband) and, loading it on the transmission carrier (RF carrier). Detection mainly, receiving only a pre defined frequency range. Matched filter a filter that is match to the transmitted signal, thus enables the best possible reception. Decision for every digital value received we should decide what was the original value that was transmitted. D/A Digital to Analog signal convertor.