This Lecture. BUS Computer Facilities Network Management. Communications Model. Encoding Techniques

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1 This Lecture US35 - omputer Facilities Network Management igital data, igital signals: NRL, iphase, Multilevel binary. Modulation rate, Scrambling. igital data, nalog signals Encoding techniques. SK, FSK, PSK, QM. Faculty of Information Technology Monash University nalog data, igital signals Pulse ode Modulation. elta Modulation. nalog data, nalog signals /ngle Modulation. Faculty of Information Technology 2 Faculty of Information Technology ommunications Model Encoding Techniques Recall the previous communications model... x(t) ata created by source Signal generated by the transmitter Source Trans mitter Trans mission System Receiver estination g(t) digital or analog Encoder x(t) digital ecoder g(t) t Input information m Input data g(t) Transmitted signal s(t) Received signal r(t) Four possible combinations of data and signal type:. igital data, digital signal. 2. igital data, analog signal. 3. nalog data, digital signal. 4. nalog data, analog signal. Output data g (t) Output information m 3 Faculty of Information Technology m(t) digital or analog f c (t) carrier Modulator (a) Encoding onto a digital signal s(t) analog emodulator (b) Modulation onto an analog signal 4 Faculty of Information Technology m(t) S(f) f c f

2 . igital ata, igital Signal Terms igital signal: iscrete, discontinuous voltage pulses. Each pulse is a signal element. inary data encoded into signal elements - we require an encoding scheme. The simplest method of digital encoding uses one voltage level to represent and another level to represent. igital/digital Encoding 5 Faculty of Information Technology Unipolar - ll signal elements have the same sign. Polar - One logic state represented by positive voltage the other by negative voltage. ata rate - Rate of data transmission in bits per second (R). E.g. bps. uration or length of a bit - Time taken for the transmitter to emit each bit (/R). From example, / =. secs. amplitude. sec sec Modulation/aud rate - Rate at which the signal level changes. Measured in baud = signal elements per second. Mark and Space - inary and inary respectively. 6 Faculty of Information Technology time Interpreting igital Signals at the Receiver omparison of Encoding Schemes Need to know: Timing of each bit - must know the start and end times of each bit (synchronisation). Signal levels - determine high () or low (). Factors affecting successful interpreting of signals: ata rate - increase produces higher bit error rate (ER). Signal to noise ratio - increase provides lower bit error rate. andwidth - increase allows higher data rate. Encoding scheme may improve the performance of signal interpretation. Transmitted ata Transmitted Signal +V V Time ttenuation, Noise, etc. Received Signal Sampling Signal Received ata 7 Faculty of Information Technology an compare different digital encoding techniques in terms of... Signal Spectrum: Lack of high frequencies reduces required bandwidth. Lack of component allows coupling via transformer, providing isolation (reduces interference). oncentrate power in the middle of the bandwidth (avoid poor band edges). locking: Need to synchronise the transmitter and receiver. ould provide an external clock - expensive. Sync mechanism based on signal. 8 Faculty of Information Technology

3 omparison of Encoding Schemes igital Signal Encoding Formats Error detection: an be built in to signal encoding. Signal interference and noise immunity: Some codes are better than others in the presence of noise. ost and complexity: Higher signal rate (and thus data rate) lead to higher costs. Some codes require signal rate greater than data rate. Nonreturn to Zero-Level (NRZ-L). Nonreturn to Zero Inverted (NRZI). Manchester. ifferential Manchester. ipolar-mi. Pseudoternary. 8ZS. H3. NRZ L NRZI ipolar MI (most recent preceding bit has negative voltage) Pseudoternary (most recent preceding bit has negative voltage) Manchester 9 Faculty of Information Technology ifferential Manchester Faculty of Information Technology igital Signal Encoding Formats Nonreturn to Zero-Level (NRZ-L) Simple: two different voltages for and bits. igital ata igital Signal Voltage constant during bit interval: No transition, i.e. no return to zero voltage. Unipolar Polar ipolar e.g. bsence of voltage for zero, constant positive voltage for one. NRZ L NRZ RZ iphase NRZ I Manchester ifferential Manchester MI 8ZS H3 More often, negative voltage for one value and positive for the other (i.e. polar). This is later one is known as NRZ-Level (NRZ-L). NRZ L Faculty of Information Technology 2 Faculty of Information Technology

4 Nonreturn to Zero Inverted NRZ Pros and ons onstant voltage pulse for the duration of a bit. ata encoded as presence or absence of signal transition at the beginning of a bit time. Transition (low to high or high to low) denotes a binary. No transition denotes binary. This is an example of differential encoding: ata represented by changes rather than levels. More reliable detection of transition rather than level. NRZI Pros: Easy to engineer. Make good use of bandwidth: most of the energy is between and half the bit rate ons: component. Lack of synchronisation capability. Used for magnetic recording due to simplicity and low frequency. Not often used for signal transmission applications. 3 Faculty of Information Technology 4 Faculty of Information Technology Synchronisation Problem iphase - Manchester onsider a bit per second NRZ-L digital signal. The transmitters bit duration is / =. sec or msec. In this example, the receivers clock is sightly faster than the transmitters clock (9.5 msec sample time). ms re sync 5 zeros transmitted re sync Transition in the middle of each bit period. Transition serves as clock and data. Low to high represents one. High to low represents zero. Used by IEEE baseband coax and twisted-pair SM/ bus LNs. Zero is One is 9.5ms 6 zeros received Manchester 5 Faculty of Information Technology 6 Faculty of Information Technology

5 iphase - ifferential Manchester iphase Pros and ons Mid-bit transition is used for clocking only. Transition at the start of a bit period represents zero. No transition at the start of a bit period represents one. Note: this is a differential encoding scheme. Used by IEEE STP token ring LN. ifferential Manchester on: t least one transition per bit time and possibly two. Maximum modulation rate is twice NRZ. Requires more bandwidth. Pros: Synchronisation on mid bit transition (self clocking). No component. Error detection: bsence of expected transition. Noise would have to invert both before and after expected transition. 7 Faculty of Information Technology 8 Faculty of Information Technology Modulation/aud Rate Multilevel inary - ipolar aud rate, also known as signalling rate or modulation rate: Signal elements per second (baud). The rate at which signal elements are transmitted. it rate = baud rate L, where L is the number of bits per signal element. For two-level signalling (binary), bit rate is equal to the baud rate. Example: a stream of binary ones at Mbps. NRZI is Maud. Manchester has.5 bits/signal element: aud rate = it rate/l = Mbps/.5 = 2 Maud 5 bits = 5 µsec bit = signal element = µsec bit = signal element = µsec.5 µsec 9 Faculty of Information Technology NRZI Manchester Use more than two signal levels. ipolar-mi (alternate mark inversion): Zero represented by no line signal. One represented by alternating positive and negative pulses. No loss of sync if a long string of ones (zeros still a problem). No net component due to alternating pulses. Lower bandwidth than NRZ. Simple error detection. ipolar MI (most recent preceding bit has negative voltage) 2 Faculty of Information Technology

6 Pseudoternary Tradeoff for Multilevel inary n exchange of mark for space in MI: One represented by absence of line signal. Zero represented by alternating positive and negative. No advantage or disadvantage over bipolar-mi. Pseudoternary (most recent preceding bit has negative voltage) Some degree of synchronisation provided by multilevel binary signals. Still problems with a long string of s (MI) or s (pseudoternary). Insert additional bits to force transitions (ISN). Use data scrambling techniques. 2 Faculty of Information Technology With suitable modification can overcome problems with NRZ codes. However, not as efficient as NRZ: In a 3 level system we could represent log 2 3 =.58 bits. However, each signal element only represents one bit. Receiver must distinguish between three levels (+, -, ) instead of two. Requires approx. 3d more signal power for same probability of bit error. Or, for a given SNR, the bit error rate is significantly higher than NRZ. 22 Faculty of Information Technology Scrambling Scrambling Techniques iphase techniques require high signalling rate: improve multilevel binary techniques. Use scrambling to replace sequences that would produce constant voltage. Filling sequence: Must produce enough transitions to sync. Must be recognised by receiver and replace with original data. Same length as original: no data rate increase. esign goals: No component. No long sequences of zero level line signal. No reduction in data rate. Error detection capability. 23 Faculty of Information Technology Two techniques commonly used in long-distance transmission. ased on bipolar-mi. 8ZS: ipolar with 8 Zeros Substitution. If octet of all zeros and last voltage pulse preceding was positive encode as +--+ If octet of all zeros and last voltage pulse preceding was negative encode as -++- auses two violations of MI code. Unlikely to occur as a result of noise. Receiver detects and interprets as an octet of all zeros. H3: High ensity ipolar 3 zeros. String of four zeros replaced with one or two pulses. In each case the fourth zero is replaced with a code violation. 24 Faculty of Information Technology

7 8ZS and H3 Spectral ensity of Various Signal Encoding Schemes Polarity of previous bit.4 ipolar MI 8ZS H3 (odd number of s since last substitution) V V V V V Violation Violation If the number of s since the last substitution is odd Mean square voltage per unit bandwidth NRZ l, NRZI 8ZS, H3 MI, pseudoternary MI = alternate mark inversion 8ZS = bipolar with 8 zeros substitution H3 = high density bipolar 3 zeros NRZ L = nonreturn to zero level NRZI = nonreturn to zero inverted f = frequency R = data rate Manchester differential Manchester = Valid bipolar signal V = ipolar violation If the number of s since the last substitution is even Faculty of Information Technology Normalized frequency (f/r) 26 Faculty of Information Technology 2. igital ata, nalog Signal Signals Under Limited hannel andwidth Modulation: The process of combining an input signal and a carrier frequency to produce a signal, whose bandwidth is (usually) centred on that carrier frequency. Public telephone system Voice frequency range (3Hz to 34Hz). Not suitable for digital signal. Use modem (modulator-demodulator). Why modulate analog signals? Higher frequency can give more efficient transmission. Permits frequency division multiplexing. Unguided Transmission needs high frequencies for practical antenna size. E.g. microwave. 27 Faculty of Information Technology Transmitted Signal f 3 f 5 f 7 f 9 f f low Frequency f c f low f high 28 Faculty of Information Technology f high hannel andwidth Frequency The transmitted signal s spectrum will not fit inside the channel s bandwidth: move the spectrum using modulation on a carrier f c. Transmitted Signal hannel andwidth

8 Modulation Shift Keying Perform operations on one or more of the carrier signals characteristics: shift keying (SK). Frequency shift keying (FSK). Phase shift keying (PSK). (a) SK (b) FSK Values represented by different amplitudes of the carrier. Usually, one amplitude is zero. i.e. presence and absence of carrier is used. Susceptible to sudden gain changes. Inefficient. Up to 2 bps full duplex on voice grade lines. cos(2π f c t) bin s(t) = bin igital ata nalog Signal Used over optical fibre. SK FSK PSK (c) PSK QM (a) SK 29 Faculty of Information Technology 3 Faculty of Information Technology Frequency Shift Keying Phase Shift Keying Most common form is binary FSK (FSK). Two binary values represented by different frequencies, f and f 2 which are typically offset from the carrier frequency, f c, by equal but opposite amounts. Less susceptible to error than SK. Up to 2bps on voice grade lines. High frequency radio. Even higher frequency on LNs using coaxial cable. Multiple FSK (MFSK): use more than two frequencies. cos(2π f t) bin s(t) = cos(2π f 2 t) bin Phase of carrier signal is shifted to represent data. ifferential PSK (PSK): Phase shifted relative to previous transmission rather than some reference signal. The bandwidth of PSK is the same as SK. (c) PSK cos(2π f c t + π) bin s(t) = cos(2π f c t) bin it Phase (Shift) 8 its (b) FSK 3 Faculty of Information Technology (d) PSK onstellation diagram 32 Faculty of Information Technology

9 Quadrature PSK Quadrature Modulation (QM) More efficient use by each signal element representing more than one bit: e.g. shifts of π/2 (9 ). Each signal element (phase shift) represents two bits. 2 bits 2 bits ibit Phase Shift ibit (2 bits) 33 Faculty of Information Technology 2 bits onstellation diagram 2 bits Time Modify more than one parameter of the carrier: QM changes both amplitude and phase. For example, add two amplitudes to QPSK to represent 3 bits. If the following diagram represents second, then the modulation rate would be 8 baud, and the bit rate would be 24 bps. 3 bits baud 3 bits 3 bits 3 bits 3 bits 3 bits 3 bits 3 bits onstellation diagram 34 Faculty of Information Technology Time Quadrature Modulation (QM) Performance of igital to nalog Modulation Schemes Example: 96bps modem uses 2 angles, four of which have two amplitudes. 4 bits per signal element: modulation rate is (bit rate)/4: Therefore 96 bps at 24 baud. Phase-reference signal (previous 4 bits) = R b = R log 2 L = modulation rate, R = bit rate, L = signal elements, b = bit/element. 35 Faculty of Information Technology andwidth: SK and PSK bandwidth directly related to bit rate. FSK bandwidth related to data rate for lower frequencies, but to offset of modulated frequency from carrier at high frequencies. (See Stallings or Halsall for math). In the presence of noise, bit error rate of PSK and QPSK are about 3d superior to SK and FSK. 36 Faculty of Information Technology

10 3. nalog ata, igital Signal (nalog-to-igital onversion) igitisation: onversion of analog data into digital data. igital data can then be transmitted using NRZ-L digital signal. igital data can then be transmitted using code other than NRZ-L. igital data can then be converted to analog signal. nalog to digital conversion done using a codec (coder-decoder). Pulse code modulation. elta modulation. igitizer Modulator Time PM inary Encoding Time Sampling interval = /2fm fm = highest freq (Hz) Quantisation Time nalog data (voice) igital data nalog signal (SK) 37 Faculty of Information Technology Pulse ode Modulation (PM) 38 Faculty of Information Technology 86 - Pulse Modulation (PM) Nyquist s Sampling Theory Original Signal If a signal is sampled at regular intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal. For example, consider the following signals of one second duration: Sampling Pulses rate = /Ts Ts Original signal (2Hz) sampled at 8Hz = Perfect reconstructed signal PM Pulses = Faculty of Information Technology Original signal (9Hz) sampled at 8Hz liased reconstructed signal 4 Faculty of Information Technology

11 2 - Quantisation Quantisation Noise PM Pulses PM Pulses 4 bit Faculty of Information Technology E F G H Samples are only approximations which leads to quantisation error or noise. n-bit encoding, there are 2 n levels: SNR = 2log2 n +.76d 42 Faculty of Information Technology 6nd Quantised symbols from each signal: EGHEG Non-linear Quantisation 3 - inary Encoding E F G H Quantisation levels not evenly spaced. Improves signal-to-noise ratio: lower amplitudes are less distorted. New quantised symbols from each signal: FHHFH FEFF Use -Law (Europe) or µ-law (US, Japan) ompanding (ompressing- Expanding). For example, encode using NRZ-L, MI, H3,... PM Pulses 4 bit inary NRZ L Faculty of Information Technology 44 Faculty of Information Technology

12 Example Encoding System 4. nalog ata, nalog Signals 25µsec bits 4 time LK Voice Filter PM ompander Quantizer Encoder igital signal 45 Faculty of Information Technology Modulation: combine an input signal m(t) with a carrier f c to produce a signal s(t). Why modulate analog signals? Higher frequency can give more efficient transmission. Unguided transmission needs HF. Permits frequency division multiplexing (Stallings, hapter 8). Types of analog modulation: (M). Frequency (FM). Phase (PM). 46 Faculty of Information Technology arrier Modulating sine-wave signal -modulated (ST) wave Phase-modulated wave Frequency-modulated wave Further Reading PPENIX Stallings, W., ata and omputer ommunications, Prentice Hall. hapter 5. Forouzan,.., ata ommunication and Networking, McGraw-Hill. The following slides provide more detail on data encoding and modulation. This information is provided for interest and education. It will not be used in any formal assessment. 47 Faculty of Information Technology 48 Faculty of Information Technology

13 EXTR: Shift Keying Example: 5 bps EXTR: Shift Keying Example: 5, and 2 bps arrier (2 Hz) ata (5 bps) W =.4 = 25 Hz SK signal Significant spectrum: 75 Hz to 225 Hz W = 5 Hz Faculty of Information Technology SK (5 bps): SK ( bps): SK (2 bps): Faculty of Information Technology EXTR: Shift Keying Example Patterns EXTR: Shift Keying andwidth Faculty of Information Technology fc N baud / 2 Minimum andwidth = N baud fc Frequency fc + N baud / 2 From the examples: an SK signal is equivalent to the original data signal translated up in frequency by the carrier signal. Frequency components are equally spaced either side of the carrier signal which are known as sidebands. The data is actually represented in these sidebands. 52 Faculty of Information Technology

14 EXTR: Frequency Shift Keying Example EXTR: Frequency Shift Keying andwidth Two carriers: f = 25 Hz and f 2 = 275 Hz N baud / 2 W = fc fc + N fc fc baud N baud / 2 8 ata (3 bps) FSK signal Significant spectrum: Hz to 29 Hz.5 W = 8 Hz Faculty of Information Technology fc 54 Faculty of Information Technology fc Frequency Equivalent to the addition of two separate SK modulations: carrier one modulated with the digital signal, and carrier two modulated with the complement of the digital signal. The bandwidth is therefore the same as SK with the addition of the frequency shift (difference between the carriers = f c f c ). EXTR: Full-uplex FSK on a Voice Grade Line EXTR: Phase Shift Keying Example signal strength spectrum of signal transmitted in one direction spectrum of signal transmitted in opposite direction Figure 5.8 Full-uplex FSK Transmission on a Voice-Grade Line frequency (Hz) 55 Faculty of Information Technology arrier (2 Hz) ata (5 bps) PSK signal Significant spectrum: 75 Hz to 225 Hz W = 5 Hz Faculty of Information Technology

15 EXTR: onstellation iagrams EXTR: ecision Region Represent the change of amplitude and phase visually. Points plotted on a artesian coordinate system show allowed signal changes: istance from the origin () specifies the amplitude of the signal ( = ). ( ) ngle from the horizontal axis specifies the phase change (P = arcsin ) For example, the below constellation shows a signal of amplitude and a phase shift of P = 45. That is, 45 8 π = π 4 radians, or one 8th of a period. P Signal constellation point 57 Faculty of Information Technology P ecision Region Transmitted Symbol Received Symbol Error Vector Received symbol may be different from transmitted symbol due to channel and quantisation noise. s long a received symbol is in the correct decision region, it will be interpreted as the correct bit sequence. s the constellation becomes more dense, the decision region shrinks leading to a higher error rate in the presence of noise. 58 Faculty of Information Technology EXTR: Modems EXTR: Telephone Network andwidth Modem Exchange The telephone system operates with an almost 3 Hz bandwidth. For safety, the edges of this bandwidth are not used for data. Used for voice Used for data Telephone Network amplitude modulator demodulator 59 Faculty of Information Technology frequency Hz for data Hz for voice 6 Faculty of Information Technology

16 EXTR: Modem evelopment EXTR: Modems: reakthroughs Year ITT data rate (bps) Modulation 964 V.2 3 FSK (2 freqs) 964 V.23 2/6 FSK (2 freqs) 972 V.26bis 2.4k/.2k 4-PSK 972 V k 8-PSK 976 V.27ter 4.8k/2.4k 8-PSK 984 V.29 up to 9.6k 6-QM, 32-TM 99 V.32bis up to 4.4k 28-TM 995 V.34 up to 33.6k 24-TM 997 V.9 up to 56k PM 6 Faculty of Information Technology 964: First modem was introduced, 3bps using FSK. 972: The use of equaliser and 4-PSK (up to 2.4kbps). 976: utomatic adaptive equaliser 8-PSK (up to 4.8kbps). 976: The use of 6-QM (up to 9.6kbps, 4 wires). 984: The use of TM (from 9.6k to 33.6k in 996). 984: Echo cancellation allowed modems to achieve full duplex with 2 wires. 997: igitisation of PSTN (up to 56kbps). 62 Faculty of Information Technology EXTR: Modems: it-rate 9.6kbps EXTR: Modem V.29 efore echo cancellation in the PSTN, full duplex was achieved by dividing the bandwidth in two different frequency bands for up and down directions (e.g. V.2 using FSK at 3bps). signal strength spectrum of signal transmitted in one direction spectrum of signal transmitted in opposite direction freq Hz frequency (Hz) Higher data rates are achieved using 4 wires for full duplex transmission and introducing more symbols. Figure 5.8 Full-uplex FSK Transmission on a Voice-Grade Line 63 Faculty of Information Technology Signal onstellation Signal Spectrum 9.6kbps using QM 64 Faculty of Information Technology

17 EXTR: Modems: 9.6k 33.6kbps EXTR: Modems: TM Overall data rate Trellis ode Modulation (TM): To achieve Forward Error orrection (FE) based on convolutional codes. Without TM Noise (normalised to signal strength) 96 bps 44 bps Sent: Received: With convolutional coding, the receiver is able to identify and correct this error. 65 Faculty of Information Technology O O 2 Input S S 2 S 3 O O 2 n example encoder and its tree diagram representation. Shift register for memory and modulo-2 adders S S 2 S 3 (XOR gates) for convolution. One input to two output bits: Rate = /2. Tree repeats after second branch level. Four unique branch nodes (states):,,,. ranch levels Faculty of Information Technology EXTR: Modems: TM EXTR: Modems: TM 2 3 ranch levels ranch nodes ranch levels 7 Input sequence: Encoded sequence: The simplified tree diagram can be represented by a trellis diagram. Repetitive nature can be seen and exploited after the second branching level. 67 Faculty of Information Technology 68 Faculty of Information Technology

18 EXTR: Modems: Viterbi lgorithm EXTR: Modems: TM Input sequence: Received sequence: Error bits ecision Region ecision Region ecision Region ccumulated Hamming distances Faculty of Information Technology Without TM TM: In states or TM: In states or Without TM, we must discern between four possible symbols. With TM, we halve the number of constellation points we need to consider at any time. The half to consider depends on the current state, which depends on the symbols decoded in the past. We have however doubled the data rate in this example. 7 Faculty of Information Technology EXTR: Modems: V.32 and V.34 EXTR: Modems: it-rate = 56kbps Modem PM 64kbps Telephone Network 27 V.32 for 96 bps 7 Faculty of Information Technology 27 V.32 bis for 4,4 bps V.32 (984) introduced TM (8-state, two-dimensional) using a 32 point constellation to transmit 5 bits per symbol, where 4 are data bits. 4 bits 24 symbols/sec = 96 bps. V32 bis uses 28 point constellation and TM to transmit 6 data bits per symbol = 44. V.34 uses a wider bandwidth (from 244 Hz to 3674 Hz) and adaptive symbol rate (24 to 3429). For 28.8 kbps uses a 96-point constellation and 33.6 kbps uses a 664-point constellation. For example, 8k samples/sec where each sample carries 3 bits. it rate = 8k 3bps = 24kbps. Telephone System: 8k sample/sec with 8-bit PM. Quantisation noise and bitrobbing leaves 56 kbps. Input =... proxy server 72 Faculty of Information Technology sampling pulses

19 EXTR: Example ISP on the Telephone Network EXTR: ompanding (ompressing-expanding) Modem omputer Local loop (analog, twisted pair) Medium bandwidth trunk (digital, fiber) odec End office Toll office Toll office Toll office High bandwidth trunk (digital, fiber) odec ISP 2 igital line Up to, local loops Modem bank Implement non-linear quantisation: uniform quantisation followed by compressing (expanding) the input using a logarithmic mapping. There are two standard ways to map a signal onto a logarithmic curve. -Law x sgn(x) +ln() x < F (Europe) a (x) = x = 87.6 µ-law (US, Japan) sgn(x) +ln( x ) +ln() -Law input versus output: ln( + µ x ) F µ (x) = sgn(x) ln( + µ) bit output µ = Faculty of Information Technology ISP bit input Faculty of Information Technology EXTR: daptive ifferential PM (PM) EXTR: elta Modulation (M) odes transmitted represent differences between predicted inputs and actual inputs. Produces a lower bit rate at the expense of quality. 64 kbit/sec s(k) s e (k) d(k) (a) TRNSMITTER Quantizer q(k) Stepsize dapter daptive Predictor Inverse Quantizer s r (k) d q (k) + + I(k) 32 kbit/sec Stepsize dapter 75 Faculty of Information Technology I(k) (b) REEIVER Inverse Quantizer q(k) d q (k) + + daptive Predictor s e (k) s r (k) Reduce complexity of PM (at the expense of quality). nalog input is sampled at the bit rate and approximated by a staircase function. Move up or down one quantisation level (δ) at each sample interval T s. inary behaviour: Function moves up or down by δ at each sample interval. Produces a stream of binary values for each sample. nalog input elay of one time unit omparator Transmission = +δ = δ Reconstructed waveform inary output 76 Faculty of Information Technology inary input elay of one time unit Reception Reconstructed waveform

20 EXTR: elta Modulation Example Signal nalog input Staircase function step size δ Slope overload noise Quantizing noise One bit: = step down = step up to encode signals. T s sampling time Time elta modulation output 77 Faculty of Information Technology