Communication Theory-2

Transcription

1 Lecture Notes-5 Communication heory-2 Assoc. Prof. Dr. Hakan DOĞAN

2 Pulse modulation methods Analog-over-analog methods: Pulse-amplitude modulation (PAM) Pulse-width modulation (PWM) Pulse-position modulation (PPM) Analog-over-digital methods: Pulse-code modulation (PCM) Delta modulation (DM or Δ-modulation) Darbe Modülasyonunun Üç üründe (PAM, PWM, PPM) Gürültünün Etkisi Gürültü altında PWM ve PPM nin başarımları PAM a göre daha iyidir. PPM'in başarımı ise PWM e göre daha iyidir. Bunun nedenini şöyle açıklayabiliriz; her iki modülasyon türünde de bilgi, darbelerin kendilerinde değil, darbelerin kenarlarında taşınır. PPM in performansı FM in performansına benzer. Güç açısından PPM in PWM e göre daha verimli olduğu söylenebilir. Çünkü, PPM darbeyi değil de yalnız kenarı göndermeye daha yakındır. PWM boşuna enerji harcar. Please note that PAM, PPM and PWM are analogue modulation schemes

3 An analog-to-digital converter (abbreviated ADC, A/D or A to D) is a device that converts a continuous physical quantity (usually voltage) to a digital number that represents the quantity's amplitude.

4 Sampling - the conversion of a signal from continuous to discrete in time Quantization - the conversion of the signal samples from continuous to discrete in amplitude Sampling Quantization Coding

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9 Sampled values are continues , 0.011, v.s. (infinitive values.) We need to limit total number number of levels to send it as digital. Round For example, > > 0 Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a (countable) smaller set such as rounding values to some unit of precision. We assume that the amplitude of m(t) is confined to range -mp,+mp. his range is divided in L zones, each of step size "delta". delta= 2mp/L

10 4 khz Sampling 8kHz 8000 samples/sn, each sample 8 bit bit/second 64 kbps Music Sampling 44.1 khz samples/sn, each sample 16 bit bit/second 2 channel bit/second Mbps Uniform quantizing is optimum if the input signal has uniform distribution. In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. his error is either due to rounding or truncation. Signal-to-quantization-noise ratio (SQNR)

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12 sig=1.01*cos(2*pi*[0:0.02:1.5]) [index,quants,distor]=quantiz(sig,-1:0.2:1,-1.1:0.2:1.1) plot([0:0.02:1.5],sig),hold on,plot([0:0.02:1.5],quants) x x x x x x x x x x x x

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14 sig=2*rand(100000,1)-1; [index,quants,distor]=quantiz(sig,-1:0.2:1,-1.1:0.2:1.1) distor = e-003 distor = sum((quants-sig.').^2)/length(sig) >> 0.2^2/12 ans = e-003

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16 Nonuniform nicemleyicilerin yapımı zor ve pahalıdır. Alternatif bir yol, ses sinyalini önce bir nonlineer sistemden geçirip sonra uniform olarak nicemlemektir. Nonlineerlik sinyal genliğini compress eder (sıkıştırır) Nicemleyici girişi daha uniform bir dağılıma sahip olur. Alıcıda, nonlineerliğin tersine expand edilir (genleştirilir). Compressing and Expanding işlemi Companding olarak adlandırılır

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18 help compand COMPAND Source code mu-law or A-law compressor or expander. OU = COMPAND(IN, PARAM, V) computes mu-law compressor with mu given in PARAM and the peak magnitude given in V. OU = COMPAND(IN, PARAM, V, MEHOD) computes mu-law or A-law compressor or expander computation with the computation method given in MEHOD. PARAM provides the mu or A value. V provides the input signal peak magnitude. MEHOD can be chosen as one of the following: MEHOD = 'mu/compressor' mu-law compressor. MEHOD = 'mu/expander' mu-law expander. MEHOD = 'A/compressor' A-law compressor. MEHOD = 'A/expander' A-law expander. he prevailing values used in practice are mu=255 and A=87.6.

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21 Digital output of the PCM coder is converted to an appropriate waveform for transmission over channel line coding or transmission coding In communication systems, a line code is a code chosen for use within a communications system for baseband transmission purposes. (digital baseband modulation or digital baseband transmission method)

22 he waveform representation of voltage or current that are employed to represent the 1s and 0s of a digital data on a channel (transmission link) is called line encoding. Aims of Line codes: Self-synchronization: he ability to recover timing from the signal itself. Long series of ones and zeros could cause a problem. Low probability of bit error: he receiver needs to be able to distinguish the waveform associated with a mark from the waveform associated with a space, even if there is a considerable amount of noise and distortion in the channel. Spectrum that is suitable for the channel: In some cases DC components should be avoided if the channel has a DC blocking capacitance. he transmission bandwidth should be minimized.

23 input bits a k, p(t) pulse shape, b symbol duration. b =s/n, Rb =1/b Unipolar nonreturn-to-zero x t a p t k k k b a k A, Xk 1 0, X k 0 pt t b Self-synchronization Problem because of long zeros and ones DC component Unfortunately, most long-distance communication channels cannot transport a DC component. he DC component is also called the disparity, the bias, or the DC coefficient. he simplest possible line code, called unipolar nonreturn-to-zero (UP- NRZ) because it has an unbounded DC component, gives too many errors on such systems.

24 * Its drawbacks are that it is not self-clocking *It has a significant DC component, *he normalized power is double for polar NRZ (we need less power for unipolar retun-to-zero) DC component can be solved by using return-to-zero structure, where the signal returns to zero in the middle of the bit period. Unipolar Return Zero Line Codes a k A, Xk 1 0, X k 0 pt t b 2 Darbe süresi NRZ darbe süresinin yarısı. Dolayısı ile bantgenişliği ise iki katıdır. Uzun 1 dizileri artık eş zamanlama da sorun olmaz. Ancak, 0 dizileri hala problem

25 Polar Non return-to-zero (P-NRZ) No DC components a k A, Xk 1 A, Xk 0 Polar Return-to-zero (P-RZ) No DC components Bu durumda uzun 0 dizileri de olsa eşzamanlama yönünden sorun yok.

26 Manchester Line Codes pt t b 4 t b 4 b 2 b 2 Kutuplu RZ koduna göre, daha kolay eşzamanlama ve daha iyi spektral özelliğe sahiptir. In Manchester encoding, the transition at the middle of the bit is used for synchronization he is no DC component he minimum bandwidth of Manchester is 2 times that of Non returnto-zero.

27 Alternate Mark Inversion 0, X k 0 ak A, X k 1 and if former is +A A, Xk 1 and if former is -A Üçlümsü (pseudoternary) veya alternate mark inversion sinyalleşme olarak da adlandırılır. RZ veya NRZ darbe şekilleri ile kullanılabilirler. Code uses 3 voltage levels: - +, 0, -, to represent the symbols Has no DC component Has no self synchronization because long runs of 0 s results in no signal transitions

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29 Multilevel Schemes In these schemes we increase the number of data bits per symbol thereby increasing the bit rate. We can combine the 2 data elements into a pattern of m elements to create 2 m symbols wo-binary, one-quaternary (2B1Q) is a line code used in the U interface of the Integrated Services Digital Network (ISDN) Basic Rate Interface (BRI). 2B1Q is a four-level pulse amplitude modulation (PAM-4) scheme, mapping two bits (2B) into one quaternary symbol (1Q). If the voltage is misread as an adjacent level, this will only cause a 1-bit error in the decoded data

30 mv -150 mv +150 mv +450 mv

31 Hat Kodlarının Güç Spektral Yoğunluğu (GSY) (Power Spectral Density, PSD) Power and Energy Spectral Density he power spectral density (PSD) S x (w) for a signal is a measure of its power distribution as a function of frequency. It is a useful concept which allows us to determine the bandwidth required of a transmission system Consider a signal x(t) with Fourier ransform (F) X(w) X ( w ) x( t) e jwt dt We wish to find the energy and power distribution of x(t) as a function of frequency

32 Deterministic Signals If x(t) is the voltage across a R=1W resistor, the instantaneous power is, ( x( t)) R 2 ( x( t)) 2 hus the total energy in x(t) is, From Parseval s heorem, Energy Energy X ( w) x( t) 2 df 2 dt X (2f ) 2 E(2f ) df df Where E(2f) is termed the Energy Density Spectrum (EDS),

33 he above definitions of energy spectral density require that the Fourier transforms of the signals exist, that is, that the signals are integrable/summable In this case one would need to use the power spectral density (PSD), which describes how the power of a signal or time series is distributed with frequency.

34 For communications signals, the energy is effectively infinite (the signals are of unlimited duration), so we usually work with Power quantities. We find the average power by averaging over time Average power lim 1 2 ( x 2 ( t)) 2 dt Where x (t) is the same as x(t), but truncated to zero outside the time window -/2 to /2 lim S lim x 1 (2f X ) df X (2f ) (2f ) 2 2 df df Where S x (w) is the Power Spectral Density (PSD)

35 Power Spectral Density (PSD) S x ( w) lim X ( w) 2 S x (.) has units Watts/Hz Wiener-Khintchine heorem Since a signal is not square integrable, the Fourier transforms do not exist in this case. Fortunately, the Wiener-Khinchin theorem provides a simple alternative. It can be shown that the PSD is also given by the F of the autocorrelation function (ACF), r xx (t), S x ( w) rxx ( t ) e j wt d t Where, r xx ( t ) lim x( t) x( t t ) dt

36 PSD, random signals Results can be extended to cover random signals by the inclusion of an extra averaging or expectation step, over all possible values of the random signal x(t) S x ( w) lim E[ X ( w) 2 ] Where E[.] is the expectation operator Note: Only applies for ergodic signals where the time averages are the same as the corresponding ensemble averages

37 Linear Systems and Power Spectra Passing x (t) through a linear filter H(w) gives the output spectrum, ) ( ) ( ) ( w w w X H Y Hence, the output PSD is, X H E Y E S y ] ) ( ) ( [ lim ] ) ( [ lim ) ( 2 2 w w w w X E H S y ] ) ( [ lim ) ( ) ( 2 2 w w w ) ( ) ( ) ( 2 w w w x y S H S

38 he periodogram is an estimate of the spectral density of a signal. A periodogram is formed after taking the average magnitude squared of the FF FF stands for Fast Fourier ransform Electronics engineering he concept and use of the power spectrum of a signal is fundamental in electronic engineering, especially in electronic communication systems (radio & microwave communications, radars, and related systems). Much effort has been made and millions of dollars spent on developing and producing electronic instruments called "spectrum analyzers" for aiding electronics engineers, technologists, and technicians in observing and measuring the power spectrum of electronic signals. he cost of a spectrum analyzer varies according to its bandwidth and its accuracy. he spectrum analyzer measures essentially the magnitude of the short-time Fourier transform (SF) of an input signal. If the signal being analyzed is stationary, the SF is a good smoothed estimate of its power spectral density.

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