Formatting & Baseband Modulation CHAPTER 2 Formatting & Baseband Modulation School of Computer and Communication Engineering, Amir Razif Arief b. Jamil Abdullah EKT 431: Digital Communications

Last time, we talked about: Important features of digital communication systems Some basic concepts and definitions such as as signal classification, spectral density, random process, linear systems and signal bandwidth.

Today, we are going to talk about: The first important step in any DCS: Transforming the information source to a form compatible with a digital system

Formatting and Transmission of Baseband Signal Digital data, textual information, analog information Transmitted through baseband channel  pulses Pulse modulate~ bit stream  pulse modulate Demodulated~ pulse waveform demodulated to produce estimate transmitted digit, recover estimate of source information. Encode Transmit Pulse modulate Sample Quantize Demodulate/ Detect Channel Receive Low-pass filter Decode waveforms Bit stream Format Digital info. Textual info. Analog source sink

Format Analog Signals To transform an analog waveform into a form that is compatible with a digital communication system, the following steps are taken: Sampling Quantization and encoding Baseband transmission formatting~ transfer information into digital message, in ‘1’ or ‘0’.

modulated (PAM) signal Sampling Theorem Sampling process Analog signal Pulse amplitude modulated (PAM) signal Sample and hold  output is pulse amplitude modulation (PAM) ~ Can retrieve analog signal through LPF ~ Original waveform? Sampling theorem: A bandlimited signal with no spectral components beyond , can be uniquely determined by values sampled at uniform intervals of The sampling rate, is called Nyquist rate. - Allow analog signal to be reconstructed completely.

Sampling ~ impulse sampling Time and frequency domain Time domain

Aliasing Effect aliasing - Aliasing ~undersampling (1) Higher sampling rate require. (2) Antialiasing filters fm reduced to fs/2 or less – LPF Transition bandwidth.. $ LP filter Nyquist rate aliasing

Quantization Source of corruption~ (1) sampling & quantization (2) channel effect. Amplitude quantizing: Mapping samples of a continuous amplitude waveform to a finite set of amplitudes. - Quantile interval (q volt) - linear quantizer, error q/2 - In Out Average quantization noise power Signal peak power Signal power to average quantization noise power Quantized values

Quantization Error Quantizing error: The difference between the input and output of a quantizer. Quantization noise~ The distortion due to a round-off or truncation error. ~ Process of encoding PAM into a quantization PAM signal involve discarding some of the original analog information. ~ Quantization noise is inversely proportional to the number of levels employed in the quantization process. ACG~ employed to extend the operating range of converter. + AGC Qauntizer Process of quantizing noise Model of quantizing noise

Quantization Error … Quantizing error: Granular or linear errors happen for inputs within the dynamic range of quantizer Saturation errors happen for inputs outside the dynamic range of quantizer Saturation errors are larger than linear errors Saturation errors can be avoided by proper tuning of AGC Quantization noise variance: s2~ Average quantization noise power Uniform q.

Encoding: Pulse Code Modulation (PCM)‏ A uniform linear quantizer is called Pulse Code Modulation (PCM). ~ PCM is class of baseband signals obtained from quantized PAM signals by encoding each quantized sample into a digital word. Pulse Code Modulation (PCM): - Encoding the quantized signals into a digital word (PCM word or codeword). Each quantized sample is digitally encoded into an l -bits codeword where L in the number of quantization levels and l = log2L. The source information is quantized into one of L levels  each quantized sample is digitally encoded into l-bit (l = log2L) codeword. For baseband transmission the codeword bits will then be transformed to pulse waveform. Increase the number of level reduce quantization noise. Should increase the data rate however result in more transmission bandwidth.

Quantization example Quant. levels boundaries x(nTs): sampled values Analog signal from -4v to 4v, step size 1v, 8 quantize level (code#). Example: to improve terrible music Increase quantization level  reduce noise cause greater transmission bandwidth Pg 80 text amplitude x(t)‏ x(nTs): sampled values xq(nTs): quantized values boundaries Quant. levels 111 3.1867 110 2.2762 101 1.3657 100 0.4552 011 -0.4552 010 -1.3657 001 -2.2762 000 -3.1867 Ts: sampling time t PCM codeword 110 110 111 110 100 010 011 100 100 011 PCM sequence

Statistics of Speech Amplitudes In speech, weak signals (low amplitude) are more frequent than strong ones (high amplitude). Using equal step sizes (uniform quantizer) gives low for weak signals and high for strong signals. Adjusting the step size of the quantizer by taking into account the speech statistics improves the SNR for the input range. ~ non-uniform quantization provides fine quantization for weak signal and coarse quantization for strong signal. 0.0 1.0 0.5 2.0 3.0 Normalized magnitude of speech signal Probability density function

Uniform and Non-Uniform Quantization Uniform (linear) quantizing: No assumption about amplitude statistics and correlation properties of the input. Not using the user-related specifications Robust to small changes in input statistic by not finely tuned to a specific set of input parameters Simple implementation Application of linear quantizer: Signal processing, graphic and display applications, process control applications Non-uniform quantizing: Using the input statistics to tune quantizer parameters Larger SNR than uniform quantizing with same number of levels Non-uniform intervals in the dynamic range with same quantization noise variance Provide fine quantization for weak signal. Application of non-uniform quantizer: Commonly used for speech

Non-uniform Quantization It is achieved by uniformly quantizing the “compressed” signal (1) distort signal through logarithmic compression (2) uniform quantizer input to uniform quantizer  expansion (3) companding:- process of compression & expansion At the receiver, an inverse compression characteristic, called “expansion” is employed to avoid signal distortion. compression+expansion companding Compress Qauntize Expand Channel Transmitter Receiver

Cont’d… Companding Characteristics (1) u-law (2) A-Law

Companding Characteristics Today most PCM use a piecewise linear approximation to the logarithmic compression characteristics. Method of Companding • For the compression, two laws are adopted: the μ-law in US and Japan and the A-law in Europe. μ-law A-law The typical values used in practice are: μ=255 and A=87.6. After quantization the different quantized levels have to be represented in a form suitable for transmission. This is done via an encoding process. Vmax= Max uncompressed analog input voltage Vin= amplitude of the input signal at a particular of instant time Vout= compressed output amplitude A & μ= parameter define the amount of compression

Baseband Transmission analog waveform transformed into binary digits via use of PCM. binary digits representation with electrical pulse to transmit them through baseband channel. To transmit information through physical channels, PCM sequences (codewords) are transformed to pulses waveforms. Each waveform carries a symbol from a set of size M. Each transmit symbol represents bits of the PCM words. PCM waveforms (line codes) are used for binary symbols (M=2). M-ary pulse modulation are used for non-binary symbols (M>2).

(b) Pulse representation of PCM (3) Pulse Waveform. Cont’d… Pg 86 Figure 2.21: Waveform representation of binary digits. (a) PCM sequence (b) Pulse representation of PCM (3) Pulse Waveform.

PCM Waveforms Types PCM waveforms is when pulse modulation applied to a binary symbol resulting binary waveform. PCM types; telephony application called line code, PCM applied to nonbinary symbol called M-ary pulse modulation waveform. PCM waveform groups; (1) Nonreturn-to-zero (NRZ) (2) Return-to-zero (RZ)‏ (3) Phase encoded (4) Multilevel binary 1 0 1 1 0 0 T 2T 3T 4T 5T +V -V NRZ-L Unipolar-RZ Bipolar-RZ Manchester Miller Dicode NRZ

(i) Unipolar-RZ~ ‘1’ half-bit wide pulse, ‘0’ absence of pulse. Cont’d… NRZ types; very commonly used. (i) NRZ-L (L for level)~ used extensively in digital logic. (ii) NRZ-M (M for mark)~ mark or “1” represent change in level & “0” or space no change. “differential encoding”. Used in magnetic tape recording. (iii) NRZ-S (s for space)~ compliment of NRZ-M. RZ types: (i) Unipolar-RZ~ ‘1’ half-bit wide pulse, ‘0’ absence of pulse. (ii) Bipolar-RZ~ ‘1’ and ‘0’ opposite pulse that is one-half bit wide. (iii) RZ-AMI (alternate mark inversion)~ equal amplitude alternating pulse. ‘0’ is represent by absence of pulse. Bi phase~ used in magnetic recording & optic comm. (i) bi-f-L (bi phase level) or Manchester cooding~’1’ half bit wide pulse 1st half of interval & ‘0’ half bit wide pulse 2nd half of interval (ii) bi-f-M (bi phase mark)~ transition occur at every bit interval. (iii) bi-f-S (bi phase space)~ transition occur at every bit interval. ‘1’ no transition & ‘0’ second transition second half bit later.

Cont’d… Figure 2.22 pg 87

PCM Waveforms … In choosing PCM, parameters to be considered; DC components Self-clocking Error detection Bandwidth Compression Differential encoding Noise immunity

Spectra of PCM Waveforms

M-ary Pulse Modulation M-ary pulse modulations category: M-ary pulse-amplitude modulation (PAM)‏ M-ary pulse-position modulation (PPM)‏ M-ary pulse-duration modulation (PDM)‏ M-ary PAM is a multi-level signaling where each symbol takes one of the M allowable amplitude levels, each representing bits of PCM words. For a given data rate, M-ary PAM (M>2) requires less bandwidth than binary PCM. For a given average pulse power, binary PCM is easier to detect than M-ary PAM (M>2). M-ary PAM one of M allowable amplitude levels are assigned to each of the M possible symbol values. M-ary PPM modulation is effected by delaying or advancing a pulse occurrence. M-ary PWM modulation is effected by varying the pulse width by an amount that corresponds to the value of the symbols.

M-ary pulse modulation block-diagram

Illustration of PCM signals

PAM example