4.2 Digital Transmission Pulse Modulation Pulse Code Modulation Outlines Pulse Modulation Pulse Code Modulation Delta Modulation Line Codes

PULSE MODULATION (PM) Sampling analog information signal Converting samples into discrete pulses Transport the pulses from source to destination over physical transmission medium.

Cont’d... Four (4) Methods 1. PAM 2. PWM 3. PPM 4. PCM Analog Pulse Modulation Digital Pulse Modulation

continue… Analog Pulse Modulation Carrier signal is pulse waveform and the modulated signal is where one of the carrier signal’s characteristic (either amplitude, width or position) is changed according to information signal.

Pulse Amplitude Modulation (PAM) The amplitude of pulses is varied in accordance with the information signal. Width & position constant.

Pulse Width Modulation (PWM) Sometimes called Pulse Duration Modulation (PDM). The width of pulses is varied in accordance to information signal. Amplitude & position constant.

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Pulse Position Modulation (PPM) Modulation in which the temporal positions of the pulses are varied in accordance with some characteristic of the information signal. Amplitude & width constant.

PULSE CODE MODULATION (PCM) The most common technique for using digital signals to encode analog data is PCM. Example: To transfer analog voice signals off a local loop to digital end office within the phone system, one uses a codec. The pulses are of fixed length and fixed amplitude PCM is a binary system where a pulse or lack of a pulse within a prescribed time slot represents either a logic 1 or a logic 0 condition.

PCM Block Diagram Four step process Most common form of analog to digital modulation Four step process Signal is sampled using PAM (Sample) Integer values assigned to signal (PAM) Values converted to binary (Quantized) Signal is digitally encoded for transmission (Encoded)

4 Steps Process

PCM Sampling The function of a sampling circuit in PCM transmitter is to periodically sample the continually changing analog input voltage and convert those samples to a series of constant-amplitude pulses that can more easily be converted to binary PCM code There are two basic techniques used to perform the sampling function: Natural sampling Flat-top sampling

Natural Sampling Tops of the sample pulses retain their natural shape during the sample interval. Frequency spectrum of the sampled output is different from an ideal sample. Amplitude of frequency components produced from narrow, finite-width sample pulses decreases for the higher harmonics Requiring the use of frequency equalizers

Natural Sampling

Flat-top Sampling The most common method used for sampling voice signals in PCM systems. Accomplish in a sample-and-hold circuit To periodically sample the continually changing analog input voltage & convert to a series of constant-amplitude PAM voltage levels. The input voltage is sampled with a narrow pulse and then held relatively constant until the next sample is taken.

continue… Sampling process alters the frequency spectrum & introduces aperture error. The amplitude of the sampled signal changes during the sample pulse time. Advantages: Introduces less aperture distortion Can operate with a slower ADC

Flat-top Sampling

Sampling rate A process of taking samples of information signal at a rate of Nyquist’s sampling frequency. Nyquist’s Sampling Theorem : The original information signal can be reconstructed at the receiver with minimal distortion if the sampling rate in the pulse modulation system equal to or greater than twice the maximum information signal frequency. fs >=2 fm (max)

Quantization A process of converting an infinite number of possibilities to a finite number of conditions (rounding off the amplitudes of flat-top samples to a manageable number of levels). Analog signals contain an infinite number of amplitude possibilities. Thus, converting an analog signal to a PCM code with a limited number of combinations requires quantization. With quantization, the total voltage range is subdivided into a smaller number of subranges as shown in Table. The PCM code shown in the Table is a 3-bit sign-magnitude code with 8 possible combinations (4 positive and 4 negative). The leftmost bit is the sign bit (1 = + and 0 = -) and the two rightmost bits represent magnitude.

continue… Each voltage level has one code assigned to it except zero volts, which has two codes, 100 (+0) and 000 (-0). The magnitude difference between adjacent steps is called the quantization interval or quantum.

continue... Analog input signal Sample pulse PAM signal PCM code

QUANTIZATION ERROR A difference between the exact value of the analog signal & the nearest quantization level.

Dynamic Range (DR) The ratio of the largest possible magnitude to the smallest possible magnitude that can be decoded by the digital-to-analog converter in the receiver. Where DR = absolute value of dynamic range Vmax = the maximum voltage magnitude Vmin = the quantum value (resolution) n = number of bits in the PCM code

Example 1 Calculate the dynamic range for a linear PCM system using 16-bit quantizing. Calculate the number of bits in PCM code if the DR = 192.6 dB

Coding Efficiency = Minimum number of bits x 100 A numerical indication of how efficiently a PCM code is utilized. The ratio of the minimum number of bits required to achieve a certain dynamic range to the actual number of PCM bits used. Coding Efficiency = Minimum number of bits x 100 Actual number of bits

Signal to Quantization Noise Ratio (SQR) The worst-case voltage SQR SQR for a maximum input signal The signal power-to-quantizing noise power ratio R =resistance (ohm) v = rms signal voltage q = quantization interval

Example 2 Calculate the SQR (dB) if the input signal = 2 Vrms and the quantization noise magnitudes = 0.02 V. Determine the voltage of the input signals if the SQR (max) = 36.82 dB and q =0.2 V.

Companding The process of compressing and then expanding. The higher amplitude analog signals are compressed prior to transmission and then expanded in receiver. Improving the dynamic range of a communication system.

Companding Functions

Methods of Companding For the compression, two laws are adopted: the -law in US and Japan and the A-law in Europe. -law A-law The typical values used in practice are: =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, = parameter define the amount of compression

continue... A-law μ-law

PCM Line Speed The data rate at which serial PCM bits are clocked out of the PCM encoder onto the transmission line. Where Line speed = the transmission rate in bits per second Sample/second = sample rate, fs Bits/sample = no of bits in the compressed PCM code

Example 4 For a single PCM system with a sample rate fs = 6000 samples per second and a 7 bits compressed PCM code, calculate the line speed.

Virtues & Limitation of PCM The most important advantages of PCM are: Robustness to channel noise and interference. Efficient regeneration of the coded signal along the channel path. Efficient exchange between BT and SNR. Uniform format for different kind of base-band signals. Flexible TDM.

continue… Secure communication through the use of special modulation schemes of encryption. These advantages are obtained at the cost of more complexity and increased BT. With cost-effective implementations, the cost issue no longer a problem of concern. With the availability of wide-band communication channels and the use of sophisticated data compression techniques, the large bandwidth is not a serious problem.

DELTA MODULATION (DM) A single-bit PCM code to achieve digital transmission of analog. Logic ‘0’ is transmitted if current sample is smaller than the previous sample Logic ‘1’ is transmitted if current sample is larger than the previous sample

Cont’d…

Operation of Delta Modulation

continue... Analog input is approximated by a staircase function Move up or down one level () at each sample interval (by one quantization level at each sampling time)  output of DM is a single bit. Binary behavior Function moves up or down at each sample interval In DM the quantization levels are represented by two symbols: 0 for - and 1 for +. In fact the coding process is performed on eq. The main advantage of DM is its simplicity.

The transmitter of a DM System Cont’d... The transmitter of a DM System

The receiver of a DM system

Delta Modulation - Example

DM circuit’s problem

continue… Slope overload distortion is due to the fact that the staircase approximation mq(t) can't follow closely the actual curve of the message signal m(t ). In contrast to slope-overload distortion, granular noise occurs when  is too large relative to the local slope characteristics of m(t). granular noise is similar to quantization noise in PCM. It seems that a large  is needed for rapid variations of m(t) to reduce the slope-overload distortion and a small  is needed for slowly varying m(t) to reduce the granular noise. The optimum  can only be a compromise between the two cases. To satisfy both cases, an adaptive DM is needed, where the step size  can be adjusted in accordance with the input signal m(t).

continue... In summary Slope overload Due to the input analog signal amplitude changes faster than the speed of the modulator to minimize : the product of the sampling step size and the sampling rate must be equal to or larger than the rate of change of the amplitude of the input analog signal. Granular noise Due to the difference between step size and sampled voltage. To minimize : increase the sampling rate, decrease the step size of modulator

DM Performance Good voice reproduction PCM - 128 levels (7 bit) Voice bandwidth 4khz Should be 8000 x 7 = 56kbps for PCM Data compression can improve on this e.g. Interframe coding techniques for video

continue... Adaptive Delta Modulation (ADM) A Delta Modulation system where the step size of the DAC is automatically varied depending on the amplitude characteristics of the analog signal. A well designed ADM scheme can transmit voice at about half the bit rate of a PCM system with equivalent quality.

LINE CODES Converting standard logic level to a form more suitable to telephone line transmission. The line codes properties: Transmission BW should be small as possible Efficiency should be as high as possible Error detection & correction capability Transparency (Encoded signal is received faithfully)

continue... Six factors must be considered when selecting a line encoding format; transmission voltage & DC component Duty cycle Bandwidth consideration Clock and framing bit recovery Error detection Ease of detection and decoding

Why Digital Signaling? Low cost digital circuits The flexibility of the digital approach (because digital data from digital sources may be merged with digitized data derived from analog sources to provide general purpose communication system)

Digital Modulation Using Digital Signals to Transmit Digital Data Bits must be changed to digital signal for transmission Unipolar encoding Positive or negative pulse used for zero or one Polar encoding Uses two voltage levels (+ and - ) for zero or one Bipolar encoding +, -, and zero voltage levels are used

Non-Return to Zero-Level (NRZ-L) Two different voltages for 0 and 1 bits. Voltage constant during bit interval. no transition, no return to zero voltage More often, negative voltage for one value and positive for the other.

Non-Return to Zero Inverted (NRZ-I) Non-return to zero inverted on ones Constant voltage pulse for duration of bit The polarity of the bit is reversed when a 1 bit is encountered All subsequent 0s following the 1 are recorded at the same polarity

Multilevel Binary(Bipolar-AMI) zero represented by no line signal one represented by positive or negative pulse one pulses alternate in polarity No loss of sync if a long string of ones (zeros still a problem) No net dc component Lower bandwidth Easy error detection 0 1 0 0 1 1 0 0 0 1 1

Pseudoternary One represented by absence of line signal Zero represented by alternating positive and negative No advantage or disadvantage over bipolar-AMI 0 1 0 0 1 1 0 0 0 1 1

Manchester There is always a mid-bit transition {which is used as a clocking mechanism}. The direction of the mid-bit transition represents the digital data. 1  low-to-high transition 0  high-to-low transition Consequently, there may be a second transition at the beginning of the bit interval. Used in 802.3 baseband coaxial cable and CSMA/CD twisted pair.

Differential Manchester mid-bit transition is ONLY for clocking. 1  absence of transition at the beginning of the bit interval 0  presence of transition at the beginning of the bit interval Differential Manchester is both differential and bi-phase. [Note – the coding is the opposite convention from NRZI.] Used in 802.5 (token ring) with twisted pair. * Modulation rate for Manchester and Differential Manchester is twice the data rate  inefficient encoding for long-distance applications.

Example 5 Sketch the data wave form for a bit stream 11010 using NRZL Bipolar AMI Pseudoternary Manchester

END OF PART 2