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

Cont’d... 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.

Cont’d...

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.

Advantages & Drawbacks of Pulse Modulation Requires greater BW to transmit & receive as compared to its analog counterpart. Special encoding & decoding methods must be used to increased transmission rates & more difficult to be recovered. Requires precise synchronization of clocks between Tx & Rx. Noise immunity. Relatively low cost digital circuitry. Able to be time division multiplexed with other pulse modulated signal. Storage of digital streams. Error detection & correction

Sampling 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 >= fm (max)

Cont’d... 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 Common used 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.

Cont’d… 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

PULSE CODE MODULATION (PCM) Basic scheme of PCM system Quantization Quantization Error Companding Block diagram & function of TDM-PCM communication system

Basic scheme of PCM system 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.

Cont’d... Because voice data limited to frequencies below 4000 Hz, a codec makes 8000 samples/sec. (i.e., 125 microsecond/sample). 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.

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

Cont’d… Analog signal is sampled. Converted to discrete-time continuous-amplitude signal (Pulse Amplitude Modulation) Pulses are quantized and assigned a digital value. A 7-bit sample allows 128 quantizing levels. PCM uses non-linear encoding, i.e., amplitude spacing of levels is non-linear There is a greater number of quantizing steps for low amplitude This reduces overall signal distortion. This introduces quantizing error (or noise). PCM pulses are then encoded into a digital bit stream. 8000 samples/sec x 7 bits/sample = 56 Kbps for a single voice channel.

PCM Example

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).

Cont’d... Analog input signal Sample pulse PAM signal PCM code

Cont’d… The quantization interval @ quantum = the magnitude difference between adjacent steps. The resolution = the magnitude of a quantum = the voltage of the minimum step size. The quantization error = the quantization noise = ½ quantum = (orig. sample voltage – quantize level) PCM code = (sample voltage/resolution)

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

Types of Quantization Midtread Midrise

Types of Quantizer 1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform.

Dynamic Range (DR) Largest possible magnitude/smallest possible magnitude. 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 = 36.82 dB and q =0.2 V.

Effect of Non-Linear Coding

Nonlinear Encoding Quantization levels not evenly spaced Reduces overall signal distortion Can also be done by companding

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 DR of a communication system.

Companding Functions

Method 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

Example 3 A companding system with µ = 255 used to compand from 0V to 15 V sinusoid signal. Draw the characteristic of the typical system. Draw an 8 level non-uniform quantizer characteristic that corresponds to the mentioned µ.

Cont’d... 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.

Cont’d… 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.

Time-Division Multiplexing This technique combines time-domain samples from different message signals (sampled at the same rate) and transmits them together across the same channel. The multiplexing is performed using a commutator (switch). At the receiver a decommutator (switch) is used in synchronism with the commutator to demultiplex the data.

Cont’d… TDM system is very sensitive to symbol dispersion, that is, to variation of amplitude with frequency or lack of proportionality of phase with frequency. This problem may be solved through equalization of both magnitude and phase. One of the methods used to synchronize the operations of multiplexing and demultiplexing is to organize the multiplexed stream of data as frames with a special pattern. The pattern is known to the receiver and can be detected very easily.

Block diagram of TDM-PCM communication system