1 4.2 digital transmission outlines □ pulse modulation □ pulse code modulation □ delta...

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4.2 Digital Transmission

Outlines

□ Pulse Modulation□ Pulse Code Modulation□ Delta Modulation□ Line Codes

EKT 231 : COMMUNICATION SYSTEMEKT 231 : COMMUNICATION SYSTEM

CHAPTER 4 : DIGITAL TRANSMISSIONCHAPTER 4 : DIGITAL TRANSMISSION

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Conversions Between Signal Types

Sampling

Quantizing

Encoding

Review

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□Sampling analog information signal□Converting samples into discrete

pulses□Transport the pulses from source to

destination over physical transmission medium.

PULSE MODULATION PULSE MODULATION (PM)(PM)



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Cont’d...Cont’d...

□Four (4) Methods of PM1. PAM

2. PWM3. PPM4. PCM

PAM–Pulse Amplitude Modulation, PWM-Pulse Width Modulation

PPM-Pulse Position Modulation, PCM-Pulse Code Modulation

Analog Pulse Modulation

Digital Pulse Modulation



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□ 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.



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• The amplitude of pulses (carrier) is varied in accordance with the information signal.

• Width & position constant.

Pulse Amplitude Modulation (PAM)



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Pulse Width Modulation (PWM)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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Cont’d...



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• Modulation in which the temporal positions of the pulses are varied in accordance with some characteristic of the information signal.

• Amplitude & width constant.

Pulse Position Modulation (PPM)



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Advantages & Drawbacks of Pulse Advantages & Drawbacks of Pulse ModulationModulation

□ 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

□ 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.



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SamplingSampling

□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 >= 2fm (max)



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Example 1Example 1

□A CD audio laser disk system has a frequency bandwidth of 20Hz to 20kHz.

What is the minimum sample rate required to satisfy the Nyquist sample rate?Ans: fs=2fm(max)=40kHz.



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□Two basic techniques used to perform the sampling function:□Natural sampling□Flat-top sampling



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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



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Natural Sampling



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Flat-top SamplingFlat-top Sampling

□Most commonly 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.



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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



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Flat-top Sampling



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□Basic scheme of PCM system□Quantization□Quantization Error□Companding□Block diagram & function of TDM-PCM

communication system



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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.



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codeccodec

□Coder-decoder



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

□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.



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PCM Block Diagram

• Most common form of analog to digital modulation (better noise and interference immunity)

• Four step process1. Signal is sampled using PAM

(Sample)2. Integer values assigned to signal

(PAM)3. Values converted to binary

(Quantized)4. Signal is digitally encoded for

transmission (Encoded)



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4 Steps Process



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Quantization Quantization □Quantization-the process of converting an

infinite number of possibilities to a finite number of conditions.

□The process of rounding off the amplitudes of flat top sample to a manageable number of levels.

□The process of segmenting a sampled signal in a PCM system into different voltage levels, each level corresponding to different binary number.

□The quantization levels determine the resolution of the digitizing system.

□Analog signals are quantized to the closest binary value.EKT 231 : COMMUNICATION SYSTEMEKT 231 : COMMUNICATION SYSTEM


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Cont’d…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.



27EKT 231 : COMMUNICATION SYSTEMEKT 231 : COMMUNICATION SYSTEM


Sampling pulses

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PCM Example



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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).



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The quantization interval or quantum = the magnitude difference between adjacent steps.

The resolution = the magnitude of a quantum = the voltage of the minimum step size.

The quantization error (Qe) = the quantization noise (Qn)

= ½ quantum = (orig. sample voltage – quantized level)

Folded PCM code = (sample voltage/resolution)

Cont’d…Cont’d…



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Analog input signal

Sample pulse

PAM signal

PCM codeEKT 231 : COMMUNICATION SYSTEMEKT 231 : COMMUNICATION SYSTEM


Exactly 2V

No Qe

Exactly -1V

No Qe

Approximately +2.6 V

Qe

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Example 2

□From the information given in the previous slide, determine the following;

(i) Resolution (ii) Sample voltage at t3

(iii) Qe at t3

(iv) Explain the quality of the generated PCM

Ans: 1V,2.6V,0.4V,



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

QUANTIZATION ERROR



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Types of Quantization

Midtread Midrise



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Example 3Example 3

□Using the same information, for the PCM code for analog sample voltage of +1.07V, determine;

(i) Quantized voltage (ii) Qe

(iii) PCM code

Ans : 1,0.07,101EKT 231 : COMMUNICATION SYSTEMEKT 231 : COMMUNICATION SYSTEM


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Types of Quantizer1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform.



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Dynamic Range (DR)

□Ratio of the 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

resolution

V

V

VDR max

min

max

12 nDR)log(20)( DRdBDR



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Example 4Example 4

1. Calculate the dynamic range for a linear PCM system using 16-bit quantizing.

2. Calculate the number of bits in PCM code if the DR = 192.6 dB



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Coding Efficiency

□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



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Example 5 Example 5

Given A PCM system with the following parametersMaximum analog input frequency = 4kHz.Maximum decoded voltage at Rx = ±2.55V.Minimum dynamic range = 46 dB

Determine : (i) Minimum sample rate. (ans: 8kHz)

(ii) Minimum number of bits used (ans :n=7.63≈8)

(iii) Resolution (ans : 0.01V )

(iv) Quantization error (ans: 0.01V/2=0.005V)

(v) Coding efficiency (ans: (8.63/9)x100%=95.89%)



1 4.2 digital transmission outlines □ pulse modulation □ pulse code modulation □ delta...

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