UNIT 3 Digital Transmission

INTRODUCTION: Digital Transmission - Transmission of digital signals from one point to other point

in a communication system. Source information signal - can be binary or any other form of discrete-level digital

pulses. Also can be analog signals that can be converted into digital signals before the

transmission and then converted back to analog signals in the receiver section. Transmission medium - Metallic wire, co-axial cable (or) an optical fiber is used to

interconnect various points of the digital transmission system.

ADVANTAGES OF DIGITAL TRANSMISSION: More noise immunity. More accurate than analog transmission. Easy for processing and multiplexing. Digital signals can be stored easier. Transmission rate can be changed easily. Use signal regeneration technique than amplification. Transmission over longer distances. Digital signals can be evaluated easily. Performance of errors can be evaluated in a better way. (i.e.,) Error signals can be

detected and corrected easily.

DISADVANTAGES OF DIGITAL TRANSMISSION: Requires more bandwidth for transmission. More cost. Need of additional encoding and decoding circuit, so that the analog signals can be

converted in to digital signals before the transmission and the analog signals are recovered back at the receiver.

Requires expensive clock recovery circuits in the receivers for the accurate time synchronization between transmit and receive clocks.

Digital transmission system facilities are incompatible with older analog transmission system.

PULSE MODULATION: Technique of converting information into pulse form for transferring pulses from

source to destination. Carrier is of discrete pulses rather than being a sine wave.

DEFINITION: Process of sampling the analog information signals. Then converting those samples into discrete pulses and transmitting the pulses from

source to destination over a physical transmission medium.

CLASSIFICATION OF PULSE MODULATION TECHNIQUE:Pulse modulation can be classified as

Analog Pulse Modulation Digital Pulse Modulation

1. Analog Pulse Modulation: Pulse width modulation (PWM) Pulse amplitude modulation (PAM) Pulse position modulation (PPM)

2. Digital Pulse Modulation: Pulse code modulation (PCM) Delta Modulation (DM) Adaptive Delta Modulation (ADM)

PWM: (Pulse Width Modulation) Also called as Pulse Duration Modulation (PDM) or Pulse Length Modulation (PLM). Width of the constant amplitude pulse is varied in accordance with the amplitude of

the analog signal.PPM: (Pulse Position Modulation)

Position of the constant width pulse is varied in accordance with the amplitude of the analog signal.

PAM: (Pulse Amplitude Modulation) Amplitude of the constant width pulse, constant position pulse is varied in accordance

with the amplitude of the analog signal.PCM : (Pulse Code Modulation)

Analog signal is sampled first, and then converted to a fixed length, serial binary number for transmission.

Binary number is varied in accordance to the amplitude of the analog signal.

(a)Analog signal (b) Sample pulse (c) PWM (d)PPM (e) PAM (f) PCM PULSE CODE MODULATION (PCM):

Most popular form of pulse modulation is pulse code modulation. Developed by AT + T in the year 1937 at Paris laboratories. Pulse code modulation refers a form of source coding. Form of digital modulation technique in which the code refers a binary word that

represents digital data. With PCM, the pulses are of fixed length and fixed amplitude. Here a pulse of prescribed time slot represents either a logic' l' (or) logic '0' condition. Not really a type of modulation but rather a form of digitally coding analog signals.

BLOCK DIAGRAM OF PCM TRANSMISSION SYSTEM:TRANSMITTER SECTION:

Analog input signal is applied to the BPF. BPF limits the frequency of the input analog signal to the standard voice-band

frequency range of 300 Hz to 3000 Hz. Sample and hold circuit periodically samples the analog input signal and converts

those samples to a multi level PAM signal. ADC converts the multilevel PAM samples to parallel PCM codes. Parallel PCM data is converted into serial data in the parallel-to-serial converter. Serial data is then passed into the transmission line as serial digital pulses. Regenerative repeaters are placed at prescribed distances to regenerate the digital

pulses. Each repeater actually reproduces the noise free PCM signal from the PCM signal

distorted by channel noise.

RECEIVER SECTION: Serial data from the transmitter is converted into parallel PCM codes by using serial-

to-parallel converter. Parallel data is then applied to the DAC which converts parallel PCM code to multi

level PAM signals. Hold circuit and the low pass filter converts the PAM signals back to its original

analog form. PCM SAMPLING:

Function of the sampling circuit in a PCM transmitter is to sample the analog signal periodically.

Then convert them into pulses, so that it can easily be converted into binary PCM code.

There are two basic techniques used to perform the sampling function:1. Natural Sampling2. Flat-top Sampling

NATURAL SAMPLING: Tops of the sampled analog waveform retain its natural shape. In natural sampling, frequency spectrum of sampled o/p is different from that of an

ideal sample. Amplitude of frequency components generated from narrow width sample pulses

decreases for the higher harmonics in (sin x)/x manner. It alters the information frequency spectrum requiring the use of frequency equalizers

before recovery by a LPF.

INPUT AND OUTPUT WAVEFORMS

NATURAL SAMPLING CIRCUIT:FUNCTION OF FET SWITCH PULSES:

Sample pulse is high àFET switch grounds the input waveform. Sample pulse is low àFET switch allows the input waveform to pass through the

output amplifier in to the input of ADC. Natural sampling output is same as the input waveform with the equally spaced

sample pulses with rounded tops.

FLAT-TOP SAMPLING: Also called as rectangular sampling. Top of the samples remains constant and is equal to the instantaneous value of the

analog signal. Used for sampling voice signals.

Achieved in a sample and hold circuit. I/p voltage is sampled with a narrow pulse and then kept relatively constant until the

next sample is taken. Sampling process alters the frequency spectrum and provides an error called aperture

error. When amplitude of the sampled signal changes during the sample pulse time, aperture

error may occur. Aperture error prevents the recovery circuit in the PCM receiver from exactly

reproducing the original analog signal voltage. SAMPLE-AND HOLD CIRCUIT:

Output of the sample and hold circuit is a fixed dc level output whose amplitude is the value at the sampling time.

When the switch is in ON condition à Q1 provides a low impedance path to deposit the analog voltage across the capacitor C1.

The time when Q1 is ON à "Aperture time" (or) acquisition time. Necessarily C1 is the hold circuit.

When Q1 is OFF position àCapacitor C1 does not have a complete path to discharge, therefore C1 stores the sampled voltage.

The storage time of the capacitor àA/D (Analog to Digital) conversion time. A/D conversion time à ADC converts the sample voltage to a PCM code.

INPUT AND OUTPUT WAVEFORMS

Short acquisition time à To ensure that a minimum change occurs in the analog signal while it is deposited across C1

.

Aperture distortion occurs à when the input to the ADC is changing during the analog to digital conversion.

Aperture distortion can be reduced by means of short aperture time and making the input to the ADC is constant.

Output impedance of voltage follower Z1 and the Q1 resistance should be small à so that the charging time of the capacitor is kept short.

There by allowing the capacitor to charge (or) discharge quickly during the short acquisition time.

Input impedance of Z2 and the leakage resistance of C1 be high as possible. Sudden drop in the capacitor voltage following each sample pulse is due to the

redistribution of the charge across C1.

Droop: The gradual discharge across the capacitor during the conversion time. Droop is caused by the discharging of capacitor thru’ its own leakage resistance and

i/p impedance of voltage follower Z2.

SAMPLING RATE: For the recovered signal to be an accurate representation of the original signal,

sampling rate is used. It has been determined that the sampling rate (fs) must be at least 2 times the highest

frequency component of the original signal to be accurately represented. i.e.,fs ≥ 2fa

where fs - Sampling rate (or) Nyquist rate (Hertz) fa - Highest frequency component of the original signal (Hz) .

If fs < 2fa, distortion will occur. This distortion is called "Aliasing" (or) "Fold over distortion".

Relationship between the original signal and the sampling frequency is called as "sampling theorem".

Sample and hold circuit is an AM modulator. Sample and hold circuit is a non-linear device which has two inputs, the sampling

pulse and the input analog signal. Hence, non linear mixing (heterodyning) occurs between these two signals. Output includes 2 original inputs (fs, fa),

their sum and difference (fs± fa), all the harmonics of fs and fa (2fs, 3fs, 2fa, 3fa) their associated cross products (2fs ± fa , 3fs± fa, etc).

The sampling pulse is made up of a series of harmonicaly related sine waves. Each of these sine wave is amplitude modulated by the analog signal and generates

sum and difference frequencies symmetrical around each of the harmonics of fs. As long as fs is twice greater than fa no other side frequencies from one harmonic

will move in to the side bands of another harmonic, thereby aliasing will not occur. When the frequency fs is less than twice the frequency of fa aliasing occurs, (i.e.,)

the frequency that folds over is an alias of the input signal.

OUTPUT SPECTRUM OF SAMPLE AND HOLD CIRCUIT:

How to eliminate the aliasing effect? Input BPF in the PCM block diagram, is called an anti-aliasing filter (or) anti fold

over filter. Its upper cut-off frequency is chosen à that the frequency greater than one half of

the sampling rate is not allowed to enter the sample and hold circuit à thereby eliminates the possibility of fold over distortion occurring.

SIGNAL-TO-QUANTIZATION NOISE RATIO: The signal voltage-to-quantization noise voltage (SQR) occurs when the input signal

is at its minimum amplitude and maximum amplitude.

QUANTIZATION: Process of converting an infinite number of possibilities into a finite number of

conditions. Process of rounding off. Analog signal contains infinite number of amplitude levels. Converting an analog signal to a PCM code with a limited number of combinations

requires quantization. Total voltage range is subdivided into a smaller number of sub ranges for quantization

process. The left most bit is the sign bit {1 = + and 0 = -}, and the two right most bits

represents the magnitude. This type of code is called a folded binary code. Because, the codes on the bottom half of the table are a mirror image of the code on

the top half, except the sign bit.

3 BIT PCM CODE:

Sign Magnitude Decimal Value Quantization Range

1 11 +3 +2.5 V to 3.5 V 1 10 +2 +1.5 V to 2.5 V 1 01 +1 +0.5 V to 1.5 V 1 00 +0 0 V to +0.5 V 0 00 -0 0 V to +0.5 V0 01 -1 -0.5 V to -1.5 V0 10 -2 -1.5 V to -2.5 V0 11 -3 -2.5 V to -3.5 V

PAM signal in the transmitter is same PAM signal as produced in the receiver. Any round-off errors in the transmitted signal are reproduced when the code is

converted back to analog in the receiver. This error is called as quantization error. This quantization error is equivalent to additive noise as it alters the signal amplitude. This error is also called as quantization noise. When the i/p signal is at its minimum amplitude (101 =+1 or 001 =-1), the worst

possible SQR occurs.SQR = minimum voltage

Quantization noise voltage = Vlsb/(Vlsb/2)

= 2where V1sb à Voltage of the least significant bit.

For the maximum amplitude of 3V (111 or 011),SQR = maximum voltage

Quantization noise voltage = Vlsb/(Vlsb/2)

= 3/(1/2) = 6

Generally SQR is not constant. For linear PCM codes, the signal power-to-quantizing noise power ratio ( or) signal-

to-distortion ratio is

where, R - Resistance (ohm)

V - rms signal voltage (Volts) q - Quantization interval (Volts) v2/R= Average signal power (watts)(q2/12)/R = Average quantization noise power

COMPANDING: Companding = Compressing + Expanding To improve the dynamic range. Companding is non-uniform companding In companding, before the transmission the higher-amplitude analog signals are

compressed. Then expanded (amplified more than the smaller amplitude levels) at the receiver.

WHY COMPANDING? In uniform quantization, once the step size is fixed, the quantization noise power

remains constant. However the signal power is not constant. Hence signal power will be small for weak

signals, but quantization noise power is constant. Therefore signal to quantization noise ratio for weak signals is very poor. This will

affect the quality of signal. The remedy is to use the companding process.

Companding can be divided into two types. They are1. Analog companding2. Digital companding

BASIC COMPANDING PROCESS: An input signal with a dynamic range of 50dB is compressed to 25dB for the purpose

of transmission, It is then expanded to 50dB at the receiver. With pulse code modulation (PCM) companding may be completed through analog

(or) digital techniques.

Early PCM systems use analog companding, but modern PCM systems use digital companding.

ANALOG COMPANDING: Analog companding = Analog compression + Analog expansion Analog compression à Implemented using specially designed diodes in analog

signal path of PCM transmitter before to the sample and hold circuit. Analog expansion à Implemented with diodes which were placed after the receive

low pass filter. Transmitter side à Analog i/p signal is filtered, compressed, sampled and converted

into parallel PCM using ADC. Parallel PCM data is converted in to serial PCM using parallel-to-serial converter.

BLOCK DIAGRAM OF DIGITAL COMPANDING:

Receiver side à Serial PCM from the transmitter is converted into parallel PCM using serial-to-parallel converter.

Received PCM code is converted into PAM signal, which is then filtered, expanded back to its original input signal.

METHODS OF ANALOG COMPANDING: Different signal distributions require different companding characteristics. For example, voice signals require constant signal-to-quantization noise ratio (SQR)

performance over a wide dynamic range. This condition requires a logarithmic compression ratio. There are two methods of analog companding used that approximate a logarithmic

function and are called as log-PCM codes. The two methods are

1. μ- law companding2. A - law companding

μ LAW COMPANDING: μ law companding is used in united states and Japan. The compression characteristic for μ- law is

where Vmax = Maximum uncompressed analog input amplitude (Volts). Vin = Amplitude of the input signal at a particular instant of time (Volts).

μ = Parameter used to define the amount of compression (no unit).

Vout = Compressed output amplitude (Volts).

μ - LAW COMPRESSION CHARACTERISTICS:

Higher the μ à more compression Lower the μ à less compression

at μ = 0; curve is linear, no compression. μ = determines the range of signal power in which SQR is relatively

constant. For constant SQR and 40 - dB dynamic range, μ = 100 (or) larger is required. Early digital transmission systems used seven-bit PCM code with μ = 100. Recent digital transmission systems use 8 - bit PCM code with μ = 255.

A-LAW COMPANDING: ITU- T has established A-law companding in Europe. A - law has flatter SQR than μ law. The compression characteristics of A-law companding is

DIGITAL COMPANDING: Digital compression à Performed at the transmit end after the conversion to linear

PCM code. Expansion àPerformed at the receiver end before PCM decoding. Analog input is first filtered by band pass filter. Linear parallel PCM code is compressed by digital compressor. Compressed parallel PCM is converted into compressed serial PCM, which is then

transmitted.

BLOCK DIAGRAM OF DIGITAL COMPANDING:

At the receiver side à Compressed serial PCM is received, then converted into compressed parallel PCM by using serial to parallel converter.

Compressed parallel PCM is then digitally expanded, then decoded, which represents the original output.

The most recently digitally compressed PCM is 12-bit linear code and an 8-bit compressed code.

This companding process resembles μ = 255 compression characteristics with set of eight straight-line segments (0 to 7).

μ - 255 COMPRESSION CHARACTERISTICS (POSITIVE VALUES ONLY) The compression curve for negative values is identical.

Though there are l6-segments (8-positive, 8-negative), this scheme is called 13-segment compression, because the curve segments +0, + 1, -0, -1 is a straight line with constant slope.

8 BIT μ -255 COMPRESSED CODE FORMAT:

The digital companding algorithm for 12-bit-linear to 8-bit compressed code is simple.

8-bit compressed code format consists of sign {1= +, 0= -} bit 3-bit segment identifier from 000 to 111 4-bit magnitude code that represents the quantization interval from 0000 to

1111.

DESCRIPTION OF ENCODING TABLE: X represents the truncated bits during compression. A, B, C, D are the bits will be transmitted as it is. Sign bit "S' is also transmitted as it is.

μ - 255 ENCODING TABLE:

COMPRESSION PROCESS: Given analog signal is sampled and converted into a linear 12-bit sign magnitude

code. Sign bit is transferred to the 8-bit code.

Segment Identifier Calculation: Segment number is calculated by counting the number of 0's in the 11-bit

magnitude begins with MSB. (i.e.,) S 0 0 0 0 01 ABCDX; count the numbers of 0's, it is 5. Then subtract the number of 0's obtained from 7 (should not exceed 7).

7 – 2 =5 The result is the segment number, which is converted to a 3 bit binary number and

inserted into 8 bit code as segment identifier. 4 magnitude bits (A, B, C, D) represent are the 4-bit quantization interval are

substituted in the LSB of 8-bit compressed code. In case of segment 0 and 1, all the 12- original bits are recovered exactly at

the output of the decoder. For segment 4, only the MSB of 9 bits are recovered. For segment 7, only the MSB of 6 bits are recovered. With the 11-bit magnitude (Except sign bit), there are 211 = 2048 possible

codes. Segment 0 and 1 à No compression. Therefore all the 16 possible codes

can be recovered. Segment 2 à there is a 2:1 compression ratio; out of 32 possible transmit

codes, only 16 can be recovered. Segment 3 à there is a 4:1 compression ratio; out of 64 possible transmit

codes only 16 possible recovered codes. Compression ratio for segment 7 is 64:1; out of 1024 transmit codes, only

16 possible recovered codes. Compression ratio doubles with each successive segment.

Sub segment: Segments 2 through 7 are subdivided into smaller sub segments. Each segment has 16 sub segments with respect to the 16 possible combinations of A,

B, C, 0 (0000-1111). In segment 2, there are 2 codes per sub segment. There are 16 sub segments

(i.e., 16 * 2 = 32) In segment 3, for each sub-segment, there are 4 codes

(i.e., 16 * 4 = 64) The number of codes per sub segment doubles with each subsequent segment.

Decompression: In decoder most significant of truncated bits are reinserted as logic 1. Remaining truncated bits are reinserted as 0’s. Maximum magnitude error due to compression and decompression process is

minimized. Decoder guesses what the truncated bits were prior to encoding. Most logical guess is halfway between the minimum and maximum magnitude codes. For example, in segment 6, the five LSB are truncated during compression. During decompression, the decoder will try to determine what those bits were. The

possibilities include any code between 00000 and 11111. The logical guess is 10000, approximated half the maximum magnitude.

DIGITAL COMPRESSION ERROR: The magnitude of the compression error is not same for all the samples. The following formula is used to compute the percentage Error introduced by Digital Compression.

% error = (12 bit encoded voltage – 12 bit decoded voltage) * 100 12 bit decoded voltage

DELTA MODULATION (DM):

In PCM, it is necessary to transmit all the bits, which are used to code a sample. Therefore channel bandwidth and signal rate are increased. To overcome this

drawback delta modulation is used. In DM, a single-bit PCM code is used to achieve digital transmission of analog

signals. With DM, Instead of transmit a coded representation of the sample, only a single bit is

transmitted, which indicates that whether the sample is larger (or) smaller than the previous sample.

Logic '0' is transmitted when the current sample is smaller than the previous sample. Logic' 1 ' is transmitted, when the current sample is larger than the previous sample.

DELTA MODULATION TRANSMITTER

Analog i/p signal is sampled and converted into a PAM signal. O/p of the PAM signal is then compared with the DAC o/p. DAC o/p is a voltage which is equal to the regenerated magnitude of the previous

sample stored in the up/down counter as binary number. Up/down counter is incremented or decremented depending on whether the previous

sample is larger or smaller than the current sample. Clock rate of up/down counter is equal to the sampling rate. Hence the up/down

counter is updated after each comparison.

OPERATION OF DM TRANSMITTER

First, the up/down counter is zeroed and the DAC o/p is 0 V. Analog i/p is first sampled and then converted to a PAM signal. PAM signal output is then compared with the DAC o/p which is 0 voltage.

O/p of the comparator is logic "1" ( +1V ), which indicates that the current sample amplitude is larger than the previous sample.

When the next clock pulse is initiated, the up/down counter is incremented to 1. Now the DAC output is a voltage which is equal to the magnitude of the minimum

step size. Step change value is equal to the clock frequency rate (sample rate). Similarly for the given input signal, the up/down counter follows the steps until the

DAC output exceeds the analog sample. Each time the up/down counter is incremented, logic "1" is transmitted, and logic '0' is

transmitted when the up/down counter is decremented.

DELTA MODULATION RECEIVER: If the logic 1's and 0's are received, then the up/down counter is incremented (or)

decremented accordingly. Based on the incremented (or) decremented values, the DAC which produces PAM

output, which is then filtered by LPF, results the original signal.

With DM, each sample requires the transmission of only one bit, there by the bit rates are lower than PCM systems.

ADVANTAGES OF DELTA MODULATION: Transmits only one bit per sample. Hence channel bandwidth and signal rate is less

compared to PCM. ADC is not required. Transmitter and receiver implementation is very easy.

DRAWBACKS OF DELTA MODULATION:1. Slope overload distortion2. Granular noise

SLOPE OVERLOAD DISTORTION: This distortion arises due to large dynamic range of the i/p signal. Figure shows that the rate of raise of the input analog signal is so high, so that the

staircase signal (DAC o/p) can’t trace it. (i.e.,) the slope of the analog signal is greater that the delta modulator can maintain.

Hence there is a large error difference between DAC o/p and the original analog signal.

This error or noise is called as “slope overload distortion”. When the slope of the analog input signal is greater than the DAC output (or) when

the analog input signal changes at a faster rate than OAC output, results in slope overload distortion.

HOW TO REDUCE THE SLOPE OVERLOAD DISTORTION? By means of increasing the clock frequency. To increase the magnitude of the minimum step size.

GRANULAR NOISE: Granular noise (or) idle noise occurs, when the step size is too large compared to

small variations in the analog i/p signal. Figure shows that when the analog signal is almost flat, the staircase signal keeps on

oscillating around the analog signal. The error between the analog i/p signal and stair case signal is called as granular

noise. To overcome this problem step size should be reduced.

Figure represents the difference between the original signal and the reconstructed signal.

Granular noise occurs, when there is a variation of amplitude in the reconstructed signal with the original signal.

HOW TO REDUCE GRANULAR NOISE? By means of decreasing the step size. Small resolution is needed.

ADAPTIVE DELTA MODULATION: Due to slope overload and granular noise, the quantization noise occurs in delta

modulation. To overcome this error, the step size of the DAC o/p is automatically varied, in

accordance with the characteristics of the analog signal. This process is called Adaptive Delta Modulation.

OPERATION OF ADAPTIVE DELTA MODULATION: • When the transmitter o/p is a consecutive of 1's (or) 0's, which indicates the slope of

the DAC o/p is less than the slope of the analog signal either in positive (or) negative direction.With ADM, the step size is automatically increased, after a pre-determined number of consecutive 1's (or) 0's sequence.

Even after the next sample, the DAC output amplitude is still below the sample amplitude then the next sample is increased until the DAC output synchronous with the analog input signal.

When an alternative sequence of 1's and 0's is occurs, which indicates the possibility of high granular noise.

With ADM, the step size of DAC output is automatically varies thereby the magnitude of the noise error is reduced.

A common algorithm is used for ADM is, when three consecutive 1's (or) 0's occurs. Then the step size of the DAC output is increased (or) decreased by a factor of 1.5

other algorithms can be used depending on system requirements.

ADVANTAGES OF ADAPTIVE DELTA MODULATION: SNR is better than delta modulation, since slope overload distortion and idle noise is

reduced. Due to variable step size, the dynamic range of ADM is wider than DM. Bandwidth utilization is better than DM.

DIFFERENTIAL PULSE CODE MODULATION: In a PCM encoded waveform, the samples of a signal are highly correlated with each

other. (i.e.,) its value from present sample to next sample doesn’t differ by large amount.

The adjacent samples of the signal will carry the same information with minor difference.

When these samples are encoded by standard PCM system, the resulting encoded signal contains some redundant information.

If the redundancy is reduced, then the overall bit rate will get decreased and the number of bits required to transmit one sample will also get reduced.

This method of pulse code modulation is Differential Pulse Code Modulation (DPCM).

With DPCM - difference between the amplitude of two successive samples is transmitted instead of the actual sample.

This is because of the range of the sample differences is less than the range of individual samples.

DPCM TRANSMITTER Analog input signal is band limited to one-half of the sample rate. Then compared with the preceding accumulated signal level in the differentiator. Output of the differentiator is the difference between the two signals. The difference signal is PCM which is then encoded and transmitted. Output of the ADC is the parallel DPCM which is then converted in to serial DPCM

with the help of parallel-to-serial converter.

DPCM RECEIVER: Each received serial DPCM is converted into parallel DPCM, and then converted

back to analog signal, then stored and added with the next received sample. Integration part is performed on the analog signals, although it could also be

performed digitally.

PULSE TRANSMISSION: All types of digital carrier system involve the transmission of pulses through a guided

medium with a finite bandwidth. A highly selective system would require more number of filter sections. It is

impractical. In practical all digital systems generally utilize filters with bandwidth that are

approximately 30% (or) more in excess of the ideal nyquist bandwidth.

TYPICAL PULSE RESPONSE OF A BAND LIMITED FILTER Figure shows that by means of band limiting a pulse causes the energy from the pulse

to be spread over a longer time in the form of secondary lobes. The secondary lobes are also called as ringing tails. The output frequency spectrum of a rectangular pulse is referred to as a (sin x) / x and

is given as

• ω= 2Πf• T = Pulse width (seconds)

SPECTRUM OF SQUARE PULSE WITH DURATION 1/T

Shows the distribution of total spectrum power. From the figure, it shows approximately 90% of the signal power lies within the first

spectral null (f = 1/T). The signal can be confined to a bandwidth B = 1/T and pass most of the energy from

the original waveform. When the bandwidth B is confined to B = 1/T, then the maximum signaling rate is

achievable with LPF without any distortion with the condition of nyquist rate is equal to twice of bandwidth i.e.,

R = 2Bwhere R = Signaling rate = 1/T

B = Specified bandwidth

INTER SYMBOL INTERFERENCE: When the channel BW is much greater than the pulse BW, the spreading of pulse is

small. When the channel BW is close to the pulse BW, the spreading will exceed symbol

duration and cause signal pulse to overlap known as ISI. (i.e.,) ISI (Inter Symbol Interference) is a form of distortion of a signal in which one

symbol interferes with subsequent symbols. ISI may be present even noise is absent.

(a) NRZ Input signal (b) Output form a perfect filter (c) Output form an imperfect filter

The figure below shows the i/p signal (NRZ) to the minimum BW LPF. I/p signal which is random, binary non-return-to-zero (NRZ) sequence. Response of a perfect LPF without any phase (or) amplitude distortion. O/p of a imperfect low pass filter with distortion. Figure (b) shows the o/p of the perfect LPF that doesn’t introduce any phase or

amplitude distortion. Where the o/p signal reaches its maximum value for each transmitted pulse at center

of each sampling interval. Figure (c) shows the o/p of the imperfect LPF that doesn’t always attain maximum

value at the sampling instants. This ringing tails of several pulses have overlapped thus interfering with the major

lobe. This interference is called as ISI. For rectangular pulses, the o/p will not remain rectangular in less than an infinite BW. For narrower BW, there will be more rounded pulses. If the phase distortion is excessive, the pulse will tilt and affect the next pulse. It

causes cross talk. When pulses from more than one sources are multiplexed together, the amplitude,

frequency and phase responses become even more critical. Equalization techniques can be used to overcome the ISI effect.

The four primary causes of ISI are:(i) Timing in accuracies:

Transmitter timing inaccuracies cause ISI if the rate of transmission doesn’t conform to the ringing frequency.

Receiver clocking information is obtained from received signals, which contains noise, results in sample timing inaccuracies in receivers than in transmitters.

(ii) In sufficient bandwidth: If the transmission rate is below the channel BW, timing error occurs. As the BW is insufficient à then the ringing frequency is reduced and ISI is more likely to occur.

(iii) Amplitude distortion: Normally filters are used to eliminate noise and interference. Filters are also used to produce a specific pulse response. However the frequency response of a channel cannot always be predicted

accurately. Pulse distortion occurs when the peaks of pulses are reduced, causing

improper ringing frequencies in time domain.(iv) Phase distortion:

Phase distortion occurs when frequency components undergo different amount of time delay while propagating through the transmission medium.

Phase distortion can be reduced by using the special delay equalizers in the transmission path.

EYE PATTERNS: Performance of the digital system can be measured by displaying the received signal

on an oscilloscope and triggering the time base at the data rate. It is also known as eye diagram.

Eye pattern is an oscilloscope display in which a digital signal from a receiver is repeatedly sampled and is applied to the vertical input, while the data rate is used to trigger the horizontal sweep.

Eye patterns à convenient technique for determining the effects of degradations in to the pulses as they pass to the regenerator.

The resulting display resembles a human eye.

EYE PATTERN MEASUREMENT SET UP

Digital source is band limited and the pulse stream is applied to the vertical input. Symbol clock is then fed to the horizontal input of the oscilloscope. Sweep rate is set approximately equal to the symbol rate.

EYE PATTERN FOR TERNARY SIGNALS In case of ternary signals, the individual pulses at the input to the regenerator have a

cosine-squared shape.Vertical:

+ 1, 0, -1 à vertical lines corresponds to received amplitudes. Vertical hairs à represents the decision times.

Horizontal: Horizontal lines separated by the signaling interval T, corresponds to the decision

times. Horizontal hairs à represent decision level.

Cross hairs à Decision levels of the regenerator.

Eye Diagram: Eye opening à Area in the middle of the eye pattern which defines a boundary within

which no waveform trajectories can exist under any code-pattern condition. To generate the pulse sequence without error, the eye must be open and the decision

level cross hairs must be within the open area. From the diagram à It can be seen that at the center of the eye, the opening is about

90% indicates minor ISI degradation. Mathematically, the ISI degradation is given as

H àideal vertical opening (cm)h à degraded vertical opening (cm)

For the eye diagram ISI is

There are many measurements that can be obtained from eye diagram are

Amplitude Measurements: Eye amplitude Eye crossing amplitude Eye crossing percentage Eye height. Eye level Eye SNR Quality factor Vertical eye opening

Time measurements: Deterministic jitter Eye crossing time Eye delay Eye fall time Eye rise time Eye width Horizontal eye opening Peak-to-peak jitter Random jitter RMS jitter

STEPS FOR COMPRESSION AND DECOMPRESSION: The digital compression is performed in the ADC. An analog signal is digitized into

12 bits using linear encoding and compressed to 8 bits:

Compression can be performed as follows: The 1st bit [sign bit] is left unaffected. Determine the segment number: subtract from 7, the number of leading

zero's in the 12-bit word [this forms the segment number and constitutes the next 3 bits of the compressed 8-bit word].

Determine the interval within the segment: copy the next 4 bits of the 12 bit word, into the next 4 bit positions of the 8 bit word.

If there are more than 7 leading zeros, set the segment number to zero and copy the last 4 bits of the 12-bit word into the last 4 bit positions of the 8 bit word.

Digital expansion occurs in the D/A converter section. The 8-bit word can be expanded to 12 bits as follows:

The 1st bit [sign bit] is left unaffected The segment number is used to regenerate the number of leading zeros The next 4 bits are inserted as is

If there are many more bit positions left in the 12 bit word, the next bit is set high, and all others are set low [since the last group of bits is not known, the mid value is chosen]

The consequences of this scheme are:•   Segments 0 & 1 in the 12-bit word are accurately reproduced•   Segment 2, which has 32 possible 12-bit codes, is compressed to 16, 8-bit codes•   Segment 3, which has 64 possible 12-bit codes, is compressed to 16, 8-bit codes etc.

EXAMPLE:1. Determine the 12 bit linear code, 8 bit compressed code, the decoded 12 bit code, the

quantization error and the compression error for a resolution of 0.01 V and analog sample voltages of (a) -0.318

Solution:(a) To determine the 12 bit linear code, Divide the sample voltage by the resolution

-0.318 V / 0.01 V = -31.8 V Round off the quotient

-31.8 V à rounded off to -32 producing a quantization errorQuantization Error Qe = -0.2 (0.01) = - 0.002 V

Convert the result to a 12 bit sign magnitude code.12 bit linear code = 0 0 0 0 0 0 1 0 0 0 0 0

S A B C D

11 bit magnitude 00000100000= 31COMPRESSION:To determine the 8 bit compressed code:

0 0 0 0 0 0 1 0 0 0 0 0 S 7-5 = 2 A B C D X

8 bit compressed code: 0 0 1 0 0 0 0 0

DECOMPRESSION:To determine the 12 bit recovered code, simply reverse the process:

0 0 1 0 0 0 0 0 S 7-2 = 5 A B C D

12 bit recovered code:0 0 0 0 0 0 1 0 0 0 0 0 1 = -33

The LSB is determined from the decoding table.Most significant of the truncated bits is always set (1) and all other truncated bits are cleared (0).

Decoded Voltage = -33(0.01) =-0.33VCompression error = 0.33 – 0.318 =0.012V