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DIGITAL COMMUNICATION

UNIT I- SAMPLING AND WAVEFORM CODING

1. Define Dirac comb or ideal sampling function. What is its Fourier Transform?

Dirac comb is nothing but a periodic impulse train in which the impulses are

spaced by a time interval of Ts seconds. The equation for the function is given by

Fourier Transform is,

2.Give the interpolation formula for the reconstruction of the original signal g(t)

from the sequence of sample values {g(n/2W)}.

where 2W is the bandwidth, n is the number of samples.

3. State sampling theorem.

If a finite energy signal g(t) contains no frequencies higher than W hertz, it is

completely determined by specifying its co-ordinates at a sequence of points spaced1/2W seconds apart.

If a finite energy signal g(t) contains no frequencies higher than Whertz, it may be

completely recovered from its co-ordinates at a sequence of points spaced 1/2W seconds

apart.

4. Define quadrature sampling.

Quadrature sampling is used for uniform sampling of band pass signals. Consider

The in-phase component gI(t) and the quadrature component gQ(t) may be

obtained by multiplying the signal by cos(2fct) and sin(2fct) respectively and then

suppressing the sum-frequency components by means of appropriate low pass filter.

Under the assumption that fc>W,we find that gI(t)&gQ(t) are both low-pass signalslimited to -W

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7. What is meant by PCM?

Pulse code modulation (PCM) is a method of signal coding in which the

message signal is sampled, the amplitude of each sample is rounded off to thenearest one of a finite set of discrete levels and encoded so that both time and

amplitude are represented in discrete form.. This allows the message to be

transmitted by means of a digital waveform.

8. Define quantizing process.

The conversion of analog sample of the signal into digital form is called

quantizing process. It represents signal discrete in both amplitude and time.9. What is a quantizer?

It is memory less, symmetric device with L number of representation levels.

Y=Q(m)

Where Q-stair case function, m-input signal, Y- output signal

10. What you mean by uniform and non-uniform quantization?

In uniform quantization the step size is constant ie the representation levels are

uniformly spaced.Non-uniform quantization the step size is variable ie the step size increases as the

separation form origin of input output amplitude is increased. Non-uniform

quantization is process of passing baseband signal through compressor and applying

compressed signal to a uniform quantizer.11. What is the disadvantage of uniform quantization over the non-uniform

quantization?

In uniform quantization the step size is constant ie the representation levels areuniformly spaced. In this case it is difficult to accommodate the input with wide varying

power levels. SNR decreases as the power level goes beyond the overload point.

Non-uniform quantization the step size is variable ie the step size increases as theseparation form origin of input output amplitude is increased. SNR is constant for wide

range of input power level. Large step size can accommodate large infrequently occurring

amplitudes and small step size can offers weak passage protection .

12. What are the two fold effects of quantizing process.

1. The peak-to-peak range of input sample values subdivided into a finite set of decisionlevels or decision thresholds

2. The output is assigned a discrete value selected from a finite set of representationlevels are reconstruction values that are aligned with the treads of the staircase.

13. What is meant by idle channel noise?

Idle channel noise is the coding noise measured at the receiver output with zerotransmitter input.

14. What is meant by prediction error?

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The difference between the actual sample of the process at the time of interest and

the predictor output is called a prediction error.

15. Define delta modulation.

Delta modulation is the one-bit version of differential pulse code modulation.

Using one bit quantization the future values are predicted from the single past sample.

16. Define adaptive delta modulation.The performance of a delta modulator can be improved significantly by making

the step size of the modulator assume a time- varying form. In particular,during a steep

segment of the input signal the step size is increased. Conversely, when the input signal isvarying slowly, the step is reduced, In this way, the step size is adapting to the level of

the signal. The resulting method is called adaptive delta modulation (ADM).

17. Name the types of uniform quantizer?

1. Mid tread type quantizer. 2. Mid riser type quantizer.

18. Define mid tread quantizer?

In mid tread quantizer Origin of the signal lies in the middle of a tread of the

staircase.Inmid-riser quantizer Origin of the signal lies in the middle of a riser of the

staircase

mid- tread quantizer mid-riser quantizer

19. Define quantization error?

Quantization error is the difference between the output and input values ofquantizer.It occurs due to the rounding off of sample values of analog baseband signal to

the nearest permissible representation levels of quantizer

Y=Q(m)where Q-stair case function, m-input signal, Y- output signal

then yk=m+q

m - input signal, yk - output signal , q - quantiztion error

20.What is the Stepsize in a uniform quantizer for the data range of (- mmax , mmax).Stepsize= 2 mmax/ L whereL- number of amplitude levels

21. What you mean by non-uniform quantization?

Step size is not uniform. Non-uniform quantizer is characterized by a step size

that increases as the separation from the origin of the transfer characteristics is increased.Non-uniform quantization is otherwise called as robust quantization

22. Draw the quantization error for the mid tread and mid-rise type of quantizer?

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For mid tread type: For mid riser type:

23. What is the disadvantage of uniform quantization over the non-uniform

quantization?

SNR decreases with decrease in input power level at the uniform quantizer but

non-uniform quantization maintains a constant SNR for wide range of input power levels.

This type of quantization is called as robust quantization.

24. What do you mean by companding? Define compander.

The signal is compressed at the transmitter and expanded at the receiver. This is called as

companding. The combination of a compressor and expander is called a compander.

25. Mention the types of companding.

1. law companding 2. A law companding

26. What is the need for speech coding at low bit rates?

The use of PCM at the standard rate of 64 Kbps demands a high channel

bandwidth for its transmission ,so for certain applications, bandwidth is at premium, in

which case there is a definite need for speech coding at low bit rates, while maintainingacceptable fidelity or quality of reproduction.

27.Compare DPCM and PCM.

In PCM signal is sampled at a rate higher than nyquist rate. The adjacent outputsamples are highly correlated (ie signal does not change form one sample from the

other).While encoding these samples lot of redundant information are seen.For wide

bandwidth data the channel bandwidth required is very high.In DPCM redundant information are removed by efficient coding. Here successive

difference between the samples alone is sent. Using differential quantization the future

values are predicted from the past samples. As it uses Compression technique the channelbandwidth required is low for wide bandwidth data

28.What are slope overload error and granular noise?Slope overload occurs when the slope of the input signal is greater than the slope

of the output. It is too difficult for the stair case approximation to follow the steepsegment of input signal. Slope overload can be avoided by increasing the step size or the

sampling frequency.

Granular noise occurs when the slope of the input signal is lesser than the slope ofthe output. It is too difficult for the stair case approximation to hunt for the flat segment

of input signal. Slope overload can be avoided by decreasing the step size or the sampling

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frequency. It is analogous to quantization error.

30.What are the limitation of delta modulation system?

1. Granular noise 2. slope overload distortion

31.Distinguish between TDM and digital multiplexing?

Time-division multiplexing (TDM) is a analog multiplexing in which two or more signals

are transferred apparently simultaneously as sub-channels in one communication channel,but are physically taking turns on the channel. The time domain is divided into several

recurrent timeslots of fixed length, one for each sub-channel.

Digital multiplexing (TDM) is multiplexing of digital signals by bit by bit interleavingprocedure. Here the digital data may have different bit rate.. Thus variable data rate is

converted into asingle data rate and transmitted over the common channel

32.Types of digital multiplexing

1. Multiplexers for low bit data stream. Here transmission is over the PSTN and itrequires MODEMS.

2. Multiplexers for high bit data stream. Here transmission is over the AT&T

networks . It constitutes the digital hierarchy where the low bit rate streams are

multiplexed into low bit rate streams.33. State the condition to avoid slope-overload error.

In delta modulation, the slope overload distortion can be reduced by increasing the stepsize or the sampling frequency.

34. What is aperture effect? How can you reduce it?

Lengthening of samples due to amplitude and delay distortions is called as apertureeffect in flat top sampling.

It can be reduced by using equilizer along with the reconstruction filters. The equilizers

decreases the in- band loss.

35.The aperture effect in flat top pulses is reduced by using an

a. Predictor b.Integrator c.Equalizer d.Compander

36.The Nyquist rate of sampling for the signal x(t) = sinc(200t) +sinc 2(200t) is

a. 200 b.400 c.300 d. 250

37. The Nyquist Sampling rate for a signal band limited to 4KHz is

a. 4KHz a. 8KHz c. 2KHz d.16KHz

38. Prior to sampling a ____________ is used to attenuate the high frequency

components of the signal that lie outside the band of interest.

39. The sampled wave in practical system consists of __________ and

____________ rather than impulses.

40. Companding is used

a. To overcome quantizing noise in PCM

b. To allow amplitude limiting in the receiver

c. To protect small signals in PCM from quantization distortion.d. To overcome impulse noise.

41. Quantizing Noise occur in

a. TDM b.FDM c. PCM d. PWM

42. The non uniform quantization leads to

a. Reduction in transmission BW b. Increase in maximum SNR

c.Increase in SNR for low level signals d.Simplification of quantization

http://en.wikipedia.org/wiki/Pulse-amplitude_modulationhttp://en.wikipedia.org/wiki/Multiplexinghttp://en.wikipedia.org/wiki/Pulse-amplitude_modulationhttp://en.wikipedia.org/wiki/Multiplexing

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43. SNR of a PCM system using 8-bit words the analog signal that does not

exceed its quantization boundary is

a. 48dB b. 54dB c. 52.7dB d. 64dB

44. For uniform quantization with 32 levels, the quantized output can be

represented by n binary digit where n is

a. 5 b.6 c. 4 d. 845. The conversion of an analog sample of the signal into digital form is called

the_____________________ process.

46. The ______________ noise occurs when the step size is too large relative to

the local slope characteristics of the input waveform.

47. Compare various line codes

binary 0 binary 1

NRZ unipolar no pulse positive pulse

NRZ polar format positive pulse Negative pulse.

NRZ bipolarformat

no pulse alternative positive andnegative pulse

manchesterformat

The first half bit durationnegative pulse and the

second half Bit duration

positive pulse

first half bit duration positivepulse and the second half Bit

duration negative pulse

PART_B

1. State & prove sampling theorem.

2. Explain the distortion occurring during sampling.3. Explain PAM.4. Explain time division multiplexing. And give the digital hierarchy principle.

5. Write short notes on: a) Aliasing b) Natural samplling6. Explain the quantization process with PCM block diagram. (8)7. Compare DM with ADM and explain linear prediction filter.

8. Derive the SNR for a companded PCM.9. .Describe a DPCM system and provide a comparison with PCM.