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ADC Assignment

Name:- Abhishek Pandey

Class:- SECMPN B

Roll No:- 17

1. Explain generation and detection of PAM. Ans:-

PAM:-

Pulse-amplitude modulation (PAM) is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses. It is an analog pulse modulation scheme in which the amplitude of train of carrier pulses are varied according to the sample value of the message signal.

PAM signal generation:-

A PAM signal is generated by using a pulse train, called the sampling signal (or clock signal) to operate an electronic switch or "chopper". This produces samples of the analog message signal, as shown in figure,

Natural sampling – generation of PAM signals.

The switch is closed for the duration of each pulse allowing the message signal at that sampling time to become part of the output. The switch is open for the remainder of each sampling period making the output zero. This type of sampling is called natural sampling.

For flat-top sampling, a sample-and-hold circuit is used in conjunction with the chopper to hold the amplitude of each pulse at a constant level during the sampling time, as shown in figure.

Flat-top sampling – generation of PAM signals.

Figure shows the relationship between the message signal, the sampling signal, and the resulting PAM signal using natural sampling.

Waveform of natural sampling

Detection of PAM:-

PAM signal Low

Demodulated PAM signal

Pass

Filter

The PAM signal can be detected (demodulated) by passing it through a low pass filter. The low pass filter cutoff frequency is adjusted to fm so that all high frequency ripples is removed and original modulating signal is recovered back.

The PAM detection and the corresponding waveforms are as shown below:-

Natural sampling – time domain appearance of a PAM signal.

Flat-top sampling – time domain appearance of a PAM signal.

From the above waveforms, it is seen that the demodulated output signal is close to the original modulating signal x(y).

2. Explain PCM in detail.

Ans:-

PCM:-

PCM is a method of converting an analog into digital signals. Information in an analog form cannot be processed by digital computers so it's necessary to convert them into digital form. PCM is a term which was formed during the development of digital audio transmission standards. Digital data can be transported robustly over long distances unlike the analog data and can be interleaved with other digital data so various combinations of transmission channels can be used. In the text which follows this term will apply to encoding technique which means digitalization of analog information in general.

PCM doesn`t mean any specific kind of compression, it only implies PAM (pulse amplitude modulation) - quantization by amplitude and quantization by time which means digitalization of the analog signal. The range of values which the signal can achieve (quantization range) is

divided into segment, each segment has a segment representative of the quantization level which lies in the middle of the segment. To every quantization segment (and quantization level) one and unique code word (stream of bits) is assigned. The value that a signal has in certain time is called a sample. The process of taking samples is called quantization by time. After quantization by time, it is necessary to condu ct quantization by amplitude. Quantization by a mplitude means that according to the amplitude o f sample one quantization segment is chosen (every quantization segment contains ann interval of amplitudes) and then record segme nts code word.

Pulse Cod e Modulation waveforms.

In the diagram, a sine wave (red curve) is sampled and quantized for PCM. The sine wave is sampled at regular intervals, shown as ticks on the x-axis. For each sample, one of the available values (ticks on the y-axis) is ch osen by some algorithm. This produces a fully discrete

representation of the input signal (shaded area) that can be easily encoded as digital data for storage or manipulation.

Demodulation:-

To recover the original signal from the sampled data, one applies the procedure of modulation in reverse. After each sampling period has passed, the demodulator reads the next value and shifts the output signal to the new value. As a result of these transitions, the signal has a significant amount of high-frequency energy caused by aliasing. To remove these undesirable frequencies and leave the original signal, the demodulator passes the signal through analog filters that suppress energy outside the expected frequency range and we get the original signal.

Advantages:-

1.Very High noise Immunity.

2.Due to Digital nature of the signal, repeaters can be placed between the transmitter and receiver. The repeaters actually regenerate the transmitted PCM Signals. This is not possible in analog systems. Repeaters further reduce the effect of noise.

3.It is possible to store the PCM signal due to its digital nature.

4.It is possible to use various coding techniques so that only the desired person can decode the received signal.

Disadvantages:-

1.The encoding, decoding and quantizing circuitry of PCM (Pulse Code Modulation) is Complex.

2.Pulse Code Modulation requires a large Band width as compared to the other systems.

Applications:-

1.To convert analog signals into digital format by taking samples of wave forms.

2.In power delivery.

3.In voltage regulation and amplification.

4.Digital audio applications.

3. Explain sampling theorem for low pass and band pass filter.

Ans:-

The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, in the literature, more commonly referred to as the Nyquist sampling theorem or simply as the sampling theorem, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal (for example, a function of continuous time or space) into a numeric sequence.

Shannon's version of the theorem states:-

If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

In other words, a band limited function can be perfectly reconstructed from an infinite sequence of samples if the band limit, B, is no greater than ½ the sampling rate . The theorem also leads to a formula for reconstruction of the original function from its samples. When the band limit is too high, the reconstruction exhibits imperfections known as aliasing. The Poisson summation formula provides a graphic understanding of aliasing and an alternative derivation of the theorem, using the perspective of the function's Fourier transform.

In practice of course, infinite sequences, perfect sampling, and perfect interpolation are all replaced by approximations that deviate from the mathematical ideal of perfect reconstruction.

Modern statements of the theorem are sometimes careful to explicitly state that x(t) must contain no sinusoidal component at exactly frequency B, or that B must be strictly less than ½ the sample rate. And the theorem does not preclude the possibility of perfect reconstruction under special circumstances that do not satisfy the sample-rate criterion. It is a sufficient, but not necessary, condition.

To formalize the statements abo ve, let X(f) be the Fourier transform of band limited function x(t):

 

X(f) =

dt,

And

X(f) = 0 f or all

 

When x(t) is sampled uniformly at intervals of T seconds, the resultant sequence is denoted by x(nT), for all integer values of n. And the sample-rate (samples per second) is:

fs = 1/T.

4. Explain Shannon’s theorem in your own words. Give examples that are directly or indirectly affected by Shannon’s theorem.

Ans:-

Shannon’s theorem:-

Shannon's Theorem gives an upp er bound to the capacity of a link, in bits per second (bps), as a function of the available bandwidth and the signal-to-noise ratio of the link. It also helps us to determine the maximum rate at which the information can be transmitted over th e communication channel of a spe cified bandwidth in presence of noise.

The equation is given as:-

C=B log2 (1+ )

Where,

C is the channel capacity in bits per second.

B is the bandwidth of the channel in hertz.

S is the average received signal power over the bandwidth.

N is the average noise or interference power over the bandwidth measured in watt.

S/N is the signal-to-noise ratio (SNR).

Example:-

1.In MIMO. When the no: of antennae beams are increased the channel capacity also gets increased. The correlation between the no: of MIMO antenna and throughput is still not linear.

2.Let’s take the example of W-CDMA (Wideband Code Division Multiple Access), the bandwidth = 5 MHz, you want to carry 12.2 kbit/s of data (AMR voice), then the required SNR is given by 212.2/5000 -1 corresponding to an SNR of -27.7 dB for a single channel. This shows that it is possible to transmit using signals which are actually much weaker than the background noise level, as in spread-spectrum communications. However, in W- CDMA the required SNR will vary based on design calculations.

3.Channel capacity is proportional to the bandwidth of the channel and to the logarithm of SNR. This means channel capacity can be increased linearly either by increasing the channel's bandwidth given a fixed SNR requirement or, with fixed bandwidth, by using higher-order modulations that need a very high SNR to operate. As the modulation rate increases, the spectral efficiency improves, but at the cost of the SNR requirement. Thus, there is an exponential rise in the SNR requirement if one adopts a 16QAM or 64QAM however, the spectral efficiency improves.

5. Compare TDM and FDM.

Ans:-

Sr. no.

TDM

FDM

 

 

 

1

The signals which are to be multiplexed can

The signals which are to be multiplexed are

 

occupy the entire bandwidth but they are

added in the time domain. but they occupy

 

isolated in the time domain

different slots in the frequency domain.

 

 

 

2

Synchronization is required.

Synchronization is not required.

 

 

 

3

TDM circuitry is not very complex.

FDM requires complex circuitry at the

 

 

transmitter and the receiver.

 

 

 

4

TDM is preferred for digital signals.

FDM is usually preferred for the analog

 

 

signals.

 

 

 

5

In TDM the problem of crosstalk is not

FDM suffers from the problem of crosstalk

 

severe.

due to imperfect band pass filters.

 

 

 

6

Due to fading only a few TDM channels will

Due to wide band fading in the transmission

 

be affected.

medium, all FDM channels are affected.

 

 

 

7

Due to slow narrow band fading, all the

Due to slow narrow band fading taking place

 

TDM channels may get wiped out.

in the transmission channel only a single

 

 

channel may be affected in FDM

 

 

 

6. Compare PWM, PAM, PPM.

Ans:-

Sr.

Parameter

PWM

PAM

PPM

no.

 

 

 

 

 

 

 

 

 

1

Type of carrier

Train of pulses

Train of pulses

Train of pulses

 

 

 

 

 

2

Variable characteristic

Width

Amplitude

Position

 

of the pulsed carrier

 

 

 

 

 

 

 

 

3

Bandwidth

High

Low

High

 

requirement

 

 

 

 

 

 

 

 

4

Noise immunity

High

Low

high

 

 

 

 

 

5

Information is

Width variation

Amplitude variations

Position variation

 

contained in

 

 

 

 

 

 

 

 

6

Transmitted power

Varies with variation

Varies with

Remains constant

 

 

in width

amplitude of pulses

 

 

 

 

 

 

7

Need to transmit

Not needed

Not needed

Necessary

 

synchronizing pulses

 

 

 

 

 

 

 

 

8

Complexity of

Easy

Complex

Complex

 

generation and

 

 

 

 

detection

 

 

 

 

 

 

 

 

9

Similarity with other

Similar to FM

Similar to AM

Similar to PM

 

modulation systems

 

 

 

 

 

 

 

 

10

Output waveforms

 

 

 

 

 

 

 

 

7. Explain intersymbol interference and equalization.

Ans:-

t

Intersymbol

Interferencce

INTERSYMBOL INTERFERENCE:

WHAT IS ISI:-

1. Due to the fact that the transmission channels are band limited , the transmitted pulses tend to spread during transmission. This pulse spreading or dispersion causes overlap of pulses into adjacent pulse time slots.

2. This signal overlap may result in an error at the point where the receiver makes a decision as to which pulse has been transmitted, especially when other impairments are present (such as noise, interference).

3. This effect of pulse overlap and the resultant difficulty of discriminating between symbols at the receiver are termed inter symbol interference (ISI).

The ISI arises due to the imperfections in the overall frequency response of the system.

EFFECT OF ISI:

1.The presence of ISI introduces errors in the decision device at the receiver input thus the receiver can make an error in deciding whether the acquired bit is logic 0 or logic 1 .The transmitted bit can be decoded correctly in the absence of noise and ISI.

2.Overlapping of adjacent pulses causes’ cross talk.

Hence it is necessary to use special filters in order to reduce the effect of ISI.

CAUSES OF ISI:

The four important causes of ISI are stated below:

(1)Timing inaccuracies:-

Timing inaccuracies occurring in either the transmitter or the receiver produce intersymbol interference .In the transmitter, timing inaccuracies cause intersymbol interference if the rate of transmission does not conform to the ringing frequency designed into the channel. Timing inaccuracies of this type are insignificant unless extremely sharp filter cutoffs are used while signalling at the Nyquist rate.

(2)Insufficient bandwidth:-

The ringing frequency is exactly equal to the theoretical minimum bandwidth of the channel. If the bandwidth is reduced further the ringing frequency is reduced and intersymbol interference necessarily results.

(3)Amplitude distortion:-

Digital transmissions systems invariably require filters to band limit transmit spectrums and to reject noise and interference in receivers. Overall, the filters are designed to produce a specific pulse response. However the frequency response of the channel cannot always be predicted adequately..A departure from the desired frequency response is referred to as amplitude distortion and causes pulse distortions in the time domain.

(4)Phase distortion:-

If the phase relationships of the components are altered, phase distortion occurs. This will cause the ISI. Compensation of phase distortion is referred to as phase equalization.

STRATEGIES FOR ELIMINATING ISI:-

Nyquist’s Method for Zero ISI:-

Nyquist proved that the theoretical value of the minimum system bandwidth needed in order to detect Rs symbol without ISI is Rs /2 Hz. This is when the transfer function H(f) is rectangular. The figure shows the transfer function of an ideal low pass filter and it is called and ideal Nyquist filter. The single side bandwidth of such filter is 1/2T ,the impulse response is obtained by taking the inverse fourier transform of the transfer function .the IFT of a rectangular pulse is a sine pulse .It shows two successive pulses h(t) and h(t-T).

Note that they do not interfere with each other and ISI is reduced to zero.

h(t)=sine(t/T)

Hence it was proved that if each pulse of received sequence is of the above form then pulses can be detected without ISI. Fig. b shows how ISI is avoided.

CONCLUSIONS:-

1.Since pulses are not possible to create due to: Infinite time duration.

Sharp transition band in the frequency domain.

2.The Sine pulse shape can cause significant ISI in the presence of timing errors.

If the received signal is not sampled at exactly the bit instant (Synchronization Errors), then ISI will occur.

3.We seek a pulse shape that has a more gradual transition in the frequency domain and is more robust to timing errors.

RAISED COSINE FILTER:-

Raised-Cosine Roll off pulse shaping use a filter at the receiver to “undo” the distortion introduced by the channel.

The two difficulties experienced by the ideal Nyquist channel can be overcome by increasing the bandwidth from its minimum value to an adjustable value. A condition is put in the overall frequency response 1/2B0 to satisfy the given condition.

This modified frequency response is shown in the fig (a.) and the filter having this response is called as raised cosine filter.

OBSERVATIONS:-

1. =0.5 and 1 the characteristics of H(f) i.e (1/2B0) changes gradually w.r.t frequency. Hence it is easier to realize this characteristic practically.

2.The time response has a sine shape and all the sine function pass through zero at t= + Tb, +2Tb…

3.The amplitude of the side lobes increases with reduction in the value of .

4.With =0,the bandwidth requirement is maximum equal to 2B0.

Equalization:-

Now we know that a signal transmission is always associated with a distortion. In order to remove the linear distortion we make use of a network called equalizer which is combined with the channel or the system.

Input Channel Equalizer To data terminal equipment

Block diagram of Equalizer

Principle of equalizer:-

Equalizer must be designed in such a way that it must be capable to compensate for an unequal frequency response of some other signal processing circuit or system.

An EQ filter typically allows the user to adjust one or more parameters that determine the overall shape of the filter's transfer function. It is generally used to improve the fidelity of sound, to emphasize certain instruments, to remove undesired noises, or to create completely new and different sounds.

Types of equalizer filters:-

1. Adaptive equalizers:-

The process of equalization is said to be adaptive if it adjusts itself continuously during the data transmission by operating on the input signal.

We generally use adaptive equalizers in order to obtain the full transmission capability of a telephone channel.

Adaptation involves following steps:-

1.Before the actual data transmission a known test sequence called training sequence is transmitted on the channel.

2.Resulting response sequence y(k) is obtained in the receiver by measuring the output of transversal filter at the sampling instants.

3.The difference between the received response sequence and desired response sequence

d(k) gives the error sequence y(k). e(k)=d(k)-y(k)

4.The error sequence is used to determine the gain coefficients.

5.A particular algorithm is used for optimum setting of the coefficient. It is based on minimizing the sum of the squares of the errors, i.e, Σe2(k);

6.The duration of the training sequence is so chosen that the adaptive equalizer converges to optimum setting.

Adaptive equalizers are used in high speed data transmissions.

Adaptive Equalizers

2. Transversal equalizer:-

The transversal equalizers are designed in such a way that along with the noisy channel it will make overall system transfer function to be close to the raised cosine filter. This will ensure zero ISI (Inter symbol Interference).

The transversal filter, illustrated in figure 2, is the most popular form of an easily adjustable equalizing filter consisting of a delay line with T-second taps (where T is the symbol duration).

`

Transversal Equalizers

From the above circuit we see that the output is feedback to the coefficient adjust block which is actually realized using software.

It will automatically adjust the coefficient (CN) values so as to obtain the desired transfer function.

3. Decision feedback equalizer:-

The basic limitation of a linear equalizer, such as the transversal filter, is the poor perform on channel having spectral nulls. A decision feedback equalizer (DFE) is a nonlinear equalizer that uses previous detector decision to eliminate the ISI on pulses that are currently being demodulated. In other words, the distortion on a current pulse that was caused by previous pulses is subtracted.

Decision Feedback Equalizers

Figure 1 shows a simplified block diagram of a DFE where the forward filter and the feedback filter can each be a linear filter, such as transversal filter. The nonlinearity of the DFE stems from the nonlinear characteristic of the detector that provides an input to the feedback filter. The basic idea of a DFE is that if the values of the symbols previously detected are known, then ISI contributed by these symbols can be canceled out exactly at the output of the forward filter by subtracting past symbol values with appropriate weighting. The forward and feedback tap weights can be adjusted simultaneously to fulfill a criterion such as minimizing the MSE.

The advantage of a DFE implementation is the feedback filter, which is additionally working to remove ISI, operates on noiseless quantized levels, and thus its output is free of channel noise.

References:-

1.en.wikipedia.org/wiki/Pulse-amplitude_modulation.

2.Pulse Modulation and Sampling (PAM/PWM/PPM) - Lab Volt.

3.Communication Engineering - A.P.Godse U.A.Bakshi - Google Books.

4.Digital telephony by John C. Bellamy (3rd Edition).

5.Data Communications And Computer Networks By Prakash C. Gupta.

6.Pulse-code modulation - Wikipedia, the free encyclopedia.

7.www.differencebetween.net/.../difference-between-fdm-and-tdm/.

8.Communications and Information Systems -Michael John Ryan, Michael R. Frater- Google Books.

9.Wireless Communication –Vikrant Vij - Google Books.