Modulation Theory Digital communication has overtaken analog communications as the Modern Digital And Analog Communication Systems 4ed by Lathi. I am extremely happy to present the book ''Analog and Digital Communication'' as per the revised syllabus (R) of Anna University. Design of a Multicode Bi-phase Encoder for Data Transmission. This NRZ level encoder converts the input binary sequence to the signal suitable for. Then, with a good understanding of modulation theory applied to analog and digital communications and relevant concepts of probability theory and.
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Analogue and Digital Communication Techniques
Analog to Digital converter, Digital to Analog converter. To transmit the information that a codeword represents one needs to map each bit to an electrical signal or waveform. As has been mentioned several times this mapping is called modulation and it, along with demodulation, is the subject of succeeding chapters.
To conclude we are finally in a position to discuss digital communications. However a few further closing remarks are in order. The quantization and encoding discussed in this chapter go under the general topic of source coding.
But some sources, as pointed out the keyboard, are already discrete in nature. Traditional source coding was concerned primarily with this step. Some aspects of this are presented in the problems at the end of the chapter but the interested reader is referred to the literature for a more comprehensive treatment. The Science of Communications involving long distances is called Telecommunication the world Tele standing for long distance The Two basic types of communication systems are i Analog.
Communication is the process of establishing connection or link between two points for information exchange. In Digital Systems: The digital pulses are transferred between two or more points in a communication system. Analog communication: The modulation systems or techniques in which one of the characteristics of the carrier is changed in proportion with the instantaneous value of modulating signal is called analog communication system. In Analog Systems: Both the information and the carrier are analog signals.
Needs for modulation: In order to carry the low frequency message signal to a longer distance. Frequency Modulation is the changing frequency of the carrier signal with respect to the instantaneous change in message signal. The above drawbacks can be overcome by means of modulation techniques: Need for Modulation: Modulation is the changing characteristics of the carrier signal with respect to the instantaneous change in message signal.
Modulation index: It is defined as ratio of amplitude of the message signal to the amplitude of the carrier signal. Phase Modulation is defined as changing the phase of the carrier signal with respect to the instantaneous change in message signal.
Percentage modulation: It is the percentage change in the amplitude of the output wave when the carrier is acted on by a modulating signal. Deviation ratio: Deviation ratio is the worst case modulation index and is equal to the maximum peak frequency deviation divided by the maximum modulating signal frequency.
Fig a Sinosoidal modulation signal b High frequency carrier c AM signal. The amplitude modulated wave form. Amplitude modulation: Amplitude Modulation is defined as changing the amplitude of the carrier signal with respect to the instantaneous change in message signal. From the above equation we have Example Problems: At this value of modulation index. Maximum Value of modulation index.
They are listed in Table 2. The values of Bessel functions depend upon modulation index m. The advantages of Minimum Shift Keying: Bit rate is the number of bits transmitted during one second between the transmitter and receiver. Frequency Shift Keying is the as changing amplitude of the carrier signal with respect to the binary information or digital signal. Digital modulation: Digital Modulation is defined as changing the amplitude of the carrier signal with respect to the binary information or digital signal.
Baud rate is the rate of change of signal on transmission medium after encoding and modulation have occurred. The minimum frequency space that allows the 2 fsk representing symbols 0s and 1s.
Bandwidth efficiency: Amplitude Shift Keying is the as changing amplitude of the carrier signal with respect to the binary information or digital signal. Phase Shift Keying is the changing amplitude of the carrier signal with respect to the binary information or digital signal Quadrature Amplitude modulation QAM: QAM is a form of digital modulation similar to PSK except the digital information is contained in both the amplitude and phase of the transmitted carrier.
Since only 4 phase angles have 2 different amplitudes, there are a total of 16 combinations. Very good noise immunity Effective utilization of available bandwidth Low error probability. Therefore coherent carrier is to be recovered from the received signal s t.
One bit forms a symbol. M-ary signaling schemes transmit bits at a time. What are the advantages of M-ary signaling scheme? This is made physically possible by allowing ISI in the transmitted signal in controlled manner. Bandwidth requirement of M-ary signaling schemes is reduced.
Hence effects of ISI are eliminated at the receiver. This increases the probability of error in M-ary systems. Four possible symbols. Two possible symbols. Two bits form a symbol. Correlative coding allows the signaling rate of 2B0 in the channel of bandwidth B0.
Correlative coding is implemented by duobinary signaling and modified duobinary signaling. Hence the symbols come closer to each other.
Minimum bandwidth is twice of fb. This ISI is known to the receiver. Minimum bandwidth is equal to fb. A multipoint line configuration is one in which more than two specific devices share a single link. Point to point communication is the link between two stations A and B ie. These dots and dashes were detected at the receiver and it is converter back into letters and numbers makes the original message. Morse code is used to send messages. The bandwidth requirement of low index systems is approximately twice of the modulating signal frequency.
Parallel transmission is speed Used for short distance communication Disadvantages: Require more lines between source and destination More cost 3. Therefore low index systems are called narrowband FM. When the modulation index is less than 1. Armstrong method generates FM from PM. In narrow band FM. If the deviation in carrier frequency is large enough so that other sidebands cannot be neglected. Hence crystal oscillators can be used in Armstrong method.
This does not cause any distortion in FM signal. Hence the frequency spectrum consists of two major sidebands like AM. This means. Therefore the bandwidth of narrowband FM is limited only to twice of the highest modulating frequency. Therefore frequency stability is better than reactance modulator. Hence it is possible to operate several independent transmitters on same frequency with minimum interference. Hence transmitter power remains constant in FM whereas it varies in AM. It is independent of depth of modulation.
Other sidebands are negligible and hence they can be neglected. But in FM the depth of modulation can be increased to any value by increasing the deviation. In direct FM type of angle modulation. Whereas it is difficult to remove amplitude variations due to noise in AM. FM has following advantages over AM. Any noise superimposing amplitude can be removed with the help of amplitude limits.
The advantage of such a system is that the system becomes simple. The detection is done by correlating received noisy signal and locally generated carrier. The choice is made such that the transmitted power and channel bandwidth are best exploited. The different digital modulation techniques are used for specific application areas. The coherent detection is a synchronous detection.
In coherent detection. FM is obtained by phase modulation of the carrier. Non coherent envelope detection: This type of detection does not need receiver carrier to be phase locked with transmitter carrier. Horizontal Redundancy Check h. M ary schemes require less bandwidth compared to binary schemes.
M-ary schemes transmit log2 M bit at a time. Check sum f. Exact count encoding d. But M-ary PSK requires a bandwidth of 2fb. Binary schemes transmit only one bit at a time. Echoplex c. Number of transmission lines is less Used for long distance communication Low cost Disadvantages: Speed is low For example binary PSK requires a bandwidth of 2fb. When available channel bandwidth is less. Vertical Redundancy Check g.
Parity e. Redundancy b. Such signals are called antipodal signals. The amplitude and position of the pulse remains unchanged.
The message signal may vary either the trailing edge or leading edge or both of the carrier pulses n order to accommodate the intelligence of information system. PAM Modulator The amplitude of a carrier pulse is altered in accordance to that of amplitude of message signal to make it accommodate the information signal. Width of pulse is proportional to the amplitude of the modulating signal. PPM demodulator It is a form of digital modulation techniques in which the code refers a binary word that represent digital data.
A baseband signal receiver increases the signal to noise at the instant of sampling. The baseband signal receiver is also called optimum receiver. The impulse response of the matched filter is matched to the shape of the input signal. Matched filter. This reduces the probability of error. Block Diagram of Transmitter Block Diagram of Receiver Pulse position modulation The position of a carrier pulse is altered in accordance with information contained in sampled waveform.
Pulse code modulation refers a form of source coding. With PCM. The matched filter is a baseband signal receiver.
Because of reduced bandwidth. For the same bit error rate. Variation in QPSK amplitude is not much. It correlates the received noisy signal f t with the locally generated replica of the known signal x t. Hence carrier power almost remains constant It is the coherent receiver. The value of maximum signal to noise ratio of the matched filter Maximum signal to noise ratio of the matched filter is the ratio of energy of the signal to psd of white noise.
Its output is given as. Code redundancy is the measure of redundancy bits in the encoded message sequence. It is represented by I Xi.
The average mutual information is defined as the amount of source information gain per received symbol. The efficient representation of data generated by a discrete source is known as source encoding. A block code of length n and 2k code words is calleda linear n. This device that performs this representation is called source encoder. The message occurring frequently can be assigned short code words. The types of error control method Error detection and retransmission Error detection and correction Channel capacity is defined as the maximum of the mutual information that may be transmitted through the channel.
Mutual information is the amount of information transferred when Xi is transmitted and Yi is received. The needs for encoding To improve the efficiency of communication To improve the transmission quality. Proof of Achievability.
Source coding theorem Given X is an i. The objectives of cyclic codes: Encoding and syndrome calculations can be easily implemented by using simple shift register with feedback connection It is possible to design codes having useful error correction properties Source Coding Theorem The source coding theorem shows that in the limit.
Channel coding theorem is applied for discrete memory less additive white gaussian noise channels. The advantages of Shannon fano coding Reduced bandwidth Reduced noise It can be used for error detection and correction. However it is possible to get the code rate arbitrarily close to the Shannon entropy.
Xn is i. Source coding theorem for symbol codes See AEP for a proof: The definition of typical sets implies that those sequences that lie in the typical set satisfy: Note that: The encoding algorithm: The encoder checks if the input sequence lies within the typical set. Proof of Converse. In particular there for large enough n. Since bits are enough to point to any string in this set.
For the proof. For the second inequality we may set so that and so and and so by Kraft's inequality there exists a prefix-free code having those word lengths.
Then where the second line follows from Gibbs' inequality and the fifth line follows from Kraft's inequality: Thus the minimal S satisfies All symbols then have the first digits of their codes assigned. In Shannon-Fano coding. The algorithm works. As long as any sets with more than one member remain. Shannon-Fano coding is a suboptimal technique for constructing a prefix code based on a set of symbols and their probabilities estimated or measured.
For a given list of symbols. Divide the list into two parts. Shannon Fano Coding Techniques In the field of data compression. When a set has been reduced to one symbol. The actual algorithm is simple: Sort the lists of symbols according to frequency. Shannon-Fano does not always produce optimal prefix codes. Given A set of symbols and their weights usually proportional to probabilities. Although Huffman coding is optimal for a symbol-by-symbol coding i. For example.
Recursively apply the steps 3 and 4 to each of the two halves. This means that the codes for the symbols in the first half will all start with 0. The left half of the list is assigned the binary digit 0. Find A prefix-free binary code a set of codewords with minimum expected codeword length equivalently.
The term refers to the use of a variable-length code table for encoding a source symbol such as a character in a file Huffman coding uses a specific method for choosing the representation for each symbol. Huffman was able to design the most efficient compression method of this type: The difference between the initial uncertainty of the source symbol xk. This difference we call as the mutual information In general. For any code that is biunique. In this example. H X Y Notice that in spite of the variations in the source probabilities.
Let be the weighted path length of code C. If this is not the case.
Analog And Digital Communication Books
Y Further. H X — H X Yj may be negative. While we can compare the JPM.
Y Also observe H X. Y The joint entropy H X. An easy method. Joint and Conditional Entropies: It is clear that all the probabilities encountered in a two dimensional communication system could be derived from the JPM. The overlap between the two circles dark gray is the mutual information so that the remaining light gray portions of H X and H Y represent respective equivocations.
The different conditional entropies. The entropy of X is represented by the circle on the left and that of Y by the circle on the right. You cannot use this diagram for proving any result. Althogh the diagram resembles a Venn-diagram. That is all. That is to say. If you want the equivocation or conditional entropy. All the five entropies so defined are all inter-related. If you want source entropy. H X Y then probability of interest will be the conditional probability p xK yj and so on.
Similarly one can define the conditional entropy H Y X by: It specifies the average amount of information n eeded to specify an input character provided we are allowed to make an observation of the output produced by that input. We have: Thus it follows that: It is one of the most common and widely used channels. For this channel we have: An interesting interpretation of the equivocation may be given if consider an idealized communication system with the above symmetric channel.
The channel diagram of a BSC is shown in Fig 3. Thus the observer supplies additional information to the receiver. Let us compute this additional information. BEC is one of the important types of channels used in digital communications. In Fig 4. The variation of the mutual information with the probability of error is shown in Fig 3. Observe that whenever an error occurs. To put the matter more formally. In this particular case.
The technique used to achieve this objective is called coding. Y p 1 0 1 Adding column wise we get: Positive statement: In such a circuit there is no loss of energy at all as the reactors have the property of storing energy rather than dissipating.
Negative statement: You should receive this without any loss. Once the tumbler is full. Recall the maximum power transfer theorem: Situation is similar to pouring water into a tumbler. Notice that the situation is analogous to an electric network that is made up of pure resistors. The situation is analogous to an electric circuit that comprises of only pure capacitors and pure inductors.
You cannot pour water more than your tumbler can hold. This theorem shows that if the information rate R exceeds a specified value C.Join with us. In Digital Systems: Such a representation is the function of the modulator as shown in Figure 5. Derive expressions for the modulation index. What is frequency hopping? The samples of Analog signal are taken, and they are quantized.
The advantage of such a system is that the system becomes simple. Model of a Digital Communication: The overall purpose of these systems are to message or or sequence of symbols that are coming out from the source to the destination point at a very high data rate and accuracy as possible.
List the standard organizations for data communications.
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