Category: digital Communication

Digital Communication – M-ary Encoding The word binary represents two bits. M represents a digit that corresponds to the number of conditions, levels, or combinations possible for a given number of binary variables. This is the type of digital modulation technique used for data transmission in which instead of one bit, two or more bits are transmitted at a time. As a single signal is used for multiple bit transmission, the channel bandwidth is reduced. M-ary Equation If a digital signal is given under four conditions, such as voltage levels, frequencies, phases, and amplitude, then M = 4. The number of bits necessary to produce a given number of conditions is expressed mathematically as $$N = log_{2}{M}$$ Where N is the number of bits necessary M is the number of conditions, levels, or combinations possible with N bits. The above equation can be re-arranged as $$2^N = M$$ For example, with two bits, 22 = 4 conditions are possible. Types of M-ary Techniques In general, Multi-level (M-ary) modulation techniques are used in digital communications as the digital inputs with more than two modulation levels are allowed on the transmitter’s input. Hence, these techniques are bandwidth efficient. There are many M-ary modulation techniques. Some of these techniques, modulate one parameter of the carrier signal, such as amplitude, phase, and frequency. M-ary ASK This is called M-ary Amplitude Shift Keying (M-ASK) or M-ary Pulse Amplitude Modulation (PAM). The amplitude of the carrier signal, takes on M different levels. Representation of M-ary ASK $S_m(t) = A_mcos (2 pi f_ct) quad A_mepsilon {(2m – 1 – M) Delta, m = 1,2… : .M} quad and quad 0 leq t leq T_s$ Some prominent features of M-ary ASK are − This method is also used in PAM. Its implementation is simple. M-ary ASK is susceptible to noise and distortion. M-ary FSK This is called as M-ary Frequency Shift Keying (M-ary FSK). The frequency of the carrier signal, takes on M different levels. Representation of M-ary FSK $S_i(t) = sqrt{frac{2E_s}{T_s}} cos left ( frac{pi}{T_s}left (n_c+iright )tright )$ $0 leq t leq T_s quad and quad i = 1,2,3… : ..M$ Where $f_c = frac{n_c}{2T_s}$ for some fixed integer n. Some prominent features of M-ary FSK are − Not susceptible to noise as much as ASK. The transmitted M number of signals are equal in energy and duration. The signals are separated by $frac{1}{2T_s}$ Hz making the signals orthogonal to each other. Since M signals are orthogonal, there is no crowding in the signal space. The bandwidth efficiency of M-ary FSK decreases and the power efficiency increases with the increase in M. M-ary PSK This is called as M-ary Phase Shift Keying (M-ary PSK). The phase of the carrier signal, takes on M different levels. Representation of M-ary PSK $S_i(t) = sqrt{frac{2E}{T}} cos left (w_o t + phi _itright )$ $0 leq t leq T quad and quad i = 1,2 … M$ $$phi _i left ( t right ) = frac{2 pi i}{M} quad where quad i = 1,2,3 … : …M$$ Some prominent features of M-ary PSK are − The envelope is constant with more phase possibilities. This method was used during the early days of space communication. Better performance than ASK and FSK. Minimal phase estimation error at the receiver. The bandwidth efficiency of M-ary PSK decreases and the power efficiency increases with the increase in M. So far, we have discussed different modulation techniques. The output of all these techniques is a binary sequence, represented as 1s and 0s. This binary or digital information has many types and forms, which are discussed further. Learning working make money

Digital Communication – Analog to Digital The communication that occurs in our day-to-day life is in the form of signals. These signals, such as sound signals, generally, are analog in nature. When the communication needs to be established over a distance, then the analog signals are sent through wire, using different techniques for effective transmission. The Necessity of Digitization The conventional methods of communication used analog signals for long distance communications, which suffer from many losses such as distortion, interference, and other losses including security breach. In order to overcome these problems, the signals are digitized using different techniques. The digitized signals allow the communication to be more clear and accurate without losses. The following figure indicates the difference between analog and digital signals. The digital signals consist of 1s and 0s which indicate High and Low values respectively. Advantages of Digital Communication As the signals are digitized, there are many advantages of digital communication over analog communication, such as − The effect of distortion, noise, and interference is much less in digital signals as they are less affected. Digital circuits are more reliable. Digital circuits are easy to design and cheaper than analog circuits. The hardware implementation in digital circuits, is more flexible than analog. The occurrence of cross-talk is very rare in digital communication. The signal is un-altered as the pulse needs a high disturbance to alter its properties, which is very difficult. Signal processing functions such as encryption and compression are employed in digital circuits to maintain the secrecy of the information. The probability of error occurrence is reduced by employing error detecting and error correcting codes. Spread spectrum technique is used to avoid signal jamming. Combining digital signals using Time Division Multiplexing (TDM) is easier than combining analog signals using Frequency Division Multiplexing (FDM). The configuring process of digital signals is easier than analog signals. Digital signals can be saved and retrieved more conveniently than analog signals. Many of the digital circuits have almost common encoding techniques and hence similar devices can be used for a number of purposes. The capacity of the channel is effectively utilized by digital signals. Elements of Digital Communication The elements which form a digital communication system is represented by the following block diagram for the ease of understanding. Following are the sections of the digital communication system. Source The source can be an analog signal. Example: A Sound signal Input Transducer This is a transducer which takes a physical input and converts it to an electrical signal (Example: microphone). This block also consists of an analog to digital converter where a digital signal is needed for further processes. A digital signal is generally represented by a binary sequence. Source Encoder The source encoder compresses the data into minimum number of bits. This process helps in effective utilization of the bandwidth. It removes the redundant bits (unnecessary excess bits, i.e., zeroes). Channel Encoder The channel encoder, does the coding for error correction. During the transmission of the signal, due to the noise in the channel, the signal may get altered and hence to avoid this, the channel encoder adds some redundant bits to the transmitted data. These are the error correcting bits. Digital Modulator The signal to be transmitted is modulated here by a carrier. The signal is also converted to analog from the digital sequence, in order to make it travel through the channel or medium. Channel The channel or a medium, allows the analog signal to transmit from the transmitter end to the receiver end. Digital Demodulator This is the first step at the receiver end. The received signal is demodulated as well as converted again from analog to digital. The signal gets reconstructed here. Channel Decoder The channel decoder, after detecting the sequence, does some error corrections. The distortions which might occur during the transmission, are corrected by adding some redundant bits. This addition of bits helps in the complete recovery of the original signal. Source Decoder The resultant signal is once again digitized by sampling and quantizing so that the pure digital output is obtained without the loss of information. The source decoder recreates the source output. Output Transducer This is the last block which converts the signal into the original physical form, which was at the input of the transmitter. It converts the electrical signal into physical output (Example: loud speaker). Output Signal This is the output which is produced after the whole process. Example − The sound signal received. This unit has dealt with the introduction, the digitization of signals, the advantages and the elements of digital communications. In the coming chapters, we will learn about the concepts of Digital communications, in detail. Learning working make money

Digital Communication Tutorial Job Search Digital communication is the process of devices communicating information digitally. This tutorial helps the readers to get a good idea on how the signals are digitized and why digitization is needed. By the completion of this tutorial, the reader will be able to understand the conceptual details involved in digital communication. Audience This tutorial is prepared for beginners who are interested in the basics of digital communications and who aspire to acquire knowledge regarding digital communication systems. Prerequisites A basic idea regarding the initial concepts of communication is enough to go through this tutorial. It will definitely help if you use our tutorial Signals and Systems as a reference. A basic knowledge of the terms involved in Electronics and Communications would be an added advantage. Learning working make money

Quadrature Phase Shift Keying The Quadrature Phase Shift Keying (QPSK) is a variation of BPSK, and it is also a Double Side Band Suppressed Carrier (DSBSC) modulation scheme, which sends two bits of digital information at a time, called as bigits. Instead of the conversion of digital bits into a series of digital stream, it converts them into bit pairs. This decreases the data bit rate to half, which allows space for the other users. QPSK Modulator The QPSK Modulator uses a bit-splitter, two multipliers with local oscillator, a 2-bit serial to parallel converter, and a summer circuit. Following is the block diagram for the same. At the modulator’s input, the message signal’s even bits (i.e., 2nd bit, 4th bit, 6th bit, etc.) and odd bits (i.e., 1st bit, 3rd bit, 5th bit, etc.) are separated by the bits splitter and are multiplied with the same carrier to generate odd BPSK (called as PSKI) and even BPSK (called as PSKQ). The PSKQ signal is anyhow phase shifted by 90° before being modulated. The QPSK waveform for two-bits input is as follows, which shows the modulated result for different instances of binary inputs. QPSK Demodulator The QPSK Demodulator uses two product demodulator circuits with local oscillator, two band pass filters, two integrator circuits, and a 2-bit parallel to serial converter. Following is the diagram for the same. The two product detectors at the input of demodulator simultaneously demodulate the two BPSK signals. The pair of bits are recovered here from the original data. These signals after processing, are passed to the parallel to serial converter. Learning working make money

Digital Communication – Sampling Sampling is defined as, “The process of measuring the instantaneous values of continuous-time signal in a discrete form.” Sample is a piece of data taken from the whole data which is continuous in the time domain. When a source generates an analog signal and if that has to be digitized, having 1s and 0s i.e., High or Low, the signal has to be discretized in time. This discretization of analog signal is called as Sampling. The following figure indicates a continuous-time signal x (t) and a sampled signal xs (t). When x (t) is multiplied by a periodic impulse train, the sampled signal xs (t) is obtained. Sampling Rate To discretize the signals, the gap between the samples should be fixed. That gap can be termed as a sampling period Ts. $$Sampling : Frequency = frac{1}{T_{s}} = f_s$$ Where, $T_{s}$ is the sampling time $f_{s}$ is the sampling frequency or the sampling rate Sampling frequency is the reciprocal of the sampling period. This sampling frequency, can be simply called as Sampling rate. The sampling rate denotes the number of samples taken per second, or for a finite set of values. For an analog signal to be reconstructed from the digitized signal, the sampling rate should be highly considered. The rate of sampling should be such that the data in the message signal should neither be lost nor it should get over-lapped. Hence, a rate was fixed for this, called as Nyquist rate. Nyquist Rate Suppose that a signal is band-limited with no frequency components higher than W Hertz. That means, W is the highest frequency. For such a signal, for effective reproduction of the original signal, the sampling rate should be twice the highest frequency. Which means, $$f_{S} = 2W$$ Where, $f_{S}$ is the sampling rate W is the highest frequency This rate of sampling is called as Nyquist rate. A theorem called, Sampling Theorem, was stated on the theory of this Nyquist rate. Sampling Theorem The sampling theorem, which is also called as Nyquist theorem, delivers the theory of sufficient sample rate in terms of bandwidth for the class of functions that are bandlimited. The sampling theorem states that, “a signal can be exactly reproduced if it is sampled at the rate fs which is greater than twice the maximum frequency W.” To understand this sampling theorem, let us consider a band-limited signal, i.e., a signal whose value is non-zero between some –W and W Hertz. Such a signal is represented as $x(f) = 0 for |flvert > W$ For the continuous-time signal x (t), the band-limited signal in frequency domain, can be represented as shown in the following figure. We need a sampling frequency, a frequency at which there should be no loss of information, even after sampling. For this, we have the Nyquist rate that the sampling frequency should be two times the maximum frequency. It is the critical rate of sampling. If the signal x(t) is sampled above the Nyquist rate, the original signal can be recovered, and if it is sampled below the Nyquist rate, the signal cannot be recovered. The following figure explains a signal, if sampled at a higher rate than 2w in the frequency domain. The above figure shows the Fourier transform of a signal $x_{s}(t)$. Here, the information is reproduced without any loss. There is no mixing up and hence recovery is possible. The Fourier Transform of the signal $x_{s}(t)$ is $$X_{s}(w) = frac{1}{T_{s}}sum_{n = – infty}^infty X(w-nw_0)$$ Where $T_{s}$ = Sampling Period and $w_{0} = frac{2 pi}{T_s}$ Let us see what happens if the sampling rate is equal to twice the highest frequency (2W) That means, $$f_{s} = 2W$$ Where, $f_{s}$ is the sampling frequency W is the highest frequency The result will be as shown in the above figure. The information is replaced without any loss. Hence, this is also a good sampling rate. Now, let us look at the condition, $$f_{s} The resultant pattern will look like the following figure. We can observe from the above pattern that the over-lapping of information is done, which leads to mixing up and loss of information. This unwanted phenomenon of over-lapping is called as Aliasing. Aliasing Aliasing can be referred to as “the phenomenon of a high-frequency component in the spectrum of a signal, taking on the identity of a low-frequency component in the spectrum of its sampled version.” The corrective measures taken to reduce the effect of Aliasing are − In the transmitter section of PCM, a low pass anti-aliasing filter is employed, before the sampler, to eliminate the high frequency components, which are unwanted. The signal which is sampled after filtering, is sampled at a rate slightly higher than the Nyquist rate. This choice of having the sampling rate higher than Nyquist rate, also helps in the easier design of the reconstruction filter at the receiver. Scope of Fourier Transform It is generally observed that, we seek the help of Fourier series and Fourier transforms in analyzing the signals and also in proving theorems. It is because − The Fourier Transform is the extension of Fourier series for non-periodic signals. Fourier transform is a powerful mathematical tool which helps to view the signals in different domains and helps to analyze the signals easily. Any signal can be decomposed in terms of sum of sines and cosines using this Fourier transform. In the next chapter, let us discuss about the concept of Quantization. Learning working make money

Digital Communication – Differential PCM For the samples that are highly correlated, when encoded by PCM technique, leave redundant information behind. To process this redundant information and to have a better output, it is a wise decision to take a predicted sampled value, assumed from its previous output and summarize them with the quantized values. Such a process is called as Differential PCM (DPCM) technique. DPCM Transmitter The DPCM Transmitter consists of Quantizer and Predictor with two summer circuits. Following is the block diagram of DPCM transmitter. The signals at each point are named as − $x(nT_{s})$ is the sampled input $widehat{x}(nT_{s})$ is the predicted sample $e(nT_{s})$ is the difference of sampled input and predicted output, often called as prediction error $v(nT_{s})$ is the quantized output $u(nT_{s})$ is the predictor input which is actually the summer output of the predictor output and the quantizer output The predictor produces the assumed samples from the previous outputs of the transmitter circuit. The input to this predictor is the quantized versions of the input signal $x(nT_{s})$. Quantizer Output is represented as − $$v(nT_{s}) = Q[e(nT_{s})]$$ $$= e(nT_{s}) + q(nT_{s})$$ Where q (nTs) is the quantization error Predictor input is the sum of quantizer output and predictor output, $$u(nT_{s}) = widehat{x}(nT_{s}) + v(nT_{s})$$ $$u(nT_{s}) = widehat{x}(nT_{s}) + e(nT_{s}) + q(nT_{s})$$ $$u(nT_{s}) = x(nT_{s}) + q(nT_{s})$$ The same predictor circuit is used in the decoder to reconstruct the original input. DPCM Receiver The block diagram of DPCM Receiver consists of a decoder, a predictor, and a summer circuit. Following is the diagram of DPCM Receiver. The notation of the signals is the same as the previous ones. In the absence of noise, the encoded receiver input will be the same as the encoded transmitter output. As mentioned before, the predictor assumes a value, based on the previous outputs. The input given to the decoder is processed and that output is summed up with the output of the predictor, to obtain a better output. Learning working make money