ANALOG COMMUNICATION -UNIT 5 Study material
- 1. UnitV SAMPLING AND QUANTIZATION INTRODUCTION Computer plays a vital role in communication which demands the need to convert the analog information to digital signal for processing and transmission. Pulse modulation is another important classification of modulation, which is fundamental to the digital transmission of analog signal. Pulse modulation is defined as the process of transmitting signals in the form of pulse by using a periodic pulse train as carrier signal.
- 2. Analog Pulse Modulation: A periodic pulse train is used as the carrier signal and some characteristics of the pulse such as amplitude, position or width is varied in accordancewith the corresponding sampled message signal. The information is transmitted in analog form but the transmission takes place at discrete times which requires only sampling. Pulse amplitude modulation, pulse position modulation and pulse width modulation are the examples of analog pulse modulation. Digital Pulse Modulation: The message signal is represented in discrete form both in time and amplitude and transmitted in digital form as a sequence of coded pulses. This type of modulation involves the process of sampling, quantization and encoding. Pulse code modulation and delta modulation are the examples of digital pulse modulation.
- 3. LOW PASS SAMPLING Sampling is the important operation in digital signal processing and digital communication. It is defined as the process of converting an analog signal into a sequence of samples spaced uniformly in time. The analog signal must be sampled in such a way that the sampled sequences uniquely define the original analog signal. So, it is important to choose the rate at which the sampling must be performed. This is the essence of sampling theorem. Low pass sampling means sampling of low pass signal, whereas band pass sampling means sampling of band pass signal.
- 4. Sampling theorem for band-limited signal A band-limited signal of finite energy, which has no frequency components higher than W Hz, may be completely described by specifying the values of the signal at instants of time separated by ½ W seconds. A band-limited signal of finite energy, which has no frequency components higher than W Hz, may be completely recovered from the knowledge of its samples taken at the rate of 2W samples per second. The minimum sampling rate of 2W samples per second for a signal bandwidth of W Hertz is called as Nyquist rate.The reciprocal of Nyquist rate ½ W is called Nyquist interval.
- 5. Aliasing & Its Effect
- 6. Aliasing effect: The sampling theorem derivation is based on the assumption that the signal is strictly band-limited. But in practice, an information bearing signal is not strictly band-limited which results in under sampling. This results in signal distortion called as aliasing. The word “alias” means false or assumed identity. Aliasing or fold over refers to the phenomenon of a high-frequency component in the spectrum of the signal taking on the identity of a lower frequency in the spectrum of its sampled version.
- 8. Effects of aliasing 1. Since high and low frequencies interfere with each other, distortion is generated. 2. Data is lost and it cannot be recovered. Different Ways to avoid aliasing 1. Using low pass anti aliasing filter (or) pre-alias filter prior to sampling which band limits the signal to W. 2. Sampling at a rate of W fs 2 fs ≥ 2W
- 9. I)Sampling at a rate of fs ≥ 2W : When the sampling rate is made higher than 2W, then the spectrums will not overlap and there will be sufficient gap between the individual spectrums.
- 10. Over Sampling When the signal is sampled at a rate much higher than Nyquist rate , it is called over sampling. It is necessary to avoid aliasing error in the signal. But it increases transmission bandwidth.
- 11. II) : Using low pass anti aliasing filter (or) pre- alias filter Sampler Band limiting LPF ) ( ' t y ) (t y ) (t y • Hence a LPF is used before sampling the signals. Thus the output of LPF is strictly bandlimited and there are no frequency components higher than “W” .Then there will be no aliasing.
- 12. Nyquist rate & Nyquist interval. Nyquist rate : When the sampling rate becomes exactly to 2W samples per second for a signal bandwidth of W Hertz is called as Nyquist rate. Nyquist interval : It is the time interval between any two adjacent samples when sampling rate is Nyquist rate. The reciprocal of Nyquist rate 1/2W is called Nyquist interval
- 13. Reconstruction Filter (Interpolation filter) The above equation provides an interpolation formula for recontructing the original signal y(t) from the sample values y(n/2W) with the sinc function playing the role of an interpolation function. Each sample is multiplied by a delayed version of the interpolation function and all the resulting waveforms are added to obtain y(t) as shown in figure
- 14. The above equation also represents the response of an ideal low pass filter of bandwidth W. So, the original signal y(t) can be recovered exactly from the sequence of samples y(n/2W) by passing through an ideal low pass filter of bandwidth W termed as reconstruction filter whose response is shown in figure .
- 17. The passband of physically realizable filter extends from –W to +W Hertz and has a non- zero transition band from W to fs-W Hertz.The region separating the passband and stopband is called as guard band with the width of fs-2W Hertz.
- 18. Nonuniform Quantization Quantization using nonuniform or unequal step size is called as non-uniform quantization or robust quantization as shown in figure 5.13. Figure 5.13 Nonuniform Quantization Need for nonuniform quantization: The uniform quantization provides better SNR for uniformly distributed signal. But signals like speech have nonuniform distribution, where the large amplitude levels are relatively rare compared to small amplitude levels. Therefore, with uniform quantization, SNR becomes worse for low amplitude levels than for high amplitude levels. Nonuniform quantization can provide fine quantization for frequently occurring low amplitude levels and coarse quantization for rarely occurring high amplitude levels. It improves the overall SNR by reducing the noise.
- 19. Companding: Non uniform quantization can be achieved by using a technique called companding, which is a combination of compression at transmitter and expander at receiver as shown in figure Compander = Compressor + Expander
- 20. Logarithmic Companding The two commonly used logarithmic compression laws are, 1. µ-law companding: The compressor characteristics is continuous. In North America, the standard practical value for µ is 255. It is used for PCM telephone systems in US, Canada and Japan.
- 21. Logarithmic Companding 2. A-law companding: The compressor characteristics is piecewise. The standard practical value for A is 87.56. It is used for PCM telephone system in Europe.
- 22. Analog Pulse Modulation A periodic pulse train is used as the carrier signal and some characteristics of the pulse such as amplitude, position or width is varied in accordance with the corresponding sampled message signal. The information is transmitted in analog form but the transmission takes place at discrete times which requires only sampling. Pulse amplitude modulation(PAM), pulse position modulation(PPM) and pulse width modulation (PWM) are the examples of analog pulse modulation.
- 23. PULSEWIDTH MODULATION(PWM) In pulse width modulation, the samples of the message signal are used to vary the width of the individual pulses keeping amplitude constant. This form of modulation is also referred to as Pulse Duration Modulation or Pulse Length Modulation. The modulating signal and periodic pulse carrier are shown in figure 5.21 (a) and (b) respectively. Figure 5.21 (c) illustrates the PWM signal, where the trailing edge of each pulse is varied in accordance with the message signal.
- 24. Figure 5.21 (a) Modulating wave (b) Pulse carrier (c) PWM signal
- 25. Generation of PWM signal: The block diagram of PWM signal generation using comparator is shown in figure 5.22. The input message signal is fed to the non-inverting terminal of the comparator and sawtooth signal is fed to the inverting terminal of the comparator. The sawtooth signal acts as carrier signal. The comparator generates PWM signal, if the maximum of the input signal is less than sawtooth signal as shown in figure 5.23.
- 26. When the sawtooth signal rises with a fixed slope and crosses input signal value, the inverting input of comparator is at higher potential and the comparator output will be negative. The duration for which the comparator stays high depends on the input signal amplitude and this decides the width of the pulse. Thus, the pulse width generated is directly proportional to the amplitude of the message signal at that instant.
- 28. Detection of PWM signal: The block diagram of PWM detection is shown in figure 5.24. The PWM signal received at the input of the detection circuit is applied to synchronous pulse generator circuit and ramp generator. The synchronous pulse generator produces a train of constant amplitude and constant width pulses. The ramp generator generates a constant slope ramp for the duration of the pulse.
- 30. The height of the ramp is proportional to the width of the PWM pulses. At the end of the pulse, a sample and hold amplifier retains the final ramp voltage until it is reset at the end of the pulse.
- 31. PULSE POSITION MODULATION (PPM) In pulse position modulation, the position of each pulse is varied in accordance with the amplitudes of the sampled values of the modulating signal, keeping the amplitude and width of the pulses constant.
- 32. Figure 5.26 (a) Modulating signal (b) Pulse signal (c) PPM signal
- 33. Generation of PPM signal: The PPM signal can be generated from the PWM. The PWM signal is fed to an inverter which reverses polarity of the pulses. • The inverted signal is then fed to a differentiator which produces positive spikes, when the original PWM signal transition is from HIGH to LOW and negative spikes, when the transition is from LOW to HIGH as shown in figure 5.28.
- 34. • These spikes are fed to a positive edge triggered fixed width pulse generator which generates pulses of fixed width when a positive spike appears, coinciding with the falling edge of original PWM signal. • The occurrences of these falling edges depends on the message signal and hence the delay in occurrence of these fixed width pulses are proportional to the amplitude of the input message at that instant.
- 35. Figure 5.28 Principle of PPM signal generation
- 36. Detection of PPM signal:
- 37. The reference pulse is generated by reference pulse generator of the receiver with the synchronization signal from the transmitter. The SR edge triggered flip-flop is set or turned ON by the positive edge of the clock. It remains set so that the output Q is high, till a positive edge from PPM signal resets it.
- 38. PULSE CODE MODULATION(PCM) Pulse code modulation (PCM) is the most basic form of digital pulse modulation. In pulse code modulation, a message signal is represented by a sequence of coded pulses which is accomplished by representing the signal in discrete form in both amplitude and time. The essential operations in the transmitter of a PCM system are sampling, quantization and encoding which are performed in the same circuit called as analog to digital converter.
- 40. I) Sampling: The incoming message signal is sampled with a train of narrow rectangular pulses so as to closely approximate the instantaneous sampling process. The sampling rate must be greater than twice the highest frequency component W of the message signal in order to ensure the perfect reconstruction of the message at receiver. In practice a low-pass pre-alias filter or anti- aliasing filter is used before sampler to band- limit the signal.
- 41. II) Quantization: The process of converting a discrete signal into a digital form is called quantization. The quantization provides the staircase approximation to the input signal. If the step size is uniform, then it is called as uniform quantization. The uniform quantization is further classified as midtread and midriser based on the origin of the quantization in the middle of a tread or riser respectively as shown in figure 5.32. Quantization noise or error is defined as the difference between the input and quantized value. The SNR of the uniform quantization depends on the number of bits used to represent the sample.
- 42. In case of speech signal, uniform quantization cannot be used as it reduces the SNR for the frequently occurring low amplitude signals. This demands the need for the signal dependent quantization. Non-uniform quantization provides fine quantization for low amplitude levels and coarse quantization of high amplitude levels. Quantization with non-uniform or unequal step size is called as non-uniform quantization. Figure : Nonuniform Quantization
- 43. Nonuniform quantization is implemented using companding technique which is the combination of compression at the transmitter and expansion at receiver. Compander = Compressor + Expander The model of non-uniform quantizer is shown in figure 5.34. At the transmitter, the original signal is first distorted by using the logarithmic compression characteristics and then using a uniform quantizer. The compressor has a much steeper slope for low amplitude levels than for high amplitude levels. Thus, the compressor provides higher gain to the low amplitude signals and lower gain to the high amplitude signals. At the receiver, expander is used to restore the original signal which has inverse characteristic of compressor. Generally compander uses a logarithmic compression, where the levels are crowded near the origin and spaced farther apart near the peak values.
- 44. The two commonly used logarithmic compression laws are, 1. µ-law companding: The compressor characteristics is continuous, approximating a linear dependence for low input levels and logarithmic for high input levels. The µ-law compressor characteristics is mathematically expressed as, where, where µ is a positive constant, x and y represent input and output voltages and xmax and ymax are the maximum positive excursions of the input and output voltages respectively. The compression characteristics for several values of μ is shown in figure 5.36(a). Uniform quantization (linear amplification) corresponds to the parameter μ = 0. In North America, the standard practical value for µ is 255. It is used for PCM telephone systems in US, Canada and Japan.
- 45. 2. A-law companding: The compressor characteristics is piecewise made up of linear segment for low level inputs and logarithmic segment for high level inputs. Where A is a positive constant, x and y represent input and output voltages, and xmax and ymax are the maximum positive excursions of the input and output voltages respectively. The compression characteristics for several values of A is shown in figure 5.36(b). Uniform quantization (linear amplification) corresponds to the parameter A=1. The standard practical value for A is 87.56. It is used for PCM telephone system in Europe.
- 47. III) Encoding: Encoding is defined as the process of translating the discrete set of sample values to a more appropriate form suited for transmission through communication channel. The member of each discrete set of values are represented as a particular arrangement of discrete events called code. One of the discrete events in a code is called as code element or symbol.
- 48. A particular arrangement of symbols used in a code to represent a single value of the discrete set is called as code word or character. In a binary code, each symbol may be either of two distinct values, such as a negative pulse or positive pulse. The two symbols of the binary code are denoted as 0 and 1.
- 49. In a binary code, each code word consists of R bits, which denotes the number of bits per sample. Hence, by using such a code, we represent a total of 2R distinct values. For example, a sample quantized into one of 256 levels may be represented by an 8-bit code word.
- 50. The electrical representation of the binary sequence is called as line codes. The important line codes are listed as follows: Unipolar nonreturn-to-zero or On–off signaling: In this signaling format, symbol 1 is represented by transmitting a pulse of constant amplitude for the duration of the symbol, and symbol 0 is represented by switching off the pulse, as in figure 5.37(a). Polar nonreturn-to-zero signaling: In this format, symbols 1 and 0 are represented by pulses of equal positive and negative amplitudes, as illustrated in figure 5.37(b). This format is relatively easy to generate but its disadvantage is that the power spectrum is large near zero frequency. Unipolar return-to-zero signaling: In this signaling format, symbol 1 is represented by a positive rectangular pulse of half- symbol width and symbol 0 is represented by transmitting no pulse, as illustrated in figure 5.37(c).
- 51. Bipolar return-to-zero signaling: This format uses three amplitude levels as indicated in figure 5.37(d). Specifically, positive and negative pulses of equal amplitude are used alternately for symbol 1, and no pulse is always used for symbol 0. A useful property of this signaling is that the power spectrum of the transmitted signal has no dc component and relatively insignificant low-frequency components for the case when symbols 1 and 0 occur with equal probability. Split-phase (Manchester code): In this format, symbol 1 is represented by a positive pulse followed by a negative pulse, with both pulses being of equal amplitude and half-symbol width. For symbol 0, the polarities of these two pulses are reversed. The Manchester code suppresses the dc component and has relatively insignificant low-frequency components, regardless of the signal statistics. Manchester code is illustrated in figure 5.37(e).
- 52. Differential encoding: In this format, the information is encoded in terms of signal transitions, as illustrated in figure 5.37(f). Here, a transition is used to designate symbol 0, whereas no transition is used to designate symbol 1. It is apparent that a differentially encoded signal may be inverted without affecting its interpretation. The original binary information is recovered by comparing the polarity of adjacent symbols to establish whether or not a transition has occurred. Differential encoding requires the use of a reference bit, as indicated in figure 5.37(f).
- 53. Figure 5.37 Line codes (a) Unipolar nonreturn-to-zero (b) Polar nonreturn-to-zero(c) Unipolar return-to-zero (d) Bipolar return-to-zero (e) Manchester code (f) Differential encoding
- 54. IV)Regeneration: The important feature of PCM lies in the ability to control the effects of distortion and noise produced by transmitting a PCM signal through a channel. This is achieved by reconstructing the PCM signal by means of a chain of regenerative repeaters located at sufficiently close spacing along the transmission path.
- 55. The important blocks of regenerative repeater is shown in figure 5.38. The three basic functions performed by the regenerative repeaters are, Equalization – Shapes the received pulse so as to compensate for the effects of amplitude and phase distortions produced by imperfections of the channel. Timing – Provides a periodic pulse train derived from the received pulses, for sampling the equalized pulses at the instants of time where the SNR is maximum. Decision making – Enabled when at the sampling time determined by the timing circuit, amplitude of the equalized pulse plus noise exceeds a predetermined voltage level.
- 56. Figure 5.38 Components of regenerative repeater
- 57. V) Decoding: • The first operation in the receiver is to regenerate the received pulses. • These clean pulses are then regrouped into code words and decoded into a quantized PAM signal. VI) Reconstruction: • The final operation is to recover the analog signal. • This is done by passing the decoder output through a low pass reconstruction filter whose cutoff frequency is equal to the message bandwidth.
- 58. Synchronization: For PCM system with TDM to operate satisfactorily it is necessary that the timing operations at the receiver, except for the time lost in transmission and regenerative repeating follow closely the corresponding operations at the transmitter. This needs a local clock at the receiver to keep the same time as a distant standard clock at the transmitter, except that the local clock is slower by an amount corresponding to the time required to transport the message signals from the transmitter to the receiver.
- 59. Frame synchronization Set aside a code element or pulse at the end of a frame and to transmit this pulse every other frame only. A receiver search for the pattern of 1’s and 0’s alternating at half the frame rate.
- 60. Bandwidth requirement of PCM: • The bit rate (R) is = n * fs = 2nW bits/sec. • The minimum bandwidth requirement for binary transmission of R bits/sec is R/2. • Therefore, the minimum bandwidth requirement of a PCM system is nfs /2 • At Nyquist rate, Minimum BW required is nW • Thus, a PCM system expands the bandwidth of the original signal by a factor of n.
- 61. Advantages of PCM: PCM permits regeneration along the transmission path which reduces noise and interference. Multiplexing of multiple data streams is easy possible. Security can be easily incorporated using encryption and decryption. Disadvantages of PCM: Cost and complexity is high compared to other pulse modulation techniques. Bandwidth requirement is high.
- 62. MULTIPLEXING Transmitting two or more signals simultaneously can be accomplished by setting up one transmitter-receiver pair for each channel, but this is an expensive approach. Multiplexing technique reduces the cost by using the channel effectively. It is defined as the technique of combining separate message signals into a composite signal for transmission over a common channel.
- 63. The two commonly used methods for signal multiplexing are Frequency Division Multiplexing (FDM) Time Division Multiplexing (TDM) FDM may be used with either analog or digital signal transmission, whereas TDM is usually used to transmit digital information.
- 64. Frequency Division Multiplexing(FDM) Voice frequencies transmitted over telephone systems, for example, range from 300 to 3400 Hz. To transmit a number of these signals over the same channel (e.g. cable), the signals must be kept apart so that they do not interfere with each other and thus they can be separated at the receiving end.
- 65. Frequency division multiplexing (FDM) is defined as the technique of dividing the total bandwidth available in a communication medium into a series of non-overlapping frequency bands and allocating each frequency to carry a separate message signal.
- 66. In FDM all users use the same common channel at full time. But each of the users is allocated with different frequencies for transmission for avoiding the signal interference. Sometimes there is a possibility of cross talk because all the users use the transmission medium at the same time.
- 67. Block diagram of FDM Transmitter system
- 68. In FDM signals are generated by sending devices and there are multiple input lines. From the block diagram (Figure 6), channel 1 to channel n are taken as the input channels. These signals reach at the input of the corresponding modulator where it receives another signal from a crystal oscillator known as carrier signal, which is a high-frequency high-amplitude signal. The carrier signal is modulated with the input signal. Different modulators use different carrier signals for modulation.It should be noted that the frequency band of one modulator will not make any interference to the frequency band of other modulators. Each of the modulator produces the corresponding modulated signal at their output. All the output of the modulators will be given to an adder or mixer circuit; from there it is given to another modulator for further shift of total bandwidth. Finally, this higher-frequency signal will be transmitted over the
- 69. Block diagram of FDM Receiver system
- 70. The following block diagram (Figure 7) shows the concept of demodulation of FDM signal at the receiving side. The antenna receives the multiplexed modulated signal from the transmitter. This signal will be weak at the receiver. Therefore it is necessary to amplify the signal. This is done at the initial stage of the receiver. The amplified signal is then forwarded to the demodulator. The output of the demodulator will be given to the band-pass filters which are well designed with the central frequencies of the carriers as used individually at the transmitting side. Thus the output of each BPF will be the same as that of the originally modulated output of the corresponding modulator. Then we use the corresponding individual demodulators to recover the original signal.
- 71. Advantage of FDM A large number of signals (channels) can be transmitted simultaneously. Demodulation of FDM is easy. FDM does not need synchronization between its transmitter and receiver for proper operation. Due to slow narrowband fading, only a single channel gets affected. Disadvantages of FDM The communication channel must have a very large bandwidth. Inter-modulation distortion takes place. A large number of modulators and filters are required. FDM suffers from the problem of cross talk. All the FDM channels get affected due to wideband fading. Applications of FDM FDM is used for FM and AM radio broadcasting. FDM is used in television broadcasting. First-generation cellular telephone also uses FDM.
- 72. Time Division Multiplexing(TDM) An important feature of the sampling process is a conservation of time. The transmission of the message samples engages the communication channel for only a fraction of the sampling interval on a periodic basis, thus some of the time interval between adjacent samples is free for use by other independent message sources on a time-shared basis. This enables the joint utilization of a common communication channel by several independent message sources without mutual interference among them. Time division multiplexing (TDM) is defined as the technique of combining multiple data streams from independent sources by assigning each stream a different time slot. The block diagram of time division multiplexing system is shown in figure
- 74. The transmitter section of TDM consists of the following components, Prealias filter: Each input message signal is first restricted in bandwidth by a low pass prealias filter to remove the frequencies that are not used for an adequate signal representation. Commutator: The outputs of prealias filter are then applied to commutator, which is usually implemented using electronic switching circuitry. It performs two functions, 1.Sampling - To take a narrow sample of each of the N input message at a rate fs that is slightly higher than 2W, where W is the cutoff frequency of the pre-alias filter. 2.Interleaving - To sequentially interleave these N samples inside the sampling interval Ts = 1/fs
- 75. Pulse amplitude modulator: After the commutation process, the multiplexed signal is applied to a PAM, which transform the multiplexed signal into a suitable form for transmission over the communication channel. The sampling rate for each of N message signal is determined in accordance with sampling theorem. Let Ts denote the sampling period for each message signal. Let Tx denote the time spacing between the adjacent samples in the time-multiplexed signal as shown in figure 5.42. It is clear that, Tx = Ts / N Thus, the use of TDM introduces a bandwidth expansion factor N Figure 5.42 Waveform illustrating TDM for two message signal s(t) and m(t)
- 76. The receiver section of TDM consists of Pulse amplitude demodulator: It performs the reverse operation of the pulse amplitude demodulator. Decommutator: It performs the reverse operation of the commutator present in the transmitter. It separates the individual message signal from the multiplexed signal. It must operate in synchronism with the commutator. Reconstruction filter: It performs the low pass filtering for the individual message signals.
- 77. Advantages of TDM: Simple circuit compared to FDM. Immune to amplitude nonlinearities which is the source of crosstalk. Easy to add signals Disadvantages of TDM: Highly sensitive to dispersion in the channel which induces ISI. Requires equalization at the receiver. Possibility of Synchronization and timing jitter problems at high bit rates. Applications of TDM: Digital telephony Satellite access Cellular radio