![Figure shows Delta Modulator. In the block diagram of this delta modulation, the
summer block and delay circuit block are called as Accumulator. And accumulator
generates the staircase approximated signal with having delayed by one sample period of
Ts. The accumulator block summer2 adds the quantizer output signal and previous
sample approximation, and this results in u(nTs). The previous sample is achieved by
delaying the present sample period approximation u(nTs)=u([n-1]Ts) + b(nTs)
“Present sample value X(nTs) and staircase approximated signal x(nTs) both are
subtracted to know the error signal e(nTs). If e(nTs) is positive, then the one-bit quantizer
circuit increase the step size +Δ and bit 1 is transmitted. If the error is negative, then step
size is reduced by –Δ and bit 0 is transmitted to the output.”
Present sample value is X(nTs)
The previous sample value is u([n-1]Ts)
e(nTs) is an error signal between the
present sample and previous sample
b(nTs) is the quantizer output signal](https://image.slidesharecdn.com/unit-1-240925052827-f82546f0/85/Introductionto-Digitalcommunications-and-baseband-modulation-techniques-67-320.jpg)
Introductionto Digitalcommunications and baseband modulation techniques
- 1. B.Tech V Semester 20EC09 – DIGITAL COMMUNICATIONS Course Educational Objective: This course provides the knowledge on different digital modulation techniques. The course provides different concepts on information theory, block codes and convolution codes. It gives the methods of optimum receivers for digital communication systems and performance of probability of error for digital modulation techniques. Course Outcomes (COs): At the end of the course, students will be able to CO1: Understand the concepts of digital communication system (Understand – L2) CO2: Analyze the Baseband and Pass band digital modulation techniques (Analyze – L4) CO3 :Examine the optimum reception and probability of error of digital modulation(Apply – L3) CO4:Apply source coding and error control coding techniques in digital communication process(Apply – L3)
- 2. UNIT – I Pulse Digital Modulation: Elements of a Digital Communication System, Sampling and Quantization of signals- Quantization noise, Pulse Digital Modulation Systems: Pulse Code Modulation(PCM) System, Encoding, Regenerative repeaters, Decoding, Reconstruction, effect of noise in PCM-Calculation of output SNR in PCM; Need for non-uniform quantization-Companding- μ-law, A-law; Differential Pulse Code Modulation; Delta Modulation; Adaptive Delta Modulation.
- 3. Elements of a Digital Communication System, Sampling Quantization of Digital signals Introduction– Uniform Quantization Quantization noise Pulse Code Modulation(PCM) System Block diagram of Tx-Rx SNR in PCM system(output) Non -uniform quantization Need for non-uniform quantization Companding- μ-law, A-law Differential Pulse Code Modulation Delta Modulation- Drawbacks of DM Adaptive Delta Modulation
- 5. 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. Advantages of Digital Communication There are many advantages of digital communication over analog communication 1. The effect of distortion, noise, and interference is much less in digital signals as they are less affected. 2. Digital circuits are more reliable & easy to design and cheaper than analog circuits. 3. The hardware implementation in digital circuits, is more flexible than analog. 4. Signal processing functions such as encryption and compression are employed in digital circuits to maintain the secrecy of the information. 5. The probability of error occurrence is reduced by employing error detecting and error correcting codes 6. Spread spectrum technique is used to avoid signal jamming.
- 6. MODEL OF COMMUNICATION SYSTEM
- 7. The transmission of information is called communication. • Every communication has three essential elements : transmitter, channel and receiver The purpose of transmitter is to convert into suitable form of signal that can transmitted through the channel. • The channel is central to operation of a communication System. The information - carrying capacity of a communication system is proportional to the channel bandwidth. • If the o/p of the information source is a non electric signal then a transducer convert it into electric form before it pass through the channel. Moreover, noise is introduced in channel so receiver reconstruct it and send the information to user for.
- 8. Discrete
- 11. Block diagram of Digital communication Systems ----Transmitter------ ----Receiver ------ ----Channel------
- 12. In the above diagram 3 basic signal processing operations 1.Source coding (source encoder & decoder) 2.Channel coding (Channel encoder & decoder) 3.Modulation
- 15. To reduce the effect of channel noise To provide reliable communication over noisy channel Introducing redundancy in the channel encoding in prescribed format it can reconstruct the original signal as accurately as possible at the decoder output.
- 17. Sampling theorem (or Nyquist Criterion): the sampling is performed at a proper rate, no info is lost about the original signal and it can be properly reconstructed “If a signal is sampled at a rate at least, but not exactly equal to twice the maximum frequency of the signal, then the waveform can be exactly reconstructed from the samples without any distortion” Sampling frequency fs fmax The minimum sampling rate of (2W) samples per second, for an analog signal bandwidth of W Hz, is called the 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. fS = 2W where fS is the sampling frequency W is the highest frequency
- 18. Sampling is the processes of converting continuous by taking the “samples” at discrete-time intervals Sampling interval: – The time that separates sampling points (interval b/w samples), Analog-to-digital conversion is (basically) a 2 step process: – 1.Sampling - Convert from continuous-time analog signal – 1s obtained by taking the “samples” of xa (t) at discrete-time intervals, Ts 2.Quantization – Convert from discrete-time continuous valued signal Sampling Rate (or sampling frequency fs):The rate at which the signal is sampled, expressed as the number of samples per second reciprocal of the sampling interval), 1/Ts = fs Types of Sampling :1. Natural Sampling 2. Flat top Sampling
- 21. Types Of Quantization There are two types of Quantization o Uniform Quantization o Non-uniform Quantization. . Uniform Quantization The type of quantization in which the quantized levels are uniformly spaced is known as uniform quantization. In uniform quantization, each step size represents a constant amount of analog amplitude. it remains constant throughout the signal. , Quantization is the process of mapping continuous amplitude (analog) signal into discrete amplitude (digital) signal. Quantization is representing the sampled values of the amplitude by a finite set of levels, which means converting a continuous-amplitude sample into a discrete-time signal “The analog signal is quantized into countable & discrete levels known as quantization levels. Each of these levels represents a fixed input amplitude.”
- 22. Quantization The example of uniform quantization is given below
- 23. Uniform Quantization: • There are two types of uniform quantization. – Mid-Rise type The Mid-Rise type is so called because the origin lies in the middle of a raising part of the stair-case like graph. The quantization levels in this type are even in number. – Mid-Tread type. The Mid-tread type is so called because the origin lies in the middle of a tread of the stair-case like graph. The quantization levels in this type are odd in number. • Both the mid-rise and mid-tread type of uniform quantizer is symmetric about the origin.
- 25. Quantization error 0 at 0 voltage Max error =+ s/2
- 26. +s ,+3s,+5s Quantization error + s/2 at 0 voltage Max error =+ s/2
- 32. Pulse Code Modulation (PCM) Definition: A technique by which analog signal gets converted into digital form in order to have signal transmission through a digital network is known as Pulse Code Modulation. PCM systems are basically signal coders also known as waveform coders. Basics of PCM: In pulse code Modulation the analog message signal is first sampled, and then the amplitude of the sample is approximated to the nearest set of quantization level. This allows the representation of time and amplitude in a discrete manner. Thereby, generating a discrete signal. This discrete signal is then converted into its binary form for the transmission of the signal. in PCM technique the signal gets transmitted in the coded format and must be decoded at the receiver in order to have the original message signal.
- 33. Block diagram of Pulse Code Modulation
- 34. Block diagram of Pulse Code Modulation
- 35. LPF: Here, the message signal which is in the continuous time form, is allowed to pass through a low pass filter (LPF). This LPF whose cutoff frequency is fm eliminates the high-frequency components of the signal and passes only the frequency components that lie below fm. Sampler: The output of the LPF is then fed to a sampler where the analog input signal is sampled at regular intervals. The sampling of the signal is done at the rate of fs. This sampling frequency is so selected that it must follow the sampling theorem that is expressed as: fs ≥ 2fm The output of the sampler is a signal that is discrete time continuous amplitude signal denoted as nTs which is nothing but a PAM signal. Quantizer: A quantizer is a unit that rounds off each sample to the nearest discrete level. The sampler provides a continuous range signal and hence still an analog one. The quantizer performs the approximation of each sample thus assigning it a particular discrete level. As it basically rounds off the value to a certain level this shows some variation by the actual amount. Thus we can say, quantizing a signal introduces some distortion or noise into it. This is known as quantization error
- 36. Encoder The digitization of analog signal is done by the encoder. It designates each quantized level by a binary code.The sampling done here is the sample-and-hold process. These three sections LPF Sampler and Quantizer will act as an analog to digital converter. Encoding minimizes the bandwidth used. Regenerative Repeater This section increases the signal strength. The output of the channel also has one regenerative repeater circuit, to compensate the signal loss and reconstruct the signal, and also to increase its strength. Decoder The decoder circuit decodes the pulse coded waveform to reproduce the original signal. This circuit acts as the demodulator. Reconstruction Filter After the digital-to-analog conversion is done by the regenerative circuit and the decoder, a low-pass filter is employed, called as the reconstruction filter to get back the original signal. Hence, the Pulse Code Modulator circuit digitizes the given analog signal, codes it and samples it, and then transmits it in an analog form. This whole process is repeated in a reverse pattern to obtain the original signal.
- 37. PCM Transmitter LPF: Here, the message signal which is in the continuous time form, is allowed to pass through a low pass filter (LPF). This LPF whose cutoff frequency is fm eliminates the high-frequency components of the signal and passes only the frequency components that lie below fm. Sampler: The output of the LPF is then fed to a sampler where the analog input signal is sampled at regular intervals. The sampling of the signal is done at the rate of fs. This sampling frequency is so selected that it must follow the sampling theorem that is expressed as: fs ≥ 2fm. The output of the sampler is a signal that is discrete time continuous amplitude signal denoted as nTs which is nothing but a PAM signal.
- 38. Quantizer: A quantizer is a unit that rounds off each sample to the nearest discrete level. The sampler provides a continuous range signal and hence still an analog one. The quantizer performs the approximation of each sample thus assigning it a particular discrete level. Encoder: An encoder performs the conversion of the quantized signal into binary codes. This unit generates a digitally encoded signal which is a sequence of binary pulses that acts as the modulated output. Transmission path in a PCM system(Regenerative Repeater): The channel introduces distortion in the signal during transmission. This distortion is eliminated by the regenerator in order to provide a distortion less PCM signal. Resultantly, enhancing the transmission ability of the system.
- 39. The PCM signal when provided to the regenerative repeater, the equalizer circuit at the beginning performs the reshaping of the distorted signal. At the same time, the timing circuit generates a pulse train that is a derivative of input PCM pulses. This pulse train is then utilized by the decision-making device in order to sample the PCM pulses. In decision device when the output of amplifier /equalizer is exceeds the predetermine voltage level in the duration of each pulse ,the decision device takes yes then immediately a new pulse generated and transmitted otherwise a clean base line is transmitted
- 40. PCM Receiver The figure below shows the functional block diagram of a PCM receiver Regenerator: A regenerative repeater is placed at the receiving end also so as to have an exact PCM transmitted signal. Here, also the regenerator works in a similar manner as that when employed in the transmission path. It eliminates the channel induced noise and reshapes the pulse. DAC and Sampler: Digital to analog converter performs the conversion of digital signal again into its analog form by making use of the sampler. As the actual message signal was analog thus at the receiver end there is a necessity to again convert it into its original form. LPF: The sampler generates analog signal but that is not the original message signal.
- 41. Transmission bandwidth in Pulse Code Modulation: Bandwidth depends on Bit Rate and pulse shape used to represents the data . The transmission bandwidth of a PCM system is associated with a number of bits per sample. If the number of bits per sample increases, the bandwidth also increases. Let us consider each quantizer level is represented by ‘n’ binary digits. Then the levels represented by n binary digits is given as, q = 2n where q is the digital level of the quantizer. Every sample is changed into n bits, thus, a number of bit per sample is ‘n’. Hence the number of bits per second which is also termed as signalling rate is given as, Bit rate r = n fs As transmission bandwidth is half the signalling rate, hence Therefore But we know, fs ≥ 2fm Thus the bandwidth of the PCM system is BW ≥ n fm
- 42. Ex: The human voice frequency 3.5 KHz, what is the bit rate and bandwidth , assuming 8 bits per sample. Given fm=3.5KHz n=8 Bandwidth =data rate /2=56KHz/2=28KHz Where data rate r = nfs= 8x7KHz=56KHz fs =2fm= 2x3.5KHz=7KHz
- 43. Advantages of PCM 1. Immune to channel induced noise and distortion. 2. Repeaters can be employed along the transmitting channel. 3. Encoders allow secured data transmission. 4. It ensures uniform transmission quality. Disadvantages of PCM 5. Pulse code modulation increases the transmission bandwidth. 6. A PCM system is somewhat more complex than another system.
- 49. Am
- 50. Non-Uniform Quantization: In non-uniform quantization, the step size is not fixed. It varies according to certain law or as per input signal amplitude. It is also known as non-linear quantization.T he following fig shows the characteristics of Non uniform quantizer.
- 51. Companding in PCM The word Companding is a combination of Compressing and Expanding, which means that it does both. This is a non-linear technique used in PCM which compresses the data at the transmitter and expands the same data at the receiver. The effects of noise and crosstalk are reduced by using this technique There are two types of Companding techniques. They are − A-law Companding Technique Uniform quantization is achieved at A = 1, where the characteristic curve is linear and no compression is done. A-law has mid-rise at the origin. Hence, it contains a non-zero value. A-law companding is used for PCM telephone systems(European standard) µ-law Companding Technique Uniform quantization is achieved at µ = 0, where the characteristic curve is linear and no compression is done. µ-law has mid-tread at the origin. Hence, it contains a zero value. µ-law companding is used for speech and music signals. µ-law is used in North America and Japan.
- 56. A-law
- 58. The samples of a signal are highly correlated with each other. This is due to the fact that any signal does not change fast. Which means , its value from present sample to next sample does not vary by a large amount. The adjacent samples of the signal carry the same information with a little difference. When these samples are encoded by a standard PCM system, the resulting encoded signal contains some redundant information Differential Pulse Code Modulation
- 59. The sampling frequency is selected to be higher than nyquist rate. The samples are encoded by using 3 bit (7 levels) PCM. The sample is quantized to the nearest digital level as shown by small circles in fig. The encoded binary value of each sample is written on the top of the samples. We can observe from fig. that the samples taken at 4Ts , 5Ts and 6Ts are encoded to same value of (110). Redundant Information in PCM Fig shows a continuous time signal x(t) by dotted line. This signal is sampled by flat top sampling at intervals Ts , 2Ts , 3Ts ….. nTs . This information can be carried only by one sample. But three smaples are carrying the same information means that it is redundant .
- 60. Transmitter of DPCM system
- 64. Fig Differential Pulse Code Modulation Receiver
- 65. Advantages of DPCM Data rate reduction Bandwidth requirement is saved Data is compressed Delta Modulation The operating principle of DM is such that, a comparison between present and previously sampled value is performed, the difference of which decides the increment or decrement in the transmitted values. Simply put, when the two sample values are compared, either we get difference having a positive polarity or negative polarity. If the difference polarity is positive, then the step of the signal denoted by Δ is increased by 1. As against in case when difference polarity is negative then step of the signal is decreased i.e., reduction in Δ. When +Δ is noticed i.e., increase in step size, then 1 is transmitted. However, in the case of –Δ i.e., decrease in step size, 0 is transmitted. Hence, allowing only a single binary bit to get transmitted for each sample.
- 67. Figure shows Delta Modulator. In the block diagram of this delta modulation, the summer block and delay circuit block are called as Accumulator. And accumulator generates the staircase approximated signal with having delayed by one sample period of Ts. The accumulator block summer2 adds the quantizer output signal and previous sample approximation, and this results in u(nTs). The previous sample is achieved by delaying the present sample period approximation u(nTs)=u([n-1]Ts) + b(nTs) “Present sample value X(nTs) and staircase approximated signal x(nTs) both are subtracted to know the error signal e(nTs). If e(nTs) is positive, then the one-bit quantizer circuit increase the step size +Δ and bit 1 is transmitted. If the error is negative, then step size is reduced by –Δ and bit 0 is transmitted to the output.” Present sample value is X(nTs) The previous sample value is u([n-1]Ts) e(nTs) is an error signal between the present sample and previous sample b(nTs) is the quantizer output signal
- 70. Delta Demodulator(In the Receiver Section) In the block diagram of this modulation, the summer block and delay circuit block are called as Accumulator. And accumulator generates the staircase approximated signal with having delayed by one sample period of Ts. “The accumulator’s generated delayed signal is added to the input signal to this modulation receiver block diagram along with the delta modulated output sequence. And if the delta modulated output sequence is 1, then the delayed signal is increased by +Δ and if the sequence is 0, then the staircase approximated signal is reduced by –Δ. And the final staircase approximated signal is forwarded from the low pass filter (LPF) to recover the original signal X(nTs)”. Advantages of DM over DPCM 1-bit quantizer Very easy design of modulator & demodulator However, there exists some noise in DM a. Slope Over load distortion (when Δ is small) b. Granular noise (when Δ is large)
- 71. Slope Overload Distortion This distortion arises because of large dynamic range of the input signal. from fig.1 , the rate of rise of input signal x(t) is so high that the staircase signal can not approximate it, the step size ‘Δ’ becomes too small for staircase signal u(t) to follow the step segment of x(t). Hence, there is a large error between the staircase approximated signal and the original input signal x(t).This error or noise is known as slope overload distortion .To reduce this error, the step size must be increased when slope of signal x(t) is high.
- 72. Granular or Idle Noise Granular or Idle noise occurs when the step size is too large compared to small variation in the input signal. This means that for very small variations in the input signal, the staircase signal is changed by large amount (Δ) because of large step size. fig: shows that when the input signal is almost flat , the staircase signal u(t) keeps on oscillating by ±Δ around the signal. The error between the input and approximated signal is called granular noise. The solution to this problem is to make the step size small .
- 73. Adaptive Delta Modulation To overcome the quantization errors due to Slope overload and Granular noise, the step size Δ is made adaptive to variations in the input signal x(t). Particularly in the steep segment of the signal x(t), the step size is increased. Also, if the input is varying slowly, the step size is reduced. Then, this method is known as Adaptive Delta Modulation (ADM). The adaptive delta modulators can take continuous changes in step size or discrete changes in step size.
- 74. The logic for step size control is added in the diagram. Step size increased or decreased according to a specified rule and example of one-bit quantizer output. As an example, if the one-bit quantizer output is high (i.e. 1) then the step size may be doubled for the next sample. If the one-bit quantizer output is low, then the step size may be reduced by one step. Figure (2) shows the staircase waveforms of the adaptive delta modulator and the sequence of bits to be transmitted.
- 76. Receiver Part: In the receiver of the adaptive delta modulator shown in Figure there are two portions. The first portion produces the step size from each incoming bit. Exactly the same process is followed as that in the transmitter. The previous input and present input decides the step size. It is then applied to an accumulator which builds up the staircase waveform. The low- pass filter then smoothens out the staircase waveform to reconstruct the original signal.
- 77. Adaptive delta modulation has certain advantages over delta modulation: the signal to noise ratio becomes better than ordinary delta modulation because of the reduction in slope overload distortion and idle noise. because of the variable step size, the dynamic range of ADM is wider than simple DM. utilization of bandwidth is better than delta modulation. The following is a list of some of the applications for this modulation technique: This modulation is used in systems that demand faster bit transfers and better wireless voice quality. This modulation technique is employed in the transmission of television signals. In voice coding, this modulation technique is utilized. Additionally, NASA adheres to this modulation as the norm for all communications between mission control and spacecraft. Adaptive Delta Modulation operates at a rate of 12 Kbits/sec in Motorola’s SECURENET line of digital radio products.