Physics
Converting Analogue to Digital
Converting analogue to digital involves the process of representing continuous, analogue signals as discrete, digital values. This is typically achieved through sampling the analogue signal at regular intervals and quantizing the sampled values into binary numbers. The resulting digital representation allows for more efficient storage, transmission, and processing of the original analogue information.
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12 Key excerpts on "Converting Analogue to Digital"
eBook - PDF- Ian R. Sinclair(Author)
- 2016(Publication Date)
- Newnes(Publisher)
Chapter 8 Digital-analogue Conversions So much signal processing now is digital rather than analogue, and since the display of information is by now much more oriented to digital rather than to analogue methods, the conversion between digital and analogue signals has assumed considerable importance. All conversion from analogue to digital form is based on sampling a waveform and converting the amplitude of each sample into digital signals. The type of digital signal is normally a binary number whose size is proportional to the amplitude of the analogue signal, and the frequency of analogue signal that can be handled depends critically on the rate at which conversion can be achieved. Conversion in the opposite direction has been achieved in the past by methods that used the binary codes of the digital signal to generate analogue voltages which were summed but, as will be ex-plained, this method is often inadequate for precise conversions and has been replaced by other systems, some of which are not quite so new as might be thought at first. Analogue-to-digital conversion The conversion of analogue signals into digital form is the essential first step in any system that will use digital methods for counting, display or logic actions. It is often necessary to distinguish between conversion and modulation in this context. Conversion means the processing of an analogue signal into a set of digital signals, and modulation means the change from the original digital signal into a type of digital signal that can be stored or transmitted by an error-free method. The two are very often closely bound up with each other because many forms of conversion are 240 Digital-analogue Conversions 241 also forms of modulation. In general, if digital signals are to be transmitted over parallel lines only conversion is needed, but if a serial line is to be used, modulation may be necessary in addition to conversion.
eBook - PDF- Ian Sinclair, John Dunton(Authors)
- 2013(Publication Date)
- Newnes(Publisher)
Digital -Analogue Conversions 251 Analogue-to-digital conversion CHAPTER 9 DIGITAL -ANALOGUE CONVERSIONS So much signal processing now is digital rather than analogue, and since the display of information is by now much more oriented to digital rather than to analogue methods, the conversion between digital and analogue signals has assumed considerable importance. All conversion from analogue to digital form is based on sampling a waveform and converting the amplitude of each sample into digital signals. The type of digital signal is normally a binary number whose size is proportional to the amplitude of the analogue signal, and the frequency of analogue signal that can be handled depends critically on the rate at which conversion can be achieved. Conversion in the opposite direction has been achieved in the past by methods that used the binary codes of the digital signal to generate analogue voltages which were summed but, as will be explained, this method is often inadequate for precise conversions and has been replaced by other systems, some of which are not quite so new as might be thought at first. A n a l o g u e -t o -d i g i t a l conversion The conversion of analogue signals into digital form (strictly speaking, into pulse-code modulated digital form) is the essential first step in any system that will use digital methods for counting, display or logic actions. It is often necessary to distinguish between conversion and modulation in this context. Conversion means the processing of an analogue signal into a set of digital signals, and modulation means the change from the original digital signal into a type of digital signal that can be stored or transmitted by an error-free method. The two are very often closely bound up with each other because many forms of conversion are also forms of modulation.
eBook - ePub- Slawomir Tumanski(Author)
- 2006(Publication Date)
- CRC Press(Publisher)
5 Digital Processing of the Measurement Signals5.1. ANALOGUE-TO-DIGITAL CONVERTERS
5.1.1. Sampling, quantization and coding of signals
The technical world is becoming more and more digital because digital signals are very convenient for information processing. However, most physical phenomena are analogue and the sensors measure analogue quantities. For that reason, the digital signal processing is often realized in the following sequence: conversion of the analogue signal to digital form digital signal processing conversion of the digital signal back to the analogue one. The conversion is realized by the analogue-to-digital converters ADC while the reverse process is realized by digital to analogue converters DAC.The analogue signals are of continuous time – the value of such signal is determined in every instant of time. An example of the analogue signal is presented in Fig.5.1 a. The conversion of the analogue signal x(t) to the digital form is realized in such a way that in assumed moment of time the value of the signal x(n) is determined and represented by a number. We can say that the digital signal is determined in discrete time, which means that the value of the signal is known only in selected moments. Usually the discrete time is realized by collecting the samples of the analogue signal at the constant interval called the period of sampling Ts (Fig.5.1 b).Figure 5.1 . The analogue signal (a) and its conversion to the discrete one (b)The process of collection of the samples is called the sampling process of analogue signals. The frequency fs =1/Ts is called the sampling frequency and it is described in Hz or SPS – samples per second. The process of determination of the digital value of the samples is called the quantization
- Steven F. Barrett, Daniel J. Pack(Authors)
- 2022(Publication Date)
- Springer(Publisher)
We do not want the sample to vary during the conversion process. 5.4.3 Digital-to-Analog Conversion Once a signal is acquired to a digital system with the help of the analog-to digital conversion process and has been processed, frequently the processed signal is converted back to another analog signal. A simple example of such a conversion occurs in digital audio processing. Human voice is converted to a digital signal, modified, processed, and converted back to an analog signal for people to hear. The process to convert digital signals to analog signals is completed by a digital-to-analog converter. The most used technique to convert digital signals to analog signals is the summation method shown in Figure 5.9. FIGURE 5.9: A summation method to convert a digital signal into a quantized analog signal. Com- parators are used to clean up incoming signals and the resulting values are multiplied by a scalar multiplier and the results are added to generate the output signal. For the final analog signal, the quantized analog signal should be connected to a low pass filter followed by a transducer interface circuit ANALOG-TO-DIGITAL CONVERSION 81 With the summation method of digital-to-analog conversion, a digital signal, repre- sented by a set of ones and zeros, enters the digital-to-analog converter from the most sig- nificant bit to the least significant bit. For each bit, a comparator checks its logic state, high or low, to produce a clean digital bit, represented by a voltage level. Typically, in a micro- controller context, the voltage level is +5 or 0 V to represent logic one or logic zero, re- spectively. The voltage is then multiplied by a scalar value based on its significant position of the digital signal as shown in Figure 5.9. Once all bits for the signal have been processed, the resulting voltage levels are summed together to produce the final analog voltage value.
eBook - ePub- Edmund Lai(Author)
- 2003(Publication Date)
- Newnes(Publisher)
2Converting analog to digital signals and vice versa
2.1 A typical DSP system
In the previous chapter, we mentioned that some signals are discrete-time in nature, while others are continuous-time. Most of the signals encountered in engineering applications are analog. In order to process analog signals using digital techniques, they must first be converted into digital signals.Digital processing of analog signals proceeds in three stages:• The analog signal is digitized. Digitization involves two processes: sampling (digitization in time) and quantization (digitization in amplitude). This whole process is called analog-to-digital (A/D) conversion.• The appropriate DSP algorithms process the digitized signal. • The results or outputs of the processing are converted back into analog signals through interpolation. This process is called digital-to-analog (D/A) conversion.Figure 2.1 illustrates these three stages in diagram form.Figure 2.1 The three stages of analog–digital–analog conversions2.2 Sampling
We shall first consider the sampling operation. It can be illustrated through the changing temperature through a single day. The continuous temperature variation is shown in Figure 2.2 . However, the observatory may only be recording the temperature once every hour.Figure 2.2 Temperature variation throughout a dayThe records are shown in Table 2.1 . When we plot these values against time, we have a snapshot of the variation in temperature throughout the day. These snapshots are called samples of the signal (temperature). They are plotted as dots in Figure 2.2 . In this case the sampling interval, the time between samples, is two hours.Table 2.1 Temperature measured at each hour of a dayHour Temperature 0 13 2 12 4 10 6 11 8 13 10 16 12 19 14 23 16 22 18 20 20 16 22 15 24 12 Figure 2.3 shows the diagram representation of the sampling process.Figure 2.3 The sampling processThe analog signal is sampled once every T
eBook - PDFMicrochip AVR® Microcontroller Primer
Programming and Interfacing, Third Edition
- Steven F. Barrett, Daniel J. Pack(Authors)
- 2022(Publication Date)
- Springer(Publisher)
The same analysis can be performed as we move spatially from the top to the bottom of the image. Analog signals are those whose physical variable values change continuously over their independent variable. Most physical variables, your speech characteristics, movement of stars, 4.2. BACKGROUND THEORY 101 Figure 4.2: A photo of a walking robot. and the music you hear at a concert are all examples of analog signals. Digital signals, on the other hand, have their physical variables defined only for discrete instances over their indepen- dent variables. Although it may look continuous to human eyes, the photo example shown in Figure 4.2 is a discrete signal because pixels (picture elements) that make up a camera image cannot capture all space within the camera frame. The image is only a finite composition of discrete intensity values seen by a discrete number of pixels. Digital signals are important because all signals represented in digital systems, computers, and microcontrollers are in digital forms. The important task is how to faithfully represent analog signals using digital signals. For example, human voices must be converted to corresponding digital signals before they can be routed by digital switching circuits in telephone communication systems. Similarly, voice commands to robots must be converted to a digital form before robots can process the command. 102 4. ANALOG-TO-DIGITAL CONVERSION As shown in the previous examples, we live in an analog world; that is, physical variables are analog signals. It is precisely this reason why the ADC is so very important in any digital systems that interact with an analog environment. 4.2.2 SAMPLING, QUANTIZATION, AND ENCODING In this subsection, three important processes associated with the ADC are presented, starting with the subject of sampling. Imagine yourself as a photographer in an Olympic diving stadium.
eBook - ePub- Karl Stephan(Author)
- 2015(Publication Date)
- Wiley(Publisher)
The second major application of electricity to come along was the telephone, which was developed in the 1870s. The sound waves produced by the human voice are continuous variations in air pressure, which were most conveniently translated into continuous variations in voltage by a diaphragm-operated device called a transmitter. A similar device at the receiving end translated the voltage variations back into air-pressure variations to be heard by the ear. We would term the early telephone a primarily analog system, though it soon acquired digital features such as pulse-actuated automatic dialing.As a matter of statistics, the vast majority of electronic signals today are in digital form, meaning that their interpretation involves the ones and zeroes of digital technology. This is mainly because digital signal processing and related digital technologies are vastly more powerful, flexible, and better performing than their analog-signal-processing counterparts, if such counterparts exist at all. Many routine digital processes today could not be performed at all with analog-only systems, no matter how elaborate or expensive.However, many signals of interest exist in analog form—light waves, sound waves, motions of objects, positions of obstacles on a road, and so on. For digital processing to occur, all these analog signals must be transformed into a form that is easily dealt with by digital systems. And at the other end of the process, digital information and commands must often be converted back into an analog quantity or signal. So as long as there are real-world inputs and outputs that are not digital, there will be a need to convert between the analog and the digital domains. The conversion process is the subject of this chapter.We will now turn to more specific definitions and discussions of the two main ways one can represent information in electronics.8.2 ANALOG AND DIGITAL SIGNALS
8.2.1 Analog Signals and Measurements
An analog signal is a form of electrical energy (voltage, current, or electromagnetic power) for which there is (ideally) a linear relationship between the electrical quantity and the value that the signal represents. As an example, in the case of a telephone or microphone signal as discussed in Chapter 6 , there is a direct proportion between the instantaneous sound pressure change p (in pascals) at the microphone and the microphone’s output voltage v
- Nasser Kehtarnavaz, Namjin Kim(Authors)
- 2011(Publication Date)
- Newnes(Publisher)
CHAPTER Analog-to-Du'gital Signal Conversion The process of analog-to-digital signal conversion consists of converting a continu- ous time and amplitude signal into discrete time and amplitude values. Sampling and quantization constitute the steps needed to achieve analog-to-digital signal conversion. To minimize any loss of information that may occur as a result of this conversion, it is important to understand the underlying principles behind sampling and quantization. 3.1 Sampling Sampling is the process of generating discrete time samples from an analog signal. First, it is helpful to mention the relationship between analog and digital frequencies. Let us consider an analog sinusoidal signal x(t) = Acos(mt + ~). Sampling this signal at t = nT~, with the sampling time interval of Ts, generates the discrete time signal x[n]- Acos(mnT~ +~)- Acos(~n+~), n-0,1,2,..., (3.1) where e- mT s - 2rtf denotes digital frequency with units being radians (as compared fs to analog frequency m with units being radians/sec). The difference between analog and digital frequencies is more evident by observing that the same discrete time signal is obtained from different continuous time signals if the product roTs remains the same. (An example is shown in Figure 3-1.) Likewise, different discrete time signals are obtained from the same analog or continuous time signal when the sampling frequency is changed. (An example is shown in Figure 3-2.) In other words, both the frequency of an analog signal f and the sampling fre- quency fs define the frequency of the corresponding digital signal ~. 43 0.5 -0.5 -1 1 0.5 -0.5 -1 1 x(t) = cos(2rl:t) i 1.5 0.5 0 -0.5 -1 0 Ts = O.05s .......... i ............ i ............ 5 10 15 20 Chapter 3 x(t) = cos(4nt) 1.5 2 1 0.5 0 -0.5 -1 ,-- 0 5 10 15 20 Ts = 0.025s t.tT .......... } ............ i .............. Figure 3-1- Sampling of two different analog signals leading to the same digital signal.
eBook - PDF- Jocelyn O. Padallan(Author)
- 2019(Publication Date)
- Arcler Press(Publisher)
The physical movements of objects can be modeled in a spatial simulation, and real-time audio and video can be captured using a range of systems and devices with the help of digital data. This model of information capture is of great value to many parties like businesses and government agencies to explore new boundaries of data collection. This is done with the help of small microprocessors and large data storage centers and it will further improve simulation through the digital interface. 4.3. DIGITAL TO DIGITAL CONVERSION The data can be of two types, analog or digital. Also, the signals that represent the data can also be either analog or digital. In this section, we learn about representation of digital data with the help of digital signals. There are three ways of conversion. They are line coding, block coding and scrambling. In this digital to digital conversion, line coding is a must whereas block coding may or may not be needed. 4.3.1. Line Coding The first type in the conversion of digital data to digital signals is called as line coding. In this process, the data is assumed in the form of numbers, graphical images, audio, and video or even in the form of text which are stored as a series of bits in the memory of computer. With the help of line coding a sequence of bits is converted into a digital signal (Figure 4.4). Figure 4.4: Line coding ( Source: http://www.idc-online.com/technical_refer -ences/pdfs/data_communications/Digital_Transmission.pdf). Computer Networks and Communications 88 Digital data are encoded into a digital signal at the sender side and at the receiver side, the digital data are again recreated by decoding the digital signal. There are some properties of line codes which are very much important. These properties are listed below • The transmission bandwidth must be kept as small as possible. • The power efficiency is also as small as possible for a given bandwidth and probability of error.
eBook - PDFDigital Electronic Circuits
Principles and Practices
- Shuqin Lou, Chunling Yang(Authors)
- 2019(Publication Date)
- De Gruyter(Publisher)
11 Analog-to-digital and digital-to-analog converter 11.1 Introduction With the rapid development of digital technology, digital technology has already been applied to a wide range of areas besides computer system. Such applica-tions include communication systems, radar, navigation and guidance systems, military systems, medical instrumentation, industrial process control, and many others. However, digital circuits and digital systems deal with digital quantity. From physics point of view, a digital quantity is the one having a discrete set of values. Most things that can be measured quantitatively in nature with analog form. In order to process these analog quantities with digital technique, it is necessary to convert the analog quantity to a digital one. The device that converts an analog signal to a digital signal is called the analog-to-digital converter (ADC). Moreover, most electronic instruments are driven by analog signals and thus the processed digital quantity must be converted back to analog signal to drive the electronic equipment. The circuit that converts the digital signal to an analog signal is called the digital-to-analog converter (DAC). This chapter first introduces the basic concepts and then the operating princi-ples of DAC and ADC. Several typical integration DAC and ADC chips and their applications are also covered. The objectives of this chapter are to – Explain how analog signals are converted to digital forms – Describe the sample process – State the purpose of digital-to-analog conversion – Explain the operating process of several types of DACs – State the purpose of analog-to-digital conversion – Explain the operating process of several types of ADCs 11.2 Digital-to-Analog Converter (DAC) In electronics, a digital-to-analog converter (DAC, D/A, or D-to-A) is a circuit that converts a digital signal into an analog signal. DAC is an important part of a digital processing system.
eBook - PDF- BRUCE NEWBY(Author)
- 2014(Publication Date)
- Butterworth-Heinemann(Publisher)
11 Analogue and digital conversions 11.1 Introduction There is an ever increasing use of digital computers in modem process control systems and the transmission of information is increasingly undertaken using digital communication systems. However, the analogue 'ends' of the typical digital control or communications system have not been outmoded; they never will be so long as people need to interface with them. For this reason alone, there is an important requirement for the rapid and accurate translation be-tween the analogue and digital formats. Figure 11.1 is a block diagram of a typical analogue process which employs a digital microcomputer. The sensing transducer in the analogue process may be a thermocouple responding to the temperature of a tank of heated liquid. The temperature of the tank could be monitored by the digital microcomputer. It could also be required to compare the reading from the thermocouple with a pre-set value it already holds. The result of the comparison may require the microcomputer to send control signals to an analogue fuel supply valve back in the analogue process. Such a situation requires both an analogue-to-digital conversion (ADC) and the reverse digital-to-analogue (DAC) function. I I I r L. Transducer sensor Analogue controller Process Analogue signals ADC Digital signals ΐΗ Analogue signals DAC K^J Digital signals Digital microcomputer process control program Out Figure 11.1 Analogue process controlled by a digital microcomputer 222 Analogue and digital conversions 11.2 General conversion principles and terminology 11.2.1 Sampling the analogue input Figure 11.2 shows the principle involved in sampling an analogue voltage to form a series of digital pulses. The analogue waveform to be sampled is shown in (a), the times at which (a) is sampled in (b) and the train of sample digital pulses so produced in (c).
eBook - PDF- Paul Regtien, F. van der Heijden, M. J. Korsten, W Otthius(Authors)
- 2004(Publication Date)
- Butterworth-Heinemann(Publisher)
Chapter 6 Analogue to Digital and Digital to Analogue Conversion An analogue signal is not suitable for processing by a digital computer. Only after conversion into a digital signal, can it be handled by the computer. Con- versely, many actuators and other Output devices require analogue signals, hence the digital signals from a computer have to be converted into an analogue format. Analogue-to-digital converters (AD-converters or ADC's) and digital-to-analogue converters (DA-converters or DAC's) are available as modules or integrated cir- cuits. In Chapter 5 digital signals, binary codes and some digital processing elements have been introduced. This chapter starts with an overview of the main causes of conversion errors. The remaining sections are devoted to particular types of converters and their major characteristics. 6.1. Conversion errors In this section we discuss the main errors occurring in the conversion from the analogue to the digital signal domain. These errors include the quantization and sampling errors (which are independent of the converter type) and some converter- specific errors, due to shortcomings of the electronic components of the converter. 6.1.1. Quantization noise Figure 6.1 represents the transfer characteristic of an AD converter. The range of the converter is set by the reference voltage Vre f. Usually, the range is from 0 to Vref, but some converters allow a user-specific range setting, for instance from _! 2 Vref to + 1 Vref An ideal converter performs a perfect rounding off to the nearest quantization level. Obviously, the maximum error is 1LSB or - 89 LSB. For a fixed input signal and range the quantization error decreases with an increasing number of bits n. It is possible to express the quantization error in terms of noise power or in rms value. Suppose the intervals between two successive levels are all the same and equal to q (uniform quantization, see Chapter 3).
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