Digital signal

Last updated A binary signal, also known as a logic signal, is a digital signal with two distinguishable levels

A digital signal is a signal that is being used to represent data as a sequence of discrete values; at any given time it can only take on one of a finite number of values.    This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within a continuous range of values.

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set, i.e., it defines all subsets as open sets. In particular, each singleton is an open set in the discrete topology.

An analog signal is any continuous signal for which the time-varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves. It differs from a digital signal, in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values. The term analog signal usually refers to electrical signals; however, mechanical, pneumatic, hydraulic, human speech, and other systems may also convey or be considered analog signals. In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as 2. Included within the irrationals are the transcendental numbers, such as π (3.14159265...). In addition to measuring distance, real numbers can be used to measure quantities such as time, mass, energy, velocity, and many more.

Contents

Simple digital signals represent information in discrete bands of analog levels. All levels within a band of values represent the same information state. In most digital circuits, the signal can have two possible values; this is called a binary signal or logic signal.  They are represented by two voltage bands: one near a reference value (typically termed as ground or zero volts), and the other a value near the supply voltage. These correspond to the two values "zero" and "one" (or "false" and "true") of the Boolean domain, so at any given time a binary signal represents one binary digit (bit). Because of this discretization, relatively small changes to the analog signal levels do not leave the discrete envelope, and as a result are ignored by signal state sensing circuitry. As a result, digital signals have noise immunity; electronic noise, provided it is not too great, will not affect digital circuits, whereas noise always degrades the operation of analog signals to some degree. 

In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as {0, 1}, or In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable.

Digital signals having more than two states are occasionally used; circuitry using such signals is called multivalued logic. For example, signals that can assume three possible states are called three-valued logic.

In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value. This is contrasted with the more commonly known bivalent logics which provide only for true and false. Conceptual form and basic ideas were initially created by Jan Łukasiewicz and C. I. Lewis. These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945.

In a digital signal, the physical quantity representing the information may be a variable electric current or voltage, the intensity, phase or polarization of an optical or other electromagnetic field, acoustic pressure, the magnetization of a magnetic storage media, etcetera. Digital signals are used in all digital electronics, notably computing equipment and data transmission. Polarization is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves in solids. Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions in nature, together with the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force. A received digital signal may be impaired by noise and distortions without necessarily affecting the digits

Definitions

The term digital signal has related definitions in different contexts.

In digital electronics

In digital electronics a digital signal is a pulse train (a pulse amplitude modulated signal), i.e. a sequence of fixed-width square-wave electrical pulses or light pulses, each occupying one of a discrete number of levels of amplitude.   A special case is a logic signal or a binary signal, which varies between a low and a high signal level. Digital electronics, digital technology or digital (electronic) circuits are electronics that operate on digital signals. In contrast, analog circuits manipulate analog signals whose performance is more subject to manufacturing tolerance, signal attenuation and noise. Digital techniques are helpful because it is a lot easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

In signal processing In signal processing, a digital signal is an abstraction that is discrete in time and amplitude, meaning it only exists at certain time instants.

In digital signal processing, a digital signal is a representation of a physical signal that is a sampled and quantized. A digital signal is an abstraction which is discrete in time and amplitude. The signal's value only exists at regular time intervals, since only the values of the corresponding physical signal at those sampled moments are significant for further digital processing. The digital signal is a sequence of codes drawn from a finite set of values.  The digital signal may be stored, processed or transmitted physically as a pulse-code modulation (PCM) signal.

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency.

Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the amplitude of the analog signal is sampled regularly at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps.

In communications A frequency shift keying (FSK) signal is alternating between two waveforms, and allows passband transmission. It is considered digital in literature on data transmission. An AMI coded digital signal used in baseband transmission (line coding)

In digital communications, a digital signal is a continuous-time physical signal, alternating between a discrete number of waveforms,  representing a bitstream. The shape of the waveform depends the transmission scheme, which may be either a line coding scheme allowing baseband transmission; or a digital modulation scheme, allowing passband transmission over long wires or over a limited radio frequency band. Such a carrier-modulated sine wave is considered a digital signal in literature on digital communications and data transmission,  but considered as a bitstream converted to an analog signal in electronics and computer networking. 

In communications, sources of interference are usually present, and noise is frequently a significant problem. The effects of interference are typically minimized by filtering off interfering signals as much as possible and by using data redundancy. The main advantages of digital signals for communications are often considered to be the noise immunity to noise capability, and the ability, in many cases such as with audio and video data, to use data compression to greatly decrease the bandwidth that is required on the communication media.

Logic voltage levels A logic signal waveform: (1) low level, (2) high level, (3) rising edge, and (4) falling edge.

A waveform that switches representing the two states of a Boolean value (0 and 1, or low and high, or false and true) is referred to as a digital signal or logic signal or binary signal when it is interpreted in terms of only two possible digits.

The two states are usually represented by some measurement of an electrical property: Voltage is the most common, but current is used in some logic families. A threshold is designed for each logic family. When below that threshold, the signal is low, when above high.

The clock signal is a special digital signal that is used to synchronize many digital circuits. The image shown can be considered the waveform of a clock signal. Logic changes are triggered either by the rising edge or the falling edge. The rising edge is the transition from a low voltage (level 1 in the diagram) to a high voltage (level 2). The falling edge is the transition from a high voltage to a low one.

Although in a highly simplified and idealized model of a digital circuit, we may wish for these transitions to occur instantaneously, no real world circuit is purely resistive and therefore no circuit can instantly change voltage levels. This means that during a short, finite transition time the output may not properly reflect the input, and will not correspond to either a logically high or low voltage.

Modulation

To create a digital signal, an analog signal must be modulated with a control signal to produce it. The simplest modulation, a type of unipolar encoding, is simply to switch on and off a DC signal, so that high voltages represent a '1' and low voltages are '0'.

In digital radio schemes one or more carrier waves are amplitude, frequency or phase modulated by the control signal to produce a digital signal suitable for transmission.

Asymmetric Digital Subscriber Line (ADSL) over telephone wires, does not primarily use binary logic; the digital signals for individual carriers are modulated with different valued logics, depending on the Shannon capacity of the individual channel.

Clocking

Digital signals may be sampled by a clock signal at regular intervals by passing the signal through a flip-flop. When this is done, the input is measured at the clock edge, and the signal from that time. The signal is then held steady until the next clock. This process is the basis of synchronous logic.

Asynchronous logic also exists, which uses no single clock, and generally operates more quickly, and may use less power, but is significantly harder to design.

Related Research Articles Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. In amplitude modulation, the amplitude of the carrier wave is varied in proportion to that of the message signal being transmitted. The message signal is, for example, a function of the sound to be reproduced by a loudspeaker, or the light intensity of pixels of a television screen. This technique contrasts with frequency modulation, in which the frequency of the carrier signal is varied, and phase modulation, in which its phase is varied. In telecommunications and signal processing, frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave.

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted. Most radio systems in the 20th century used frequency modulation (FM) or amplitude modulation (AM) for radio broadcast.

The amplitude of a periodic variable is a measure of its change over a single period. There are various definitions of amplitude, which are all functions of the magnitude of the difference between the variable's extreme values. In older texts the phase is sometimes called the amplitude. In electronics, an analog-to-digital converter is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. A delta modulation is an analog-to-digital and digital-to-analog signal conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of differential pulse-code modulation (DPCM) where the difference between successive samples are encoded into n-bit data streams. In delta modulation, the transmitted data are reduced to a 1-bit data stream. Its main features are:

A signal generator is an electronic device that generates repeating or non-repeating electronic signals in either the analog or the digital domain. These generated signals are used as a stimulus for electronic measurements, typically used in designing, testing, troubleshooting, and repairing electronic or electroacoustic devices, though it often has artistic uses as well. Pulse width modulation (PWM), or pulse-duration modulation (PDM), is a method of reducing the average power delivered by an electrical signal, by effectively chopping it up into discrete parts. The average value of voltage fed to the load is controlled by turning the switch between supply and load on and off at a fast rate. The longer the switch is on compared to the off periods, the higher the total power supplied to the load. Along with MPPT maximum power point tracking, it is one of the primary methods of reducing the output of solar panels to that which can be utilized by a battery. PWM is particularly suited for running inertial loads such as motors, which are not as easily affected by this discrete switching, because they have inertia to react slow. The PWM switching frequency has to be high enough not to affect the load, which is to say that the resultant waveform perceived by the load must be as smooth as possible. In electronics, a digital-to-analog converter is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.

In telecommunications, node-to-node data transfer is the movement of data from one node of a network to the next. In the OSI model it is handled by the lowest two layers, the data link layer and the physical layer.

A numerically-controlled oscillator (NCO) is a digital signal generator which creates a synchronous, discrete-time, discrete-valued representation of a waveform, usually sinusoidal. NCOs are often used in conjunction with a digital-to-analog converter (DAC) at the output to create a direct digital synthesizer (DDS). In signal processing, a signal is a function that conveys information about a phenomenon. In electronics and telecommunications, it refers to any time varying voltage, current or electromagnetic wave that carries information. A signal may also be defined as an observable change in a quantity.

Video modulation is a strategy of transmitting video signal in the field of radio modulation and television technology. This strategy enables the video signal to be transmitted more efficiently through long distances. In general, video modulation means that a higher frequency carrier wave is modified according to the original video signal. In this way, carrier wave contains the information in the video signal. Then, the carrier will "carry" the information in the form of radio frequency (RF) signal. When carrier reaches its destination, the video signal is extracted from the carrier by decoding. In other words, the video signal is first combined with a higher frequency carrier wave so that carrier wave contains the information in video signal. The combined signal is called radio-frequency signal. At the end of this transmitting system, the RF signals stream from a light sensor and hence, the receivers can obtain the initial data in the original video signal. A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, a VCO can be used for frequency modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. Power electronics is the application of solid-state electronics to the control and conversion of electric power. A function generator is usually a piece of electronic test equipment or software used to generate different types of electrical waveforms over a wide range of frequencies. Some of the most common waveforms produced by the function generator are the sine wave, square wave, triangular wave and sawtooth shapes. These waveforms can be either repetitive or single-shot. Integrated circuits used to generate waveforms may also be described as function generator ICs.

Analogue electronics are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relationship between a signal and a voltage or current that represents the signal. The word analogue is derived from the Greek word ανάλογος (analogos) meaning "proportional".

Delta-sigma modulation is a method for encoding analog signals into digital signals as found in an analog-to-digital converter (ADC). It is also used to convert high bit-count, low-frequency digital signals into lower bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter (DAC).

Pulse-density modulation, or PDM, is a form of modulation used to represent an analog signal with a binary signal. In a PDM signal, specific amplitude values are not encoded into codewords of pulses of different weight as they would be in pulse-code modulation (PCM); rather, the relative density of the pulses corresponds to the analog signal's amplitude. The output of a 1-bit DAC is the same as the PDM encoding of the signal. Pulse-width modulation (PWM) is a special case of PDM where the switching frequency is fixed and all the pulses corresponding to one sample are contiguous in the digital signal. For a 50% voltage with a resolution of 8-bits, a PWM waveform will turn on for 128 clock cycles and then off for the remaining 128 cycles. With PDM and the same clock rate the signal would alternate between on and off every other cycle. The average is 50% for both waveforms, but the PDM signal switches more often. For 100% or 0% level, they are the same. Switching Noise Jitter (SNJ) is the aggregation of variability of noise events in the time-domain on the supply bias of an electronic system, in particular with a voltage regulated supply bias incorporated with closed-loop (feedback) control, for instance, SMPS. SNJ is measurable using real-time spectral histogram analysis and expressed as a rate of occurrence in percentage. The existence of SNJ was firstly demonstrated and termed by TransSiP Inc in 2016 and 2017 at the Applied Power Electronics Conference (APEC), and reviewed with experts at Tektronix prior to be featured as a case study published by Tektronix. The discovery of SNJ was also featured in multiple articles published by Planet Analog magazine and EDN Network. Difficult to filter using conventional LC networks due to variability in both time and frequency domains, SNJ can introduce random errors in analog to digital conversion, affecting both data integrity and system performance in digital communications and location-based services

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