A pulse in signal processing is a rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. [1]
A pulse in signal processing is a rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. [1]
Pulse shapes can arise out of a process called pulse-shaping. Optimum pulse shape depends on the application.
These can be found in pulse waves, square waves, boxcar functions, and rectangular functions. In digital signals the up and down transitions between high and low levels are called the rising edge and the falling edge. In digital systems the detection of these sides or action taken in response is termed edge-triggered, rising or falling depending on which side of rectangular pulse. A digital timing diagram is an example of a well-ordered collection of rectangular pulses.
A Nyquist pulse is one which meets the Nyquist ISI criterion and is important in data transmission. An example of a pulse which meets this condition is the sinc function. The sinc pulse is of some significance in signal-processing theory but cannot be produced by a real generator for reasons of causality.
In 2013, Nyquist pulses were produced in an effort to reduce the size of pulses in optical fibers, which enables them to be packed 10 times more closely together, yielding a corresponding 10-fold increase in bandwidth. The pulses were more than 99 percent perfect and were produced using a simple laser and modulator. [2] [3]
A Dirac pulse has the shape of the Dirac delta function. It has the properties of infinite amplitude and its integral is the Heaviside step function. Equivalently, it has zero width and an area under the curve of unity. This is another pulse that cannot be created exactly in real systems, but practical approximations can be achieved. It is used in testing, or theoretically predicting, the impulse response of devices and systems, particularly filters. Such responses yield a great deal of information about the system.
A Gaussian pulse is shaped as a Gaussian function and is produced by the impulse response of a Gaussian filter. It has the properties of maximum steepness of transition with no overshoot and minimum group delay.
Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in unit of hertz.
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant in which case they can be analyzed exactly using LTI system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear time-invariant filters can be completely characterized by their response to sinusoids of different frequencies, they are sometimes known as frequency filters.
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing. In practice, it is used to select band-limiting filters to keep aliasing below an acceptable amount when an analog signal is sampled or when sample rates are changed within a digital signal processing function.
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making the communication less reliable. The spreading of the pulse beyond its allotted time interval causes it to interfere with neighboring pulses. ISI is usually caused by multipath propagation or the inherent linear or non-linear frequency response of a communication channel causing successive symbols to blur together.
Pulse-width modulation (PWM), also known as pulse-duration modulation (PDM) or pulse-length modulation (PLM), is any method of representing a signal as a rectangular wave with a varying duty cycle.
In digital signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts (aliasing) when representing a high-resolution image at a lower resolution. Anti-aliasing is used in digital photography, computer graphics, digital audio, and many other applications.
In signal processing and statistics, a window function is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are symmetric around the middle of the interval, approach a maximum in the middle, and taper away from the middle. Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window". Equivalently, and in actual practice, the segment of data within the window is first isolated, and then only that data is multiplied by the window function values. Thus, tapering, not segmentation, is the main purpose of window functions.
In signal processing, a sinc filter can refer to either a sinc-in-time filter whose impulse response is a sinc function and whose frequency response is rectangular, or to a sinc-in-frequency filter whose impulse response is rectangular and whose frequency response is a sinc function. Calling them according to which domain the filter resembles a sinc avoids confusion. If the domain is unspecified, sinc-in-time is often assumed, or context hopefully can infer the correct domain.
Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or superposition, of plane waves. It has some parallels to the Huygens–Fresnel principle, in which the wavefront is regarded as being made up of a combination of spherical wavefronts whose sum is the wavefront being studied. A key difference is that Fourier optics considers the plane waves to be natural modes of the propagation medium, as opposed to Huygens–Fresnel, where the spherical waves originate in the physical medium.
Amplitude-shift keying (ASK) is a form of amplitude modulation that represents digital data as variations in the amplitude of a carrier wave. In an ASK system, a symbol, representing one or more bits, is sent by transmitting a fixed-amplitude carrier wave at a fixed frequency for a specific time duration. For example, if each symbol represents a single bit, then the carrier signal could be transmitted at nominal amplitude when the input value is 1, but transmitted at reduced amplitude or not at all when the input value is 0.
Delta-sigma modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency as part of the process of delta-sigma analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). Delta-sigma modulation achieves high quality by utilizing a negative feedback loop during quantization to the lower bit depth that continuously corrects quantization errors and moves quantization noise to higher frequencies well above the original signal's bandwidth. Subsequent low-pass filtering for demodulation easily removes this high frequency noise and time averages to achieve high accuracy in amplitude which can be ultimately encoded as pulse-code modulation (PCM).
In a mixed-signal system, a reconstruction filter, sometimes called an anti-imaging filter, is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter (DAC) or other sampled data output device.
The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-zero portion of the frequency spectrum of its simplest form is a cosine function, 'raised' up to sit above the (horizontal) axis.
In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by a communication channel, result in no intersymbol interference or ISI. It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference.
The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in electrical communication.
First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an integrator. For FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled. A mathematical model such as FOH (or, more commonly, the zero-order hold) is necessary because, in the sampling and reconstruction theorem, a sequence of Dirac impulses, xs(t), representing the discrete samples, x(nT), is low-pass filtered to recover the original signal that was sampled, x(t). However, outputting a sequence of Dirac impulses is impractical. Devices can be implemented, using a conventional DAC and some linear analog circuitry, to reconstruct the piecewise linear output for either predictive or delayed FOH.
In electronics and signal processing, mainly in digital signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function. Gaussian filters have the properties of having no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. A Gaussian filter will have the best combination of suppression of high frequencies while also minimizing spatial spread, being the critical point of the uncertainty principle. These properties are important in areas such as oscilloscopes and digital telecommunication systems.
In electronics and telecommunications, pulse shaping is the process of changing a transmitted pulses' waveform to optimize the signal for its intended purpose or the communication channel. This is often done by limiting the bandwidth of the transmission and filtering the pulses to control intersymbol interference. Pulse shaping is particularly important in RF communication for fitting the signal within a certain frequency band and is typically applied after line coding and modulation.
In signal processing, particularly digital image processing, ringing artifacts are artifacts that appear as spurious signals near sharp transitions in a signal. Visually, they appear as bands or "ghosts" near edges; audibly, they appear as "echos" near transients, particularly sounds from percussion instruments; most noticeable are the pre-echos. The term "ringing" is because the output signal oscillates at a fading rate around a sharp transition in the input, similar to a bell after being struck. As with other artifacts, their minimization is a criterion in filter design.
An acousto-optic programmable dispersive filter (AOPDF) is a special type of collinear-beam acousto-optic modulator capable of shaping spectral phase and amplitude of ultrashort laser pulses. AOPDF was invented by Pierre Tournois. Typically, quartz crystals are used for the fabrication of the AOPDFs operating in the UV spectral domain, paratellurite crystals are used in the visible and the NIR and calomel in the MIR (3–20 μm). Recently introduced lithium niobate crystals allow for high-repetition rate operation (> 100 kHz) owing to their high acoustic velocity. The AOPDF is also used for the active control of the carrier-envelope phase of few-cycle optical pulses, as a part of pulse-measurement schemes and multi-dimensional spectroscopy techniques. Although sharing a lot in principle of operation with an acousto-optic tunable filter, the AOPDF should not be confused with it, since in the former the tunable parameter is the transfer function and in the latter it is the impulse response.
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