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80-640: The core modules of the project are the Atlas passive backplane, the Ozy interface which provides a USB 2.0 data channel between the HPSDR system and the host PC, and the Mercury and Penelope receiver and exciter boards, which use high speed ADCs and DACs for direct conversion of received or transmitted signals in the DC to 55 MHz frequency range. Mercury has attracted wide interest within

160-486: A capacitor to store the analog voltage at the input, and using an electronic switch or gate to disconnect the capacitor from the input. Many ADC integrated circuits include the sample and hold subsystem internally. An ADC works by sampling the value of the input at discrete intervals in time. Provided that the input is sampled above the Nyquist rate , defined as twice the highest frequency of interest, then all frequencies in

240-437: A digital encoder logic circuit that generates a binary number on the output lines for each voltage range. ADCs of this type have a large die size and high power dissipation. They are often used for video , wideband communications , or other fast signals in optical and magnetic storage . The circuit consists of a resistive divider network, a set of op-amp comparators and a priority encoder. A small amount of hysteresis

320-449: A light field or sound field with discrete elements, as in 3D displays or wave field synthesis of sound. This aliasing is visible in images such as posters with lenticular printing : if they have low angular resolution, then as one moves past them, say from left-to-right, the 2D image does not initially change (so it appears to move left), then as one moves to the next angular image, the image suddenly changes (so it jumps right) – and

400-466: A negative frequency . Temporal aliasing frequencies in video and cinematography are determined by the frame rate of the camera, but the relative intensity of the aliased frequencies is determined by the shutter timing (exposure time) or the use of a temporal aliasing reduction filter during filming. Like the video camera, most sampling schemes are periodic; that is, they have a characteristic sampling frequency in time or in space. Digital cameras provide

480-438: A saw-tooth signal that ramps up or down then quickly returns to zero. When the ramp starts, a timer starts counting. When the ramp voltage matches the input, a comparator fires, and the timer's value is recorded. Timed ramp converters can be implemented economically, however, the ramp time may be sensitive to temperature because the circuit generating the ramp is often a simple analog integrator . A more accurate converter uses

560-470: A 500 Hz sine wave. To avoid aliasing, the input to an ADC must be low-pass filtered to remove frequencies above half the sampling rate. This filter is called an anti-aliasing filter , and is essential for a practical ADC system that is applied to analog signals with higher frequency content. In applications where protection against aliasing is essential, oversampling may be used to greatly reduce or even eliminate it. Although aliasing in most systems

640-455: A certain number of samples ( pixels ) per degree or per radian, or samples per mm in the focal plane of the camera. Audio signals are sampled ( digitized ) with an analog-to-digital converter , which produces a constant number of samples per second. Some of the most dramatic and subtle examples of aliasing occur when the signal being sampled also has periodic content. Actual signals have a finite duration and their frequency content, as defined by

720-488: A certain sample frequency is called an anti-aliasing filter . The filtered signal can subsequently be reconstructed, by interpolation algorithms, without significant additional distortion. Most sampled signals are not simply stored and reconstructed. But the fidelity of a theoretical reconstruction (via the Whittaker–Shannon interpolation formula ) is a customary measure of the effectiveness of sampling. Historically

800-491: A clocked counter driving a DAC. A special advantage of the ramp-compare system is that converting a second signal just requires another comparator and another register to store the timer value. To reduce sensitivity to input changes during conversion, a sample and hold can charge a capacitor with the instantaneous input voltage and the converter can time the time required to discharge with a constant current . An integrating ADC (also dual-slope or multi-slope ADC) applies

880-525: A constant current source . The time required to discharge the capacitor is proportional to the amplitude of the input voltage. While the capacitor is discharging, pulses from a high-frequency oscillator clock are counted by a register. The number of clock pulses recorded in the register is also proportional to the input voltage. If the analog value to measure is represented by a resistance or capacitance, then by including that element in an RC circuit (with other resistances or capacitances fixed) and measuring

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960-432: A faithful reproduction of the original signal is only possible if the sampling rate is higher than twice the highest frequency of the signal. Since a practical ADC cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter performs a conversion (called the conversion time ). An input circuit called a sample and hold performs this task—in most cases by using

1040-516: A few are available as kits of parts. Several other modules are under development. A web site and Wiki provide further information about the HPSDR projects. . The HPSDR project is open-source for software and uses a combination of licenses for the hardware. There are many complete transceivers that are based on the OpenHPSDR concept: Analog-to-digital converter In electronics , an analog-to-digital converter ( ADC , A/D , or A-to-D )

1120-498: A few years earlier in fractional factorial designs . While Tukey did significant work in factorial experiments and was certainly aware of aliasing in fractional designs, it cannot be determined whether his use of "aliasing" in signal processing was consciously inspired by such designs. Aliasing occurs whenever the use of discrete elements to capture or produce a continuous signal causes frequency ambiguity. Spatial aliasing, particular of angular frequency, can occur when reproducing

1200-446: A flow of digital values. It is therefore required to define the rate at which new digital values are sampled from the analog signal. The rate of new values is called the sampling rate or sampling frequency of the converter. A continuously varying bandlimited signal can be sampled and then the original signal can be reproduced from the discrete-time values by a reconstruction filter . The Nyquist–Shannon sampling theorem implies that

1280-422: A known voltage charging and discharging curve that can be used to solve for an unknown analog value. The Wilkinson ADC was designed by Denys Wilkinson in 1950. The Wilkinson ADC is based on the comparison of an input voltage with that produced by a charging capacitor. The capacitor is allowed to charge until a comparator determines it matches the input voltage. Then, the capacitor is discharged linearly by using

1360-436: A longer time to measure than smaller one. And the accuracy is limited by the accuracy of the microcontroller clock and the amount of time available to measure the value, which potentially might even change during measurement or be affected by external parasitics . A direct-conversion or flash ADC has a bank of comparators sampling the input signal in parallel, each firing for a specific voltage range. The comparator bank feeds

1440-409: A pulse of a particular amplitude is always converted to the same digital value. The problem lies in that the ranges of analog values for the digitized values are not all of the same widths, and the differential linearity decreases proportionally with the divergence from the average width. The sliding scale principle uses an averaging effect to overcome this phenomenon. A random, but known analog voltage

1520-451: A sampler. It cannot improve the linearity, and thus accuracy does not necessarily improve. Quantization distortion in an audio signal of very low level with respect to the bit depth of the ADC is correlated with the signal and sounds distorted and unpleasant. With dithering, the distortion is transformed into noise. The undistorted signal may be recovered accurately by averaging over time. Dithering

1600-515: A sampling rate greater than twice the bandwidth of the signal, then per the Nyquist–Shannon sampling theorem , near-perfect reconstruction is possible. The presence of quantization error limits the SNDR of even an ideal ADC. However, if the SNDR of the ADC exceeds that of the input signal, then the effects of quantization error may be neglected, resulting in an essentially perfect digital representation of

1680-608: A snapshot of the lower right frame of Fig.2 shows a component at the actual frequency f {\displaystyle f} and another component at alias f − 1 ( f ) {\displaystyle f_{_{-1}}(f)} . As f {\displaystyle f} increases during the animation, f − 1 ( f ) {\displaystyle f_{_{-1}}(f)} decreases. The point at which they are equal ( f = f s / 2 ) {\displaystyle (f=f_{s}/2)}

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1760-432: Is a major concern in the sampling of video and audio signals. Music, for instance, may contain high-frequency components that are inaudible to humans. If a piece of music is sampled at 32,000 samples per second (Hz), any frequency components at or above 16,000 Hz (the Nyquist frequency for this sampling rate) will cause aliasing when the music is reproduced by a digital-to-analog converter (DAC). The high frequencies in

1840-430: 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 analog input 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

1920-451: Is a very small amount of random noise (e.g. white noise ), which is added to the input before conversion. Its effect is to randomize the state of the LSB based on the signal. Rather than the signal simply getting cut off altogether at low levels, it extends the effective range of signals that the ADC can convert, at the expense of a slight increase in noise. Dither can only increase the resolution of

2000-535: Is added to the sampled input voltage. It is then converted to digital form, and the equivalent digital amount is subtracted, thus restoring it to its original value. The advantage is that the conversion has taken place at a random point. The statistical distribution of the final levels is decided by a weighted average over a region of the range of the ADC. This in turn desensitizes it to the width of any specific level. These are several common ways of implementing an electronic ADC. Resistor-capacitor (RC) circuits have

2080-471: Is also used in integrating systems such as electricity meters . Since the values are added together, the dithering produces results that are more exact than the LSB of the analog-to-digital converter. Dither is often applied when quantizing photographic images to a fewer number of bits per pixel—the image becomes noisier but to the eye looks far more realistic than the quantized image, which otherwise becomes banded . This analogous process may help to visualize

2160-484: Is an axis of symmetry called the folding frequency , also known as Nyquist frequency . Aliasing matters when one attempts to reconstruct the original waveform from its samples. The most common reconstruction technique produces the smallest of the f N ( f ) {\displaystyle f_{_{N}}(f)} frequencies. So it is usually important that f 0 ( f ) {\displaystyle f_{0}(f)} be

2240-428: Is built into the comparator to resolve any problems at voltage boundaries. At each node of the resistive divider, a comparison voltage is available. The purpose of the circuit is to compare the analog input voltage with each of the node voltages. The circuit has the advantage of high speed as the conversion takes place simultaneously rather than sequentially. Typical conversion time is 100 ns or less. Conversion time

2320-427: Is limited only by the speed of the comparator and of the priority encoder. This type of ADC has the disadvantage that the number of comparators required almost doubles for each added bit. Also, the larger the value of n, the more complex is the priority encoder. A successive-approximation ADC uses a comparator and a binary search to successively narrow a range that contains the input voltage. At each successive step,

2400-467: Is proportional to the input, but there are other possibilities. There are several ADC architectures . Due to the complexity and the need for precisely matched components , all but the most specialized ADCs are implemented as integrated circuits (ICs). These typically take the form of metal–oxide–semiconductor (MOS) mixed-signal integrated circuit chips that integrate both analog and digital circuits . A digital-to-analog converter (DAC) performs

2480-445: Is referred to as spatial aliasing . Aliasing is generally avoided by applying low-pass filters or anti-aliasing filters (AAF) to the input signal before sampling and when converting a signal from a higher to a lower sampling rate. Suitable reconstruction filtering should then be used when restoring the sampled signal to the continuous domain or converting a signal from a lower to a higher sampling rate. For spatial anti-aliasing ,

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2560-402: Is seen. An example of spatial aliasing is the moiré pattern observed in a poorly pixelized image of a brick wall. Spatial anti-aliasing techniques avoid such poor pixelizations. Aliasing can be caused either by the sampling stage or the reconstruction stage; these may be distinguished by calling sampling aliasing prealiasing and reconstruction aliasing postaliasing. Temporal aliasing

2640-459: Is the ADC's resolution in bits and E FSR is the full-scale voltage range (also called 'span'). E FSR is given by where V RefHi and V RefLow are the upper and lower extremes, respectively, of the voltages that can be coded. Normally, the number of voltage intervals is given by where M is the ADC's resolution in bits. That is, one voltage interval is assigned in between two consecutive code levels. Example: In many cases,

2720-414: Is the number of ADC bits. Clock jitter is caused by phase noise . The resolution of ADCs with a digitization bandwidth between 1 MHz and 1 GHz is limited by jitter. For lower bandwidth conversions such as when sampling audio signals at 44.1 kHz, clock jitter has a less significant impact on performance. An analog signal is continuous in time and it is necessary to convert this to

2800-517: Is the overlapping of frequency components resulting from a sample rate below the Nyquist rate . This overlap results in distortion or artifacts when the signal is reconstructed from samples which causes the reconstructed signal to differ from the original continuous signal. Aliasing that occurs in signals sampled in time, for instance in digital audio or the stroboscopic effect , is referred to as temporal aliasing . Aliasing in spatially sampled signals (e.g., moiré patterns in digital images )

2880-407: Is uniformly distributed between − 1 ⁄ 2 LSB and + 1 ⁄ 2 LSB, and the signal has a uniform distribution covering all quantization levels, the signal-to-quantization-noise ratio (SQNR) is given by where Q is the number of quantization bits. For example, for a 16-bit ADC, the quantization error is 96.3 dB below the maximum level. Quantization error is distributed from DC to

2960-404: Is unwanted, it can be exploited to provide simultaneous down-mixing of a band-limited high-frequency signal (see undersampling and frequency mixer ). The alias is effectively the lower heterodyne of the signal frequency and sampling frequency. For economy, signals are often sampled at the minimum rate required with the result that the quantization error introduced is white noise spread over

3040-573: Is used intentionally on signals with no low-frequency content, called bandpass signals. Undersampling , which creates low-frequency aliases, can produce the same result, with less effort, as frequency-shifting the signal to lower frequencies before sampling at the lower rate. Some digital channelizers exploit aliasing in this way for computational efficiency.   (See Sampling (signal processing) , Nyquist rate (relative to sampling) , and Filter bank .) Sinusoids are an important type of periodic function, because realistic signals are often modeled as

3120-456: The Fourier transform , has no upper bound. Some amount of aliasing always occurs when such functions are sampled. Functions whose frequency content is bounded ( bandlimited ) have an infinite duration in the time domain. If sampled at a high enough rate, determined by the bandwidth , the original function can, in theory, be perfectly reconstructed from the infinite set of samples. Sometimes aliasing

3200-475: The Nyquist frequency . Consequently, if part of the ADC's bandwidth is not used, as is the case with oversampling , some of the quantization error will occur out-of-band , effectively improving the SQNR for the bandwidth in use. In an oversampled system, noise shaping can be used to further increase SQNR by forcing more quantization error out of band. In ADCs, performance can usually be improved using dither . This

3280-470: The bandlimited analog input signal. The resolution of the converter indicates the number of different, i.e. discrete, values it can produce over the allowed range of analog input values. Thus a particular resolution determines the magnitude of the quantization error and therefore determines the maximum possible signal-to-noise ratio for an ideal ADC without the use of oversampling . The input samples are usually stored electronically in binary form within

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3360-463: The effective number of bits (ENOB) below that predicted by quantization error alone. The error is zero for DC, small at low frequencies, but significant with signals of high amplitude and high frequency. The effect of jitter on performance can be compared to quantization error: Δ t < 1 2 q π f 0 {\displaystyle \Delta t<{\frac {1}{2^{q}\pi f_{0}}}} , where q

3440-570: The frequency spectrum of real-valued samples, such as Fig.4.. Complex sinusoids are waveforms whose samples are complex numbers , and the concept of negative frequency is necessary to distinguish them. In that case, the frequencies of the aliases are given by just :   f N ( f ) = f + N f s .   Therefore, as   f   increases from   0   to   f s ,   f −1 ( f )   also increases (from   – f s   to 0).  Consequently, complex sinusoids do not exhibit folding . When

3520-408: The signal-to-noise ratio performance of the ADC and thus reduce its effective resolution. When digitizing a sine wave x ( t ) = A sin ⁡ ( 2 π f 0 t ) {\displaystyle x(t)=A\sin {(2\pi f_{0}t)}} , the use of a non-ideal sampling clock will result in some uncertainty in when samples are recorded. Provided that

3600-477: The 4 black dots in Fig.3. The red lines depict the paths ( loci ) of the 4 dots if we were to adjust the frequency and amplitude of the sinusoid along the solid red segment (between   f s /2   and   f s ).  No matter what function we choose to change the amplitude vs frequency, the graph will exhibit symmetry between 0 and   f s .   Folding is often observed in practice when viewing

3680-421: The ADC, so the resolution is usually expressed as the audio bit depth . In consequence, the number of discrete values available is usually a power of two. For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels (2  = 256). The values can represent the ranges from 0 to 255 (i.e. as unsigned integers) or from −128 to 127 (i.e. as signed integer), depending on

3760-475: The HPSDR community as a general-coverage, high performance, HF receiver. It uses a 16-bit 135MSPS analog-to-digital converter that provides performance over the range 0 to 55 MHz comparable to that of a conventional analog HF radio. The receiver will also operate in the VHF and UHF range using either mixer image or alias responses. The host computer uses DSP techniques to process the digital bitstream it receives from

3840-616: The HPSDR system. Currently, the HPSDR hardware has been interfaced with the Flex-Radio PowerSDR Windows-based software, which is licensed under the GPL . As of February, 2011, the following HPSDR modules have been released: Other modules nearing release include: Replaced by newer modules: In cooperation with the HPSDR group, TAPR has provided (or will provide) all the modules listed above. Most have been made available as either fully assembled units or as bare circuit boards;

3920-519: The actual sampling time uncertainty due to clock jitter is Δ t {\displaystyle \Delta t} , the error caused by this phenomenon can be estimated as E a p ≤ | x ′ ( t ) Δ t | ≤ 2 A π f 0 Δ t {\displaystyle E_{ap}\leq |x'(t)\Delta t|\leq 2A\pi f_{0}\Delta t} . This will result in additional recorded noise that will reduce

4000-650: The analog signal will appear as lower frequencies (wrong alias) in the recorded digital sample and, hence, cannot be reproduced by the DAC. To prevent this, an anti-aliasing filter is used to remove components above the Nyquist frequency prior to sampling. In video or cinematography, temporal aliasing results from the limited frame rate, and causes the wagon-wheel effect , whereby a spoked wheel appears to rotate too slowly or even backwards. Aliasing has changed its apparent frequency of rotation. A reversal of direction can be described as

4080-409: The application. Resolution can also be defined electrically, and expressed in volts . The change in voltage required to guarantee a change in the output code level is called the least significant bit (LSB) voltage. The resolution Q of the ADC is equal to the LSB voltage. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of intervals: where M

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4160-522: The condition   f s /2 > f   is met for the highest frequency component of the original signal, then it is met for all the frequency components, a condition called the Nyquist criterion . That is typically approximated by filtering the original signal to attenuate high frequency components before it is sampled. These attenuated high frequency components still generate low-frequency aliases, but typically at low enough amplitudes that they do not cause problems. A filter chosen in anticipation of

4240-419: The conversion periodically, sampling the input, and limiting the allowable bandwidth of the input signal. The performance of an ADC is primarily characterized by its bandwidth and signal-to-noise and distortion ratio (SNDR). The bandwidth of an ADC is characterized primarily by its sampling rate . The SNDR of an ADC is influenced by many factors, including the resolution , linearity and accuracy (how well

4320-415: The converter compares the input voltage to the output of an internal digital-to-analog converter (DAC) which initially represents the midpoint of the allowed input voltage range. At each step in this process, the approximation is stored in a successive approximation register (SAR) and the output of the digital-to-analog converter is updated for a comparison over a narrower range. A ramp-compare ADC produces

4400-417: The effect of dither on an analog audio signal that is converted to digital. An ADC has several sources of errors. Quantization error and (assuming the ADC is intended to be linear) non- linearity are intrinsic to any analog-to-digital conversion. These errors are measured in a unit called the least significant bit (LSB). In the above example of an eight-bit ADC, an error of one LSB is 1 ⁄ 256 of

4480-448: The following audio demonstration. Six sawtooth waves are played in succession, with the first two sawtooths having a fundamental frequency of 440 Hz (A4), the second two having fundamental frequency of 880 Hz (A5), and the final two at 1760 Hz (A6). The sawtooths alternate between bandlimited (non-aliased) sawtooths and aliased sawtooths and the sampling rate is 22050 Hz. The bandlimited sawtooths are synthesized from

4560-589: The frequency and amplitude of this side-to-side movement corresponds to the angular resolution of the image (and, for frequency, the speed of the viewer's lateral movement), which is the angular aliasing of the 4D light field. The lack of parallax on viewer movement in 2D images and in 3-D film produced by stereoscopic glasses (in 3D films the effect is called " yawing ", as the image appears to rotate on its axis) can similarly be seen as loss of angular resolution, all angular frequencies being aliased to 0 (constant). The qualitative effects of aliasing can be heard in

4640-499: The full signal range, or about 0.4%. All ADCs suffer from nonlinearity errors caused by their physical imperfections, causing their output to deviate from a linear function (or some other function, in the case of a deliberately nonlinear ADC) of their input. These errors can sometimes be mitigated by calibration , or prevented by testing. Important parameters for linearity are integral nonlinearity and differential nonlinearity . These nonlinearities introduce distortion that can reduce

4720-494: The logarithm of the resolution, i.e. the number of bits. Flash ADCs are certainly the fastest type of the three; The conversion is basically performed in a single parallel step. There is a potential tradeoff between speed and precision. Flash ADCs have drifts and uncertainties associated with the comparator levels results in poor linearity. To a lesser extent, poor linearity can also be an issue for successive-approximation ADCs. Here, nonlinearity arises from accumulating errors from

4800-464: The measured run-down time period. The run-down time measurement is usually made in units of the converter's clock, so longer integration times allow for higher resolutions. Likewise, the speed of the converter can be improved by sacrificing resolution. Converters of this type (or variations on the concept) are used in most digital voltmeters for their linearity and flexibility. Aliasing In signal processing and related disciplines, aliasing

4880-410: The performance of the ADC can be greatly increased at little or no cost. Furthermore, as any aliased signals are also typically out of band, aliasing can often be eliminated using very low cost filters. The speed of an ADC varies by type. The Wilkinson ADC is limited by the clock rate which is processable by current digital circuits. For a successive-approximation ADC , the conversion time scales with

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4960-411: The quantization levels match the true analog signal), aliasing and jitter . The SNDR of an ADC is often summarized in terms of its effective number of bits (ENOB), the number of bits of each measure it returns that are on average not noise . An ideal ADC has an ENOB equal to its resolution. ADCs are chosen to match the bandwidth and required SNDR of the signal to be digitized. If an ADC operates at

5040-439: The reconstruction matches the actual waveform (upper left frame). After that, it is the low frequency alias of the upper frame. The figures below offer additional depictions of aliasing, due to sampling. A graph of amplitude vs frequency (not time) for a single sinusoid at frequency   0.6 f s   and some of its aliases at   0.4 f s ,   1.4 f s ,   and   1.6 f s   would look like

5120-410: The reverse function; it converts a digital signal into an analog signal. An ADC converts a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal . The conversion involves quantization of the input, so it necessarily introduces a small amount of quantization error . Furthermore, instead of continuously performing the conversion, an ADC does

5200-559: The samples produces equally strong responses at all those frequencies. Without collateral information, the frequency of the original function is ambiguous. So the functions and their frequencies are said to be aliases of each other. Noting the trigonometric identity : we can write all the alias frequencies as positive values:  f N ( f ) ≜ | f + N f s | {\displaystyle f_{_{N}}(f)\triangleq \left|f+Nf_{\rm {s}}\right|} . For example,

5280-494: The sawtooth waveform's Fourier series such that no harmonics above the Nyquist frequency are present. The aliasing distortion in the lower frequencies is increasingly obvious with higher fundamental frequencies, and while the bandlimited sawtooth is still clear at 1760 Hz, the aliased sawtooth is degraded and harsh with a buzzing audible at frequencies lower than the fundamental. A form of spatial aliasing can also occur in antenna arrays or microphone arrays used to estimate

5360-449: The signal can be reconstructed. If frequencies above half the Nyquist rate are sampled, they are incorrectly detected as lower frequencies, a process referred to as aliasing. Aliasing occurs because instantaneously sampling a function at two or fewer times per cycle results in missed cycles, and therefore the appearance of an incorrectly lower frequency. For example, a 2 kHz sine wave being sampled at 1.5 kHz would be reconstructed as

5440-406: The subtraction processes. Wilkinson ADCs have the best linearity of the three. The sliding scale or randomizing method can be employed to greatly improve the linearity of any type of ADC, but especially flash and successive approximation types. For any ADC the mapping from input voltage to digital output value is not exactly a floor or ceiling function as it should be. Under normal conditions,

5520-488: The summation of many sinusoids of different frequencies and different amplitudes (for example, with a Fourier series or transform ). Understanding what aliasing does to the individual sinusoids is useful in understanding what happens to their sum. When sampling a function at frequency f s (intervals 1/ f s ), the following functions of time ( t ) yield identical sets of samples: {sin(2π( f+Nf s ) t + φ), N = 0, ±1, ±2, ±3,... }. A frequency spectrum of

5600-446: The term aliasing evolved from radio engineering because of the action of superheterodyne receivers . When the receiver shifts multiple signals down to lower frequencies, from RF to IF by heterodyning , an unwanted signal, from an RF frequency equally far from the local oscillator (LO) frequency as the desired signal, but on the wrong side of the LO, can end up at the same IF frequency as

5680-571: The term "aliasing" in this context is due to Blackman and Tukey in 1958. In their preface to the Dover reprint of this paper, they point out that the idea of aliasing had been illustrated graphically by Stumpf ten years prior. The 1949 Bell technical report refers to aliasing as though it is a well-known concept, but does not offer a source for the term. Gwilym Jenkins and Maurice Priestley credit Tukey with introducing it in this context, though an analogous concept of aliasing had been introduced

5760-415: The time it takes to charge (and/or discharge) its capacitor from 1 ⁄ 3   V supply to 2 ⁄ 3   V supply . By sending this pulse into a microcontroller with an accurate clock, the duration of the pulse can be measured and converted using the capacitor charging equation to produce the value of the unknown resistance or capacitance. Larger resistances and capacitances will take

5840-550: The time to charge the capacitance from a known starting voltage to another known ending voltage through the resistance from a known voltage supply, the value of the unknown resistance or capacitance can be determined using the capacitor charging equation: V capacitor ( t ) = V supply ( 1 − e − t R C ) {\displaystyle V_{\text{capacitor}}(t)=V_{\text{supply}}\left(1-e^{-{\frac {t}{RC}}}\right)} and solving for

5920-406: The types of anti-aliasing include fast approximate anti-aliasing (FXAA), multisample anti-aliasing , and supersampling . When a digital image is viewed, a reconstruction is performed by a display or printer device, and by the eyes and the brain. If the image data is processed incorrectly during sampling or reconstruction, the reconstructed image will differ from the original image, and an alias

6000-462: The unique minimum.  A necessary and sufficient condition for that is f s / 2 > | f | , {\displaystyle f_{s}/2>|f|,} called the Nyquist condition . The lower left frame of Fig.2 depicts the typical reconstruction result of the available samples. Until f {\displaystyle f} exceeds the Nyquist frequency,

6080-411: The unknown input voltage to the input of an integrator and allows the voltage to ramp for a fixed time period (the run-up period). Then a known reference voltage of opposite polarity is applied to the integrator and is allowed to ramp until the integrator output returns to zero (the run-down period). The input voltage is computed as a function of the reference voltage, the constant run-up time period, and

6160-464: The unknown resistance or capacitance using those starting and ending datapoints. This is similar but contrasts to the Wilkinson ADC which measures an unknown voltage with a known resistance and capacitance, by instead measuring an unknown resistance or capacitance with a known voltage. For example, the positive (and/or negative) pulse width from a 555 Timer IC in monostable or astable mode represents

6240-418: The useful resolution of a converter is limited by the signal-to-noise ratio (SNR) and other errors in the overall system expressed as an ENOB. Quantization error is introduced by the quantization inherent in an ideal ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The error is nonlinear and signal-dependent. In an ideal ADC, where the quantization error

6320-470: The wanted one. If it is strong enough it can interfere with reception of the desired signal. This unwanted signal is known as an image or alias of the desired signal. The first written use of the terms "alias" and "aliasing" in signal processing appears to be in a 1949 unpublished Bell Laboratories technical memorandum by John Tukey and Richard Hamming . That paper includes an example of frequency aliasing dating back to 1922. The first published use of

6400-433: The whole passband of the converter. If a signal is sampled at a rate much higher than the Nyquist rate and then digitally filtered to limit it to the signal bandwidth produces the following advantages: Oversampling is typically used in audio frequency ADCs where the required sampling rate (typically 44.1 or 48 kHz) is very low compared to the clock speed of typical transistor circuits (>1 MHz). In this case,

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