|
|
| Line 1: |
Line 1: |
| {{merge from|Sampling rate|discuss=Talk:Sampling rate#Merge to Sampling (signal processing)|date=September 2013}}
| | Msvcr71.dll is an important file that assists help Windows process different components of the system including significant files. Specifically, the file is employed to help run corresponding files inside the "Virtual C Runtime Library". These files are significant inside accessing any settings which support the different applications plus programs inside the program. The msvcr71.dll file fulfills various important functions; however it's not spared from getting damaged or corrupted. Once the file gets corrupted or damaged, the computer will have a difficult time processing and reading components of the system. However, consumers require not panic considering this problem could be solved by following many procedures. And I usually show you certain strategies regarding Msvcr71.dll.<br><br>So 1 day my computer suddenly started being strange. I was thus frustrated, considering my files were missing, and I cannot open the files which I needed, plus then, suddenly, everything stopped functioning!<br><br>It doesn't matter whether you are not surprisingly clear about what rundll32.exe is. But remember that it plays an important character inside preserving the stability of our computers plus the integrity of the program. When some software or hardware couldn't respond usually to the system operation, comes the rundll32 exe error, that will be caused by corrupted files or lost information in registry. Usually, error message will shows up at booting or the beginning of running a system.<br><br>There may be many reasons why the computer will lose speed. Normal computer utilize, including surfing the Internet could get the running system in a condition where it has no choice nevertheless to slow down. The constant entering and deleting of temporary files which occur when you surf the Web leave our registries with thousands of false indicators inside the running system's registry.<br><br>Google Chrome crashes on Windows 7 when the registry entries are improperly modified. Missing registry keys or registry keys with improper values will lead to runtime errors plus thereby the issue occurs. You are recommended to scan the whole program registry and review the outcome. Attempt the registry repair procedure using third-party [http://bestregistrycleanerfix.com/registry-mechanic pc tools registry mechanic] software.<br><br>Although I usually utilize the most recent variation of browser, often different extensions and plugins become the cause of errors with my browser plus the system. The same is the story with my browser that was crashing frequently potentially due to the Flash player error.<br><br>We require a choice to automatically delete unwelcome registry keys. This usually conserve you hours of laborious checking from a registry keys. Automatic deletion is a key element whenever you compare registry cleaners.<br><br>Registry products have been crafted to fix all broken files inside your program, allowing the computer to read any file it wants, when it wants. They work by scanning from the registry and checking every registry file. If the cleaner sees which it is corrupt, then it can substitute it automatically. |
| [[Image:Signal Sampling.png|thumb|300px|Signal sampling representation. The continuous signal is represented with a green colored line while the discrete samples are indicated by the blue vertical lines.]]
| |
| In [[signal processing]], '''sampling''' is the reduction of a [[continuous signal]] to a [[discrete signal]]. A common example is the conversion of a [[sound wave]] (a continuous signal) to a sequence of samples (a discrete-time signal).
| |
| | |
| A '''sample''' refers to a value or set of values at a point in time and/or space.
| |
| | |
| A '''sampler''' is a subsystem or operation that extracts samples from a [[continuous signal]].
| |
| | |
| A theoretical '''ideal sampler''' produces samples equivalent to the instantaneous value of the continuous signal at the desired points.
| |
| | |
| == Theory ==
| |
| :''See also: [[Nyquist–Shannon sampling theorem]]''
| |
| | |
| Sampling can be done for functions varying in space, time, or any other dimension, and similar results are obtained in two or more dimensions.
| |
| | |
| For functions that vary with time, let ''s''(''t'') be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every ''T'' seconds, which is called the [[sampling interval]]. Thus, the sampled function is given by the sequence''':'''
| |
| | |
| :''s''(''nT''), for integer values of ''n''.
| |
| | |
| The [[sampling frequency]] or sampling rate '''f<sub>s</sub>''' is defined as the number of samples obtained in one second (samples per second), thus '''f<sub>s</sub> = 1/T'''.
| |
| | |
| Reconstructing a continuous function from samples is done by interpolation algorithms. The [[Whittaker–Shannon interpolation formula]] is mathematically equivalent to an ideal [[lowpass filter]] whose input is a sequence of [[Dirac delta functions]] that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant (''T''), the sequence of delta functions is called a [[Dirac comb]]. Mathematically, the modulated [[Dirac comb]] is equivalent to the product of the comb function with ''s''(''t''). That purely mathematical function is often loosely referred to as the sampled signal.
| |
| | |
| Most sampled signals are not simply stored and reconstructed. But the fidelity of a theoretical reconstruction is a customary measure of the effectiveness of sampling. That fidelity is reduced when ''s''(''t'') contains frequency components higher than '''f<sub>s</sub>'''/2 [[Hz]], which is known as the [[Nyquist frequency]] of the sampler. Therefore ''s''(''t'') is usually the output of a [[lowpass filter]], functionally known as an "anti-aliasing" filter. Without an anti-aliasing filter, frequencies higher than the Nyquist frequency will influence the samples in a way that is misinterpreted by the interpolation process. For details, see [[Aliasing]].
| |
| | |
| == Practical implications ==
| |
| | |
| In practice, the continuous signal is sampled using an [[analog-to-digital converter]] (ADC), a device with various physical limitations. This results in deviations from the theoretically perfect reconstruction, collectively referred to as distortion.
| |
| | |
| Various types of distortion can occur, including:
| |
| * [[Aliasing]]. A precondition of the sampling theorem is that the signal be bandlimited. However, in practice, no time-limited signal can be bandlimited. Since signals of interest are almost always time-limited (e.g., at most spanning the lifetime of the sampling device in question), it follows that they are not bandlimited. However, by designing a sampler with an appropriate [[guard band]], it is possible to obtain output that is as accurate as necessary.
| |
| * [[Analog-to-digital_converter#Aperture_error|Aperture error]] results from the fact that the sample is obtained as a time average within a sampling region, rather than just being equal to the signal value at the sampling instant. In a [[capacitor]]-based [[sample and hold]] circuit,aperture error is introduced because the capacitor cannot instantly change voltage thus requiring the sample to have non-zero width.
| |
| * [[Jitter]] or deviation from the precise sample timing intervals.
| |
| * [[Noise (physics)|Noise]], including thermal sensor noise, [[analog circuit]] noise, etc.
| |
| * [[Slew rate]] limit error, caused by the inability of the ADC input value to change sufficiently rapidly.
| |
| * [[Quantization (signal processing)|Quantization]] as a consequence of the finite precision of words that represent the converted values.
| |
| * Error due to other [[non-linear]] effects of the mapping of input voltage to converted output value (in addition to the effects of quantization).
| |
| | |
| Although the use of [[oversampling]] can completely eliminate aperture error and aliasing by shifting them out of the pass band, this technique cannot be practically used above a few GHz, and maybe prohibitively expensive at much lower frequencies. Furthermore, while oversampling can reduce quantization error and non-linearity, it cannot eliminate these entirely. Consequently, practical ADCs at audio frequencies typically do not exhibit aliasing, aperture error, and are not limited by quantization error. Instead, analog noise dominates. At RF and microwave frequencies where oversampling is impractical and filters are expensive, aperture error, quantization error and aliasing can be significant limitations.
| |
| | |
| Jitter, noise, and quantization are often analyzed by modeling them as random errors added to the sample values. Integration and zero-order hold effects can be analyzed as a form of [[low-pass filter]]ing. The non-linearities of either ADC or DAC are analyzed by replacing the ideal [[linear function]] mapping with a proposed [[Nonlinear|nonlinear function]].
| |
| | |
| == Applications ==
| |
| | |
| === Audio sampling ===
| |
| | |
| [[Digital audio]] uses [[pulse-code modulation]] and digital signals for sound reproduction. This includes analog-to-digital conversion (ADC), digital-to-analog conversion (DAC), storage, and transmission. In effect, the system commonly referred to as digital is in fact a discrete-time, discrete-level analog of a previous electrical analog. While modern systems can be quite subtle in their methods, the primary usefulness of a digital system is the ability to store, retrieve and transmit signals without any loss of quality.
| |
| | |
| ==== Sampling rate ====
| |
| | |
| When it is necessary to capture audio covering the entire 20–20,000 Hz range of [[auditory system|human hearing]], such as when recording music or many types of acoustic events, audio waveforms are typically sampled at 44.1 kHz ([[Compact disc|CD]]), 48 kHz ([[professional audio]]), or 96 kHz. The approximately double-rate requirement is a consequence of the [[Nyquist theorem]].
| |
| | |
| There has been an industry trend towards sampling rates well beyond the basic requirements; 96 kHz and even 192 kHz are available.<ref>{{cite web|url=http://www.digitalprosound.com/Htm/SoapBox/soap2_Apogee.htm |title=Digital Pro Sound |accessdate=8 January 2014}}</ref> This is in contrast with laboratory experiments, which have failed to show that [[Ultrasound|ultrasonic]] frequencies are audible to human observers; however in some cases ultrasonic sounds do interact with and modulate the audible part of the frequency spectrum ([[intermodulation distortion]]). It is noteworthy that intermodulation distortion is not present in the live audio and so it represents an artificial coloration to the live sound.<ref>{{cite web |url=http://world.std.com/~griesngr/intermod.ppt |archiveurl=https://web.archive.org/web/20080501000000/http://world.std.com/~griesngr/intermod.ppt |archivedate=2008-05-01 |title=Perception of mid frequency and high frequency intermodulation distortion in loudspeakers, and its relationship to high-definition audio |author=David Griesinger |format=Powerpoint presentation}}</ref>
| |
| | |
| One advantage of higher sampling rates is that they can relax the low-pass filter design requirements for [[analog-to-digital converter|ADCs]] and [[digital-to-analog converter|DACs]], but with modern oversampling [[sigma-delta converter]]s this advantage is less important.
| |
| | |
| ==== Bit depth (quantization) ====
| |
| | |
| Audio is typically recorded at 8-, 16-, and 20-bit depth, which yield a theoretical maximum [[Signal-to-quantization-noise ratio]] (SQNR) for a pure [[sine wave]] of, approximately, 49.93 [[Decibel|dB]], 98.09 dB and 122.17 dB.<ref>{{cite web|url=http://www.analog.com/static/imported-files/tutorials/MT-001.pdf |title=MT-001: Taking the Mystery out of the Infamous Formula, "SNR=6.02N + 1.76dB," and Why You Should Care}}</ref> CD quality audio is recorded at 16-bit. [[Thermal noise]] limits the true number of bits that can be used in quantization. Few analog systems have [[Signal-to-noise_ratio|signal to noise ratios (SNR)]] exceeding 120 dB. However, [[digital signal processing]] operations can have very high dynamic range, consequently it is common to perform mixing and mastering operations at 32-bit precision and then convert to 16 or 24 bit for distribution.
| |
| | |
| ==== Speech sampling ====
| |
| | |
| Speech signals, i.e., signals intended to carry only human [[Speech communication|speech]], can usually be sampled at a much lower rate. For most [[phoneme]]s, almost all of the energy is contained in the 5Hz-4 kHz range, allowing a sampling rate of 8 kHz. This is the [[sampling rate]] used by nearly all [[telephony]] systems, which use the [[G.711]] sampling and quantization specifications.
| |
| | |
| === Video sampling ===
| |
| | |
| [[Standard-definition television]] (SDTV) uses either 720 by 480 [[pixels]] (US [[NTSC]] 525-line) or 704 by 576 [[pixels]] (UK [[PAL]] 625-line) for the visible picture area.
| |
| | |
| [[High-definition television]] (HDTV) is currently moving towards three standards referred to as [[720p]] (progressive), [[1080i]] (interlaced) and [[1080p]] (progressive, also known as Full-HD) which all 'HD-Ready' sets will be able to display.
| |
| | |
| [[File:Samplerates.svg|thumb|right|255px|Plot of sample rates (y axis) versus the upper edge frequency (x axis) for a band of width 1; grays areas are combinations that are "allowed" in the sense that no two frequencies in the band alias to same frequency. The darker gray areas correspond to [[undersampling]] with the lowest allowable sample rate.]]
| |
| | |
| == Undersampling ==
| |
| {{main|Undersampling}}
| |
| | |
| When a [[bandpass]] signal is sampled slower than its [[Nyquist rate]], the samples are indistinguishable from samples of a low-frequency [[aliasing|alias]] of the high-frequency signal. That is often done purposefully in such a way that the lowest-frequency alias satisfies the [[Nyquist criterion]], because the bandpass signal is still uniquely represented and recoverable. Such [[undersampling]] is also known as ''bandpass sampling'', ''harmonic sampling'', ''IF sampling'', and ''direct IF to digital conversion.''<ref>
| |
| {{cite book
| |
| | title = Mixed-signal and DSP design techniques
| |
| | author = Walt Kester
| |
| | publisher = Newnes
| |
| | year = 2003
| |
| | isbn = 978-0-7506-7611-3
| |
| | page = 20
| |
| | url = http://books.google.com/books?id=G8XyNItpy8AC&pg=PA20
| |
| | accessdate = 8 January 2014
| |
| }}</ref>
| |
| | |
| == Oversampling ==
| |
| {{main|Oversampling}}
| |
| | |
| Oversampling is used in most modern analog-to-digital converters to reduce the distortion introduced by practical [[digital-to-analog converter]]s, such as a [[zero-order hold]] instead of idealizations like the [[Whittaker–Shannon interpolation formula]].
| |
| | |
| == Complex sampling ==
| |
| | |
| ''Complex sampling'' refers to the simultaneous sampling of two different, but related, waveforms, resulting in pairs of samples that are subsequently treated as [[complex numbers]]. Usually one waveform<math>, \hat s(t),</math> is the [[Hilbert transform]] of the other waveform<math>, s(t),\,</math> and the complex-valued function, <math>s_a(t)\ \stackrel{\text{def}}{=}\ s(t) + j\cdot \hat s(t),</math> is called an [[analytic signal]], whose Fourier transform is zero for all negative values of frequency. In that case, the [[Nyquist rate]] for a waveform with no frequencies '''≥ B''' can be reduced to just ''B'' (complex samples/sec), instead of ''2B'' (real samples/sec).<ref group="note">When the complex sample-rate is B, a frequency component at 0.6 B, for instance, will have an alias at -0.4 B, which is unambiguous because of the constraint that the pre-sampled signal was analytic. Also see [[Aliasing#Complex_sinusoids]]</ref> More apparently, the
| |
| [[Baseband#Equivalent baseband signal|equivalent baseband waveform]], <math>s_a(t)\cdot e^{-j 2\pi \frac{B}{2} t},</math> also has a Nyquist rate of ''B'', because all of its non-zero frequency content is shifted into the interval [-B/2, B/2).
| |
| | |
| Although complex-valued samples can be obtained as described above, they are much more commonly created by manipulating samples of a real-valued waveform. For instance, the equivalent baseband waveform can be created without explicitly computing <math>\hat s(t),</math> by processing the product sequence<math>, \left [s(nT)\cdot e^{-j 2 \pi \frac{B}{2}Tn}\right ],</math><ref group="note">When s(t) is sampled at the Nyquist frequency (1/T = 2B), the product sequence simplifies to <math>\left [s(nT)\cdot (-j)^n\right ].</math></ref> through a digital lowpass filter whose cutoff frequency is B/2.<ref group="note">The sequence of complex numbers is convolved with the impulse response of a filter with real-valued coefficients. That is equivalent to separately filtering the sequences of real parts and imaginary parts and reforming complex pairs at the outputs.</ref> Computing only every other sample of the output sequence reduces the sample-rate commensurate with the reduced Nyquist rate. The result is half as many complex-valued samples as the original number of real samples. No information is lost, and the original s(t) waveform can be recovered, if necessary.
| |
| | |
| === Notes ===
| |
| {{reflist|group=note}}
| |
| | |
| == See also ==
| |
| * [[Beta encoder]]
| |
| * [[Digitizing]]
| |
| * [[Kell factor]]
| |
| * [[Downsampling]]
| |
| * [[Upsampling]]
| |
| * [[Multidimensional sampling]]
| |
| | |
| ==References==
| |
| | |
| * Matt Pharr and Greg Humphreys, ''Physically Based Rendering: From Theory to Implementation'', Morgan Kaufmann, July 2004. ISBN 0-12-553180-X. The chapter on sampling ([http://graphics.stanford.edu/~mmp/chapters/pbrt_chapter7.pdf available online]) is nicely written with diagrams, core theory and code sample.
| |
| * Shannon, Claude E. (January 1949). Communications in the presence of noise, [[Proc. IRE]], vol. 37, pp. 10–21.
| |
|
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| * [http://www.vanosta.be/pcrnyq.htm Nyquist sampling in digital microscopy]{{dead link|date=August 2011}}
| |
| * [http://www.stsip.org Journal devoted to Sampling Theory]
| |
| * [http://whiteboard.ping.se/SDR/IQ I/Q Data for Dummies] A page trying to answer the question ''Why I/Q Data?''
| |
| | |
| [[Category:Signal processing]]
| |
Msvcr71.dll is an important file that assists help Windows process different components of the system including significant files. Specifically, the file is employed to help run corresponding files inside the "Virtual C Runtime Library". These files are significant inside accessing any settings which support the different applications plus programs inside the program. The msvcr71.dll file fulfills various important functions; however it's not spared from getting damaged or corrupted. Once the file gets corrupted or damaged, the computer will have a difficult time processing and reading components of the system. However, consumers require not panic considering this problem could be solved by following many procedures. And I usually show you certain strategies regarding Msvcr71.dll.
So 1 day my computer suddenly started being strange. I was thus frustrated, considering my files were missing, and I cannot open the files which I needed, plus then, suddenly, everything stopped functioning!
It doesn't matter whether you are not surprisingly clear about what rundll32.exe is. But remember that it plays an important character inside preserving the stability of our computers plus the integrity of the program. When some software or hardware couldn't respond usually to the system operation, comes the rundll32 exe error, that will be caused by corrupted files or lost information in registry. Usually, error message will shows up at booting or the beginning of running a system.
There may be many reasons why the computer will lose speed. Normal computer utilize, including surfing the Internet could get the running system in a condition where it has no choice nevertheless to slow down. The constant entering and deleting of temporary files which occur when you surf the Web leave our registries with thousands of false indicators inside the running system's registry.
Google Chrome crashes on Windows 7 when the registry entries are improperly modified. Missing registry keys or registry keys with improper values will lead to runtime errors plus thereby the issue occurs. You are recommended to scan the whole program registry and review the outcome. Attempt the registry repair procedure using third-party pc tools registry mechanic software.
Although I usually utilize the most recent variation of browser, often different extensions and plugins become the cause of errors with my browser plus the system. The same is the story with my browser that was crashing frequently potentially due to the Flash player error.
We require a choice to automatically delete unwelcome registry keys. This usually conserve you hours of laborious checking from a registry keys. Automatic deletion is a key element whenever you compare registry cleaners.
Registry products have been crafted to fix all broken files inside your program, allowing the computer to read any file it wants, when it wants. They work by scanning from the registry and checking every registry file. If the cleaner sees which it is corrupt, then it can substitute it automatically.