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Topic: Sampling frequency

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Sampling rate

Undersampling

Oversampling

Digital signal processing

Frequency spectrum

Aliasing

Bandwidth

Digital

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	An Introduction to Sampling Theory
		To be precise, the frequency components of the analog signal are repeated at the sample rate.
		The Sampling Theorem states that a signal can be exactly reproduced if it is sampled at a frequency F, where F is greater than twice the maximum frequency in the signal.
		Frequencies "fold" around half the sampling frequency - which is why this frequency is often referred to as the folding frequency.
	www2.egr.uh.edu /~glover/applets/Sampling/Sampling.html (926 words)

	Digital signal processor and control method for changeover of sampling frequency - Patent 6154154
		If a control circuit is notified that the sampling frequency of the input digital signal changes according to a signal from the frequency counter, it temporarily stops accumulation of input digital signal in a data memory.
		According to a preferred embodiment of the present invention, upon detecting that the sampling frequency of the input digital signal is changed over, the control means sets a processing program and a processing data corresponding to the changed-over sampling frequency in the operation processing circuit.
		As a result, the sampling frequency of the digital signal DATA is changed over, so that the frequency counter 62 detects this phenomenon with reference to a frequency of the left/right identification clock LRCK, and notifies the control circuit 63 that the sampling frequency has been changed over and further of a detected frequency.
	www.freepatentsonline.com /6154154.html (3203 words)

	Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm
		Frequencies above one-half the sampling frequency are not distinguishable by viewing the sampled data.
		The first frequency value is the same distance from zero as the other four frequencies are from the sampling frequency and twice the sampling frequency.
		Finally, the frequencies of each of the five sinusoids specified in Figure 10 is progressively closer to the folding frequency with the frequency of the fifth sinusoid being equal to the folding frequency.
	www.developer.com /java/other/article.php/3380031 (9009 words)

	FlexVoice - FAQ
		The 8 kHz sampling frequency mode is recommended for telephony applications; 11 kHz is needed for some full-duplex sound cards and some popular telephony boards.
		During initialization, specify the sampling frequency in the WaveFormatSet function, which is described in detail in the MS SDK 4.0 documentation.
		Because the default frequency may not correspond to that of the speech recognition system, recognition errors may result.
	www.flexvoice.com /faq.html (1747 words)

	[No title]
		Noting that 2pi/w is the number of "cycles" of the sampling* comb function per unit length, in other words, the sampling frequency, we conclude that in order to sample an s0-frequency-limited function, we have to sample with a frequency larger than 2 * s0.
		When reconstructing a function from its sampled version using linear interpolation, the scaled comb function representing the sample set is convolved with the triangle function of the same distance parameter.
		This is the same misunderstanding of sampling theory that lead to the common rule of thumb "sample twice as often to get rid of aliasing" that is often quoted when using linear interpolation as reconstruction filter.
	graphics.cs.ucdavis.edu /~okreylos/PhDStudies/Winter2000/SamplingTheory.html (3840 words)

	Sampling.nb
		The Nyquist Criterion states that to correctly reconstruct a signal, the sample rate must be at least as large as twice that of the highest frequency present in a band-limited signal.
		When the frequency of the sampling signal is low, it is next to impossible to recognize the original signal.
		When the sampling frequency is low, the signal can not be reconstructed correctly (in most cases).
	www.d.umn.edu /ece/lis/wireless/classes/ece2111/Sampling.html (370 words)

	Science Fair Projects - Sampling frequency
		The Nyquist-Shannon sampling theorem states that the sampling frequency has to be greater than twice the Nyquist frequency or, equivalently, twice the bandwidth of the signal being sampled.
		In some cases, it is desirable to have a sampling frequency more than twice the bandwidth so that a digital filter can be used in exchange for a weaker analog anti-aliasing filter.
		All modern TV cameras use CCDs, and the image sampling frequency is the repetition rate of the CCD integration period.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Sampling_frequency (426 words)

	Sampling frequency
		In digital signal processing, sampling frequency is the rate at which sampling is done.
		Sampling frequency is usually measured in hertz, or samples per second.
		The sampling frequency is the inverse of this number: the smaller the interval, the higher the frequency, and, in general, higher frequencies imply higher-quality sampling.
	www.teachersparadise.com /ency/en/wikipedia/s/sa/sampling_frequency.html (212 words)

	Establishing Effective Sampling Frequencies
		Each frequency is assigned not a fixed value that can be cross-referenced to similar machines in similar industries, but is based on a critical assessment of those parameters that affect a specific machine on a case-by-case basis.
		The Sample Frequency Generator (Figure 2) provides a systematic method with which to estimate the optimized sampling frequency, taking into account economic penalty of failure, fluid environment severity, machine age, oil age and the tightness of goal-based target like contamination control.
		Sampling frequencies must be modified according to the classic ‘bathtub’ curve used to explain the probability of equipment failure (Figure 3).
	www.practicingoilanalysis.com /article_detail.asp?articleid=250 (1288 words)

	Olympus Microscopy Resource Center: Digital Image Processing - Digital Image Sampling Frequency - Interactive Java ...
		According to Shannon's sampling theorem, in order to preserve the spatial resolution of the original image, the digitizing device must utilize a sampling interval that is no greater than one-half the size of the smallest resolvable feature of the optical image.
		This is equivalent to acquiring samples at twice the highest spatial frequency contained in the image, a reference point commonly referred to as the Nyquist criterion.
		It should be noted that while the spatial frequency of the resultant image is artifactually altered by aliasing, the amplitude of the signal is not significantly changed.
	www.olympusmicro.com /primer/java/digitalimaging/processing/samplefrequency/index.html (962 words)

	4200 - Conversion Principles - Sampling (Site not responding. Last check: )
		For a given sampling frequency, calculate the Nyquist frequency and the expected frequency response.
		The waveform is measured, or sampled, at periodic intervals.
		If there are at least two samples for a given frequency, that frequency can then be reproduced, since there is a sample for the positive and the negative portion of each cycle.
	www.mtsu.edu /~djbrown/4200_Site/Conversion_Sampling.html (923 words)

	Nyquist Theorem Details (Site not responding. Last check: )
		Nyquist's frequency is the frequency that no part of the source material may attain or exceed, which is half of the sampling frequency.
		Here's a secret: the angular waveform in the center has a fundamental frequency equal to half the sampling frequency (not exactly the frequency of the original waveform), also it comprises many harmonics, or sine waves that are multiples of the fundamental, as well.
		But as a hint we will state that the sampling frequency is the frames per second rate and the frequency we are trying to reproduce is the rate at which spokes pass the "6 o'clock position" on the wheel.
	members.aol.com /ajaynejr/nyquist.htm (2368 words)

	Frequency Limits of Sampling - Aliasing
		The effect of sampling a waveform too slowly can be seen in Figure 3 where a sinewave with a high frequency 'noise' signal superimposed, is sampled (the samples are shown a crosses).
		The frequency limitation on the use of a sampling system is governed by the Sampling Theory and the result of violating this theory is known as aliasing.
		The Sampling Theory relates the rate of sampling to the highest frequency components in the measurements and it simply states that the sampling frequency used must be twice the bandwidth of the measurement system.
	www.npl.co.uk /electromagnetic/dclf/sampling_systems/sampling_aliasing.html (483 words)

	Analog Sampling Basics- Developer Zone - National Instruments
		Sampling rate is the speed at which the digitizerâs ADC converts the input signal, after the signal has passed through the analog input path, to digital values.
		The sampling rate of a high-speed digitizer is based on the sample clock that controls when the ADC converts the instantaneous analog voltage to digital values.
		The alias frequency is the absolute value of the difference between the frequency of the input signal and the closest integer multiple of the sampling rate.
	zone.ni.com /devzone/cda/tut/p/id/3016 (2316 words)

	Chapter 11 sampling
		While sampling technology has been available for a long time, only in the last decade has the speed of computers and availability of cost effective hardware made sampling with digital recorders the standard in the industry.
		The frequency of the 'snapshots' of the audio stream in a single second, is known as the sample rate.
		High sample rates are better at capturing high frequency waveforms, but if you are sampling lower frequency sounds, such as kick drum, bass, etc., you might consider sampling at the lower rate to save hard drive space.
	csunix1.lvc.edu /~snyder/2ch11.html (1616 words)

	The Open Door Web Site : IB Physics : Sampling Frequency (or Sampling Rate)
		For this reason, a digital instrument should operate with a sampling frequency much higher than the expected frequency of variation of the quantity being measured.
		At this sampling frequency the original wave is recognisable and could be reproduced accurately with the aid of filters.
		It has been shown (by C. Shannon in 1948) that, to be able to obtain a good "copy" of the original sound, the sampling frequency must be at least twice as high as the highest frequency of sound to be recorded.
	www.saburchill.com /physics/chapters/0080.html (400 words)

	Molecular Expressions Microscopy Primer: Digital Image Processing - Digital Image Sampling Frequency - Interactive Java ...
		Beneath the window is a Sampling Frequency slider that enables the user to vary the frequency within a range of one sample for every pixel to one sample for each 32 pixels.
		According to Shannon's sampling theorem, in order to preserve the spatial resolution of the original image, the digitizing device must utilize a sampling interval that is no greater than one-half the size of the smallest resolvable feature of the optical image.
		This is equivalent to acquiring samples at twice the highest spatial frequency contained in the image, a reference point commonly referred to as the Nyquist criterion.
	micro.magnet.fsu.edu /primer/java/digitalimaging/processing/samplefrequency/index.html (1021 words)

	Sampling Frequency (Site not responding. Last check: )
		Theoretically the frequency range is half the sampling frequency (Nyquist criterion).
		The supported sampling frequencies is sound card-dependent, most sound cards support 11025, 22050 and 44100 Hz.
		You may select the sampling frequency from the list of the most usual sampling frequencies, but you can also write the number directly in the window.
	www.winmls.com /hjelpfiler/samplingfrequency1.htm (138 words)

	Nyquist Sampling in Digital Microscopy
		The sampling theorem states that in order to reconstruct a function after discrete sampling, the samples should be taken at intervals equal to 1/2 of the upper cutoff (Nyquist) frequency of the original function.
		The Nyquist sampling theorem states that, when converting from an analog signal (sound or a microscope image) to digital, the sampling frequency must be greater than twice the highest frequency of the input signal in order to be able to reconstruct the original perfectly from the sampled version.
		If the sampling frequency is less than this limit, then frequencies in the original signal that are above half the sampling rate will be aliased and will appear in the resulting signal as lower frequencies (seen as the blocks in the undersampled image shown above).
	ourworld.compuserve.com /homepages/pvosta/pcrnyq.htm (391 words)

	Fundamentals of Digital Audio (Site not responding. Last check: )
		A continuous band-limited signal can be replaced by a discrete sequence of samples without loss of any information, and the original continuous signal can be reconstructed from the samples; furthermore, the sampling frequency must be at least twice the highest signal frequency.
		The alias frequency is the difference between the frequency recorded above the Nyquist frequency and the sampling frequency.
		The sampling frequency is usually made higher than twice the highest audio frequency recorded to allow the filter to roll off more gently.
	mtsu.edu /~jakins/4200/4200fundamentals.html (747 words)

	Rane Professional Audio Reference (S)
		Sampling (Nyquist) Theorem A theorem stating that a bandlimited continuous waveform may be represented by a series of discrete samples if the sampling frequency is at least twice the highest frequency contained in the waveform.
		sampling frequency or sampling rate The frequency or rate at which an analog signal is sampled or converted into digital data.
		The amplitudes (coefficients multiplying the magnitude of the fundamental sine wave) of the odd-ordered harmonics are the same as a square wave, while the amplitudes (re the fundamental) for the even-ordered harmonics are -1/n, where n is the even harmonic number.
	www.rane.com /par-s.html (8233 words)

	eFunda: Introduction to Nyquist Sampling Rate
		The sampling theorem is considered to have been articulated by Nyquist in 1928 and mathematically proven by Shannon in 1949.
		The sampling theorem clearly states what the sampling rate should be for a given range of frequencies.
		According to the sampling theorem, one should sample sound signals at least at 40 kHz in order for the reconstructed sound signal to be acceptable to the human ear.
	www.efunda.com /designstandards/sensors/methods/DSP_nyquist.cfm (380 words)

	Image Processing Fundamentals - Image Sampling (Site not responding. Last check: )
		Sampling with an impulse function corresponds to sampling with an infinitesimally small point.
		The combined effect of the aperture and sampling are best understood by examining the Fourier domain representation.
		is the sampling frequency in the y direction.
	www.ph.tn.tudelft.nl /Courses/FIP/noframes/fip--4.html (163 words)

	The Theory of the Sample (Site not responding. Last check: )
		In reality, losses occur when the sampling rate (time period of quanta) and the resolution (bits per sample) are of a small enough value to audibly interfere with the precision of the resultant wave.
		This frequency is simply one half of the sampling rate that is in use, and is the very highest frequency that can be represented.
		The wave frequency is in a ratio of 1:2.1 to the sampling frequency, and was generated at a constant amplitude of -1 dB.
	www.themusicpage.org /articles/SamplingTheory.html (3026 words)

	Linguistics 525 / CIS 558 -- Resampling and the wavetable oscillator
		The usual approach to sampling theory starts by considering the circumstances under which a continuous signal can be reconstructed from knowledge of its values only at certain sample points, equally spaced in time (or space, or whatever).
		The sampling process is modeling by multiplying the original signal by an impulse train, which is another continuous signal that has the value zero except at a set of discrete, equally-spaced points.
		Suppose we use a table of 1200 samples of one period of a sine wave, and then use wosc to generate 1200 samples of a sine wave with frequency 10 at sampling rate 12000.
	www.ling.upenn.edu /courses/Spring_2005/ling525/sampling1.html (4463 words)

	Intermediate Frequency (IF) Sampling Receiver Concepts
		Nyquist's sampling theorem states that if a signal is sampled at least twice as fast as the highest sampled frequency component, no information will be lost when the signal is reconstructed.
		The sample rate divided by two (Fs/2) is known as the Nyquist frequency and the frequency range from DC (or 0 Hz) to Fs/2 is called the first Nyquist zone.
		If the sampled signal moves into the second Nyquist zone from 39 MHz to 78 MHz, it can still be recovered but the absolute frequency information is lost.
	www.national.com /nationaledge/mar06/article.html (1104 words)

	sampling frequency (Site not responding. Last check: )
		The sampling frequency (or sample rate) is the number of samples per second in a Sound.
		For example: if the sampling frequency is 44100 Hertz, a recording with a duration of 60 seconds will contain 2,646,000 samples.
		Usual values for the sampling frequency are 44100 Hz (CD quality) and 22050 Hz (just enough for speech, since speech does not contain relevant frequencies above 11025 Hz; see aliasing).
	www.fon.hum.uva.nl /praat/manual/sampling_frequency.html (83 words)

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