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Topic: Nyquist Shannon sampling theorem

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	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)

	Nyquist-Shannon sampling theorem - Biocrawler (Site not responding. Last check: )
		when sampling a signal (e.g., converting from an analog signal to digital), the sampling frequency must be greater than twice the bandwidth of the input signal in order to be able to reconstruct the original perfectly from the sampled version.
		The theorem is satisfied when downsampling by filtering the signal appropriately with an anti-aliasing filter.
		A well-known consequence of the sampling theorem is that a signal cannot be both bandlimited and time-limited.
	www.biocrawler.com /encyclopedia/Nyquist_Frequency (1386 words)

	Nyquist-Shannon sampling theorem
		The theorem states that, when converting from an analog signal to digital (or otherwise sampling a signal at discrete intervals), 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.
		The theorem was first formulated by Harry Nyquist in 1928 ("Certain topics in telegraph transmission theory"), but was only formally proved by Claude E. Shannon in 1949 ("Communication in the presence of noise").
		The minimum sample frequency that allows reconstruction of the original signal, that is 2W samples per unit distance, is known as the Nyquist frequency, (or Nyquist rate).
	www.ebroadcast.com.au /lookup/encyclopedia/ny/Nyquist's_theorem.html (296 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)

	Harry Nyquist Summary
		Nyquist was born on February 7, 1889, in Nilsby, Sweden.
		Nyquist developed a method to transmit pictures—a crude but working facsimile (fax) machine—in which a photographic transparency was scanned, the scanned data was converted to electric signals in proportion to the intensity of shades and tones of the image, and these signals were sent over telephone lines to a photographic negative film.
		In 1927 Nyquist determined that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel.
	www.bookrags.com /Harry_Nyquist (984 words)

	Nyquist–Shannon sampling theorem - Wikipedia, the free encyclopedia
		The sampling theorem means that the discrete samples are a complete representation of the signal if the highest frequency component is less than half the sampling rate, which is referred to as the Nyquist frequency.
		From a signal processing perspective, the theorem describes two processes; a sampling process, in which a continuous or analog signal is converted into a discrete or digital signal, and a reconstruction process, in which the continuous/analog signal is recovered from the discrete/digital signal.
		That is the essence of the sampling theorem.
	www.physics.utah.edu /~springer/phys6620/lectures/lec04_20060124/Nyquist-Shannon_sampling_theorem.htm (2932 words)

	News \| TimesDaily.com \| TimesDaily \| Florence, Alabama (AL)
		Sampling is the process of converting a signal (for example, a function of continuous time or space) into a numeric sequence (a function of discrete time or space).
		From a signal processing perspective, the theorem describes two processes; a sampling process, in which a continuous time signal is converted to a discrete time signal, and a reconstruction process, in which the continuous signal is recovered from the discrete signal.
		The sampling theorem was implied by the work of Harry Nyquist in 1928 ("Certain topics in telegraph transmission theory"), in which he showed that up to 2B independent pulse samples could be sent through a system of bandwidth B; but he did not explicitly consider the problem of sampling and reconstruction of continuous signals.
	www.timesdaily.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Nyquist_theorem (4605 words)

	Definition of Nyquist-Shannon sampling theorem
		The sampling rate must be greater than twice the bandwidth and not just the maximum/highest frequency.
		Stating the theorem with the latter assumes that signal is low-pass in nature.
		When sampling a non-baseband signal, the theorem states that the sampling rate need only be twice the bandwidth.
	www.wordiq.com /definition/Nyquist-Shannon_sampling_theorem (1180 words)

	Reference Encyclopedia - ZOH
		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.
		The filter can then be analyzed in the frequency domain, for comparison with other reconstruction methods such as the Whittaker–Shannon interpolation formula suggested by the Nyquist–Shannon sampling theorem, or such as the first-order hold or linear interpolation between sample values.
		This droop is a consequence of the hold property of a conventional DAC, and is not due to the sample and hold that might precede a conventional analog-to-digital converter (ADC).
	www.referenceencyclopedia.com /?title=ZOH (585 words)

	nyquist freq.
		Nyquist says that your sample rate must be greater than two times the signal's bandwidth.
		when sampling a signal (e.g., converting from an analog signal to digital), the sampling frequency must be greater than twice the bandwidth of the input signal in order to be able to reconstruct the original perfectly from the sampled version.
		In simpler words, it states that if you would like to sample an analog signal of one-sided bandwidth of f0, and be able to reproduce the analog signal later (without any loss of information, otherwise known as perfect reconstruction), then the sampling frequency must be at least 2f0.
	www.edaboard.com /ftopic131115.html (437 words)

	Signal sampling - Techretriever (Site not responding. Last check: )
		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.
		The sample rate of a high-speed digitizer is based on the sample clock that tells the ADC when to convert the instantaneous analog voltage to the digital values.
		The primary uses of the sample detector are in the measurement of noise and noise-like signals, and near-noise CW amplitudes.
	www.techretriever.org /topics/Sample-(signal) (2934 words)

	Sampling Theory
		In this appendix, sampling theory is derived as an application of the DTFT and the Fourier theorems developed in Appendix C.
		An early derivation of the sampling theorem is often cited as a 1928 paper by Harold Nyquist, and Claude Shannon is credited with reviving interest in the sampling theorem after World War II when computers became public.
		As a result, the sampling theorem is often called ``Nyquist's sampling theorem,'' ``Shannon's sampling theorem,'' or the like.
	www-ccrma.stanford.edu /~jos/mdft/Sampling_Theory.html (233 words)

	4200 - Conversion Principles - Sampling
		The waveform is measured, or sampled, at periodic intervals.
		The theorem that defines the sampling process is generally attributed to Harry Nyquist, and is known as the Nyqist Theorem.
		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)

	The Nyquist-Shannon Sampling Theorem
		A precise statement of the Nyquist-Shannon sampling theorem is now possible.
		A formal proof of this theorem is not trivial (it was first proved by Claude Shannon of Bell Labs in the late 1940s).
		Notice that in the sampled signal, the frequencies in the vicinity of
	ptolemy.eecs.berkeley.edu /eecs20/week13/nyquistShannon.html (226 words)

	The Sampling Theorem
		There is nothing in the sampled data to suggest that the original analog signal had a frequency of 0.95 rather than 0.05.
		Frequently this is called the Shannon sampling theorem, or the Nyquist sampling theorem, after the authors of 1940s papers on the topic.
		Sampling the signal in (a) by using an impulse train produces the signal shown in (c), and its frequency spectrum shown in (d).
	www.dspguide.com /ch3/2.htm (1949 words)

	Abtasttheorem - bedeutung definition erklärung glossar zu Abtasttheorem
		Ebensowenig fallen periodische Signale, wie z.B. reine Sinusschwingungen, in den Bereich dieses Theorems; genausowenig Signale mit Knicken oder Sprüngen.
		Eventuell enthaltene Signalanteile mit einer Frequenz größer der halben Abtastfrequenz müssen vor der Abtastung mit einem (analogen) Tiefpass-Filter aus dem Signal entfernt werden, da es sonst zu Artefakten
		Harry Nyquist: Certain topics in telegraph transmission theory,Trans.
	abtasttheorem.lexikona.de /art/Abtasttheorem.html (1317 words)

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