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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.
		Graphically, if the sampling rate is sufficiently high, i.e., greater than the Nyquist rate, there will be no overlapped frequency components in the frequency domain.
	www.efunda.com /designstandards/sensors/methods/DSP_nyquist.cfm (380 words)

	Nyquist-Shannon sampling theorem - Wikipedia, the free encyclopedia
		The theorem was first formulated by Harry Nyquist in 1928 ("Certain topics in telegraph transmission theory"), but was only formally proven by Claude E. Shannon in 1949 ("Communication in the presence of noise").
		A well-known consequence of the sampling theorem is that a signal cannot be both bandlimited and time-limited.
		When sampling a non-baseband signal, the theorem states that the sampling rate need only be twice the bandwidth W if the frequency band is some interval [NW,(N+1)W].
	en.wikipedia.org /wiki/Nyquist-Shannon_sampling_theorem (1543 words)

	Nyquist-Shannon sampling theorem : Nyquist 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.fastload.org /ny/Nyquist_sampling_theorem.html (335 words)

	Sensors Magazine Online - July 1999 - Understanding Frequency Domain Measurements (Site not responding. Last check: 2007-10-11)
		Suppose that during your measurement normal braking causes the brake assembly to squeal and that the squeal noise is composed of a fundamental frequency at 750 Hz and harmonics at 1500 Hz and 2250 Hz.
		Nyquist stated, "The minimum bandwidth required for unambiguous interpretation is substantially equal, numerically, to the speed of signaling.
		So the minimum sampling rate, fs (known as the Nyquist rate), does indeed contain the signal bandwidth, whose highest frequency is limited to the Nyquist frequency, fs/2.
	www.sensorsmag.com /articles/0799/40/main.shtml (3137 words)

	Bandwidth, Sample Rate, and Nyquist Theorem - Tutorial - Development Library - National Instruments
		Sample rate is the speed at which the digitizer’s ADC converts the input signal, after the signal has passed through the analog input path, to digital values that represent the voltage level.
		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.
		he Nyquist theorem states that a signal must be sampled at a rate greater than twice the highest frequency component of the signal to accurately reconstruct the waveform; otherwise, the high-frequency content will alias at a frequency inside the spectrum of interest (passband).
	zone.ni.com /devzone/conceptd.nsf/webmain/0B04C09D4A44C78186256C3F007F8B02 (840 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		However, for signals which do not extend to dc, the minimum required sampling rate is a function of the bandwidth of the signal as well as its position in the frequency spectrum.
		In 1928, Henry Nyquist published an important paper titled "Certain Topics in Telegraph Transmission Theory." In it, he postulated a theorem which proposed that a sample of twice the highest signal frequency rate, captures the signal’s frequency content in a manner that enables it to be reconstructed without fear of aliasing.
		2-4 to calculate the minimum sampling rate, any increase to that sampling rate must be an integer multiple of the minimum sampling rate until you reach a frequency that is twice the highest frequency component in the input signal.
	www.dspengineering.com /articles/neagoe_and_fugerer/include/print.php (3156 words)

	Sensors Magazine Online - July 1999 - Demystifying Piezoresistive Pressure Sensors (Site not responding. Last check: 2007-10-11)
		Frequency components above half the sample rate, referred to as the Nyquist frequency or Nyquist rate, are aliased or "folded" into the range between zero and the Nyquist frequency.
		With reasonably high sampling rates, anti-aliasing filters actually may not be needed with most piezoresistive and capacitive MEMS accelerometers, since these accelerometers have a built-in two-pole mechanical filter that is typically in the 15 kHz range.
		Second, the very large quantization noise from a 1-bit quantizer is spread over the very large frequency band up to the Nyquist rate, with the result that only a small amount of the noise appears in the 010 Hz band of interest.
	www.sensorsmag.com /articles/0799/55/main.shtml (2256 words)

	BROADCASTPAPERS.COM (Site not responding. Last check: 2007-10-11)
		In other words, remove energy from the frequency range between the Nyquist rate (5.381118881 MHz plus pilot or 5.690559441 MHz) and the upper channel edge, and compensate for the loss of energy by increasing the signal amplitude between pilot plus 5.071678322 MHz and pilot plus 5.381118881 MHz.
		So, removing voltage from any frequency above the Nyquist rate, and replacing it at the same frequency below the Nyquist rate such that the frequency-transposed energy is the same at the receiver's demodulator after its RRC filtering, will not change the demodulated I channel signal after it is sampled.
		This is because the signal components above and below the Nyquist rate are mirror images of each other, and sampling a frequency component above the Nyquist rate by a frequency f will produce the same result as sampling a frequency component below the Nyquist rate by frequency f.
	www.broadcastpapers.com /tvtran/narrowband03.htm (642 words)

	SVI-wiki: Nyquist Rate
		The Nyquist-Shannon sampling theorem establishes that "when sampling a signal (e.g., converting from an analog signal to digital), the sampling frequency must be greater than twice the Band Width of the input signal in order to be able to reconstruct the original perfectly from the sampled version" (wikipedia).
		The ideal sampling rate is better defined in terms of the system Band Width, which is determined by the Point Spread Function.
		Since the wavelength for excitation and emission are approximately equal, and the blurring effect of a finite sized detection pinhole doesn't alter the bandwidth of the detection system, the Band Width of the overall PSF is twice as large as any of them.
	support.svi.nl /wiki/NyquistRate (1690 words)

	The Nyquist Frequency
		Summary: The Nyquist Frequency corresponds to the highest frequency at which a signal can contain energy and still be compatible with the Sampling Theorem.
		If indeed the Nyquist frequency equals the signal's highest frequency, at least two samples will occur within the period of the signal's highest frequency sinusoid.
		Reducing the sampling rate would result in fewer samples/period, and these samples would appear to have arisen from a lower frequency sinusoid.
	cnx.rice.edu /content/m0090/latest (513 words)

	Nyquist's Theorem (Fs > 2F )
		The sampling frequency is chosen somewhat higher than the Nyquist rate since practical filters needed to prevent aliasing have a finite slope.
		The sampling rate of such a system is constrained to relate simply to the field rate and field structure of the television standard used, so that an integer number of samples can be stored on each usable TV line in the field.
		multiplying the field rate by the number of active lines in a field (blanking lines cannot be used) and again by the number of samples in a line.
	home.fuse.net /injanius (998 words)

	Anti-Aliasing in Computer Graphics
		The Nyquist Theorem states that the sampling rate must be twice the frequency of the signal or an effect known as aliasing occurs.
		The top wave is sampled at a frequency within the Nyquist limit and the digital sample produces the original frequency.
		The bottom wave on the other hand is sampled beyond the Nyquist limit and the resulting sampled wave has a much lower frequency than the source.
	www.cc.gatech.edu /classes/AY2001/cs4451_spring/projects/Five (1033 words)

	Data Converters for Communication Systems
		The basic Nyquist rate converter performs a sample-by-sample mapping from the analog to the digital domain, as shown in Fig.
		Nyquist rate converters all share a similarity in that an N-bit converter generally requires the analog circuit components to have an accuracy on the order of 1/2
		The passband quantization error is reduced relative to the Nyquist converter at the cost of increased stopband noise.
	www.comsoc.org /ci/private/1998/oct/Tao.html (3241 words)

	MUS 319 Study Guide, Test Three
		The Nyquist frequency is the frequency whose value is half that of the sampling rate.
		A sampling rate of 800 samples per second is more than adequate to represent the fundamental frequency, and is also sufficient to represent the frequency of the overtone.
		A sampling rate of 800 samples per second is more than adequate to represent the fundamental frequency, but is not sufficient to represent the frequency of the overtone.
	spider.georgetowncollege.edu /music/burnette/Mus319/319-T3.htm (549 words)

	baudline manual - glossary
		GSM 6.10 is a lossy CBR audio compression codec which has an audio sample rate of 8000 samples/second and a data rate of 13 Kbps.
		For real signals; half the sampling rate is known as the Nyquist frequency limit.
		Complex quadrature signals have twice the bandwidth for a given sample rate.
	www.baudline.com /manual/glossary.html (2016 words)

	BROADCASTPAPERS.COM (Site not responding. Last check: 2007-10-11)
		When the symbols are extracted, which reduces the sampling rate to the symbol rate, energy above the Nyquist rate aliases to frequencies below the Nyquist rate.
		In the Hilbert transform modulator, the frequency response of the I channel at any modulation frequency must be proportional to the sum of the voltages to be produced in the upper and lower sidebands at that frequency.
		The result is that the demodulated I channel, when resampled at the symbol rate, is exactly the same as it would have been with standard RRC modulation.
	www.broadcastpapers.com /tvtran/narrowband-print.htm (4258 words)

	[No title]
		This includes the sample rate parameter [73], the actual sample frequency, the cooresponding note frequency as well as the name of the equal tempered note (A=440) that is closest.
		Nyquist showed that to prevent aliasing, the sample rate must be AT LEAST twice the highest frequency component.
		First is to make sure that the sample rate is high enough - often difficult on a Mirage due to the limits of the hardware, and the second is to filter out most or all of the frequency components of the sound that are above the Nyquist rate.
	www.webcom.com /jawknee/Mirage/C64/moreinfo.txt (1605 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		The CD sampling rate has to be larger than about 40 kHz to fulfill the Nyquist criterion that requires sampling at twice the maximum analog frequency, which is about 20 kHz for audio.
		The allowable sampling rates in a pseudo-video system can be deduced by multiplying the field rate by the number of active lines in a field (blanking lines cannot be used) and again by the number of samples in a line.
		The sampling rate of 44.1 KHz came to be that of the Compact Disc.
	www.cs.columbia.edu /~hgs/audio/44.1.html (460 words)

	Sound Lab
		One half the sampling rate is often referred to as the Nyquist frequency or the Nyquist rate.
		Any frequency that exceeds the Nyquist rate is indistinguishable from a negative frequency the same amount less than the Nyquist rate.
		In this case the sampling rate is quite adequate because the maximum frequency we are trying to record is well below the Nyquist frequency.
	cfaonline.asu.edu /dan521/digital.html (2706 words)

	Appendix 1: Extending Nyquist
		Many of the Nyquist signal processing operations are similar in form, but they differ in details.
		Nyquist signals can have different sample rates, different block sizes, different block boundaries, and different start times, all of which must be taken into account.
		Nyquist assumes all arguments are used in the inner loop, so specify them here if not.
	www.cs.cmu.edu /afs/cs.cmu.edu/user/rbd/www/doc/nyquist/part13.html (3044 words)

	Break Nyquist Criterion Using Undersampling Technique - News - National Instruments
		Usually, Harry Nyquist, an ATandT scientist, is quoted as saying that the sample rate used to acquire a signal must be at least double the signal’s highest frequency component.
		You still are not breaking the Nyquist criterion because Nyquist actually said the sampling rate must be at least double the signal’s bandwidth, not the signal’s highest frequency component.
		For a signal that contains frequencies reaching from DC to 40 MHz, for example, the Nyquist criterion reduces to the common definition, and the sample rate must be at least 80 MS/s.
	digital.ni.com /worldwide/bwcontent.nsf/web/all/80F86BCF42FCE5AF86256F9E00593AD2 (581 words)

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