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Topic: Nyquist frequency

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	Nyquist-Shannon sampling theorem : Nyquist sampling theorem (Site not responding. Last check: 2007-11-04)
		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.
		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.
		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)

	Nyquist Theorem Details
		Nyquist's theorem states that it is only necessary to take samples at a rate of slightly over two per cycle of the highest frequency component of the source analog signal.
		Nyquist's theorem states that, if we sample the complex waveform uniformly at a rate just a tad over twice the highest frequency component sine wave contained within, the conglomeration of samples thus obtained are sufficient information to reconstruct the waveform.
		Nyquist's frequency is the frequency that no part of the source material may attain or exceed, which is half of the sampling frequency.
	members.aol.com /ajaynejr/nyquist.htm (2368 words)

	Nyquist frequency - Wikipedia, the free encyclopedia
		The Nyquist frequency, named after Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system.
		The Nyquist frequency is defined differently from the Nyquist rate, which is the minimum sampling frequency that meets the Nyquist sampling criterion for a given signal or family of signals.
		Nyquist rate, as commonly used with respect to sampling, is a property of a signal, not of a system.
	en.wikipedia.org /wiki/Nyquist_frequency (463 words)

	Nyquist Plots
		Bode' plots use frequency as the horizontal axis and use two separate plots to display amplitude and phase of the frequency response.
		Nyquist plots display both amplitude and phase angle on a single plot, using frequency as a parameter in the plot.
		The frequency is a parameter of the plot, and unless we do something, there will be no indication of what frequency corresponds to a particular point on the plot.
	www.facstaff.bucknell.edu /mastascu/eControlHTML/Freq/Freq6.html (2535 words)

	How do we Set Filter Parameters
		Overall, the cut-off frequency should be chosed based on the frequency space distribution of the data (i.e.
		According to discrete sampling theory, the maximum usable frequency is 0.5 cycles per pixel because at least two pixels are required to define the one cycle of the wave.
		The choice of cut-off frequency is a compramise between smoothness of the image and spatial resolution.
	www.uab.edu /radiography/Nmt422/Setting_Filter_Parameters.htm (668 words)

	Analog Sampling Basics- Developer Zone - National Instruments
		In this case f is equal to the Nyquist frequency.
		The Nyquist frequency in this case is (4f / 3) / 2 = 2f / 3.
		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)

	nyquist (Function Reference) (Site not responding. Last check: 2007-11-04)
		Nyquist plots are used to analyze system properties including gain margin, phase margin, and stability.
		explicitly specifies the frequency range or frequency points to be used for the plot.
		H = tf([2 5 1],[1 2 3]) nyquist(H) The nyquist function has support for M-circles, which are the contours of the constant closed-loop magnitude.
	www-rohan.sdsu.edu /doc/matlab/toolbox/control/ref/nyquist.html (342 words)

	Bandwidth, Sample Rate, and Nyquist Theorem- Developer Zone - National Instruments
		Sample rate is the frequency at which the ADC converts the analog input waveform to digital data.
		Bandwidth is specified as the frequency at which a sinusoidal input signal is attenuated to 70.7% of its original amplitude, also known as the -3 dB point.
		The 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/cda/tut/p/id/2709 (952 words)

	Nyquist–Shannon sampling theorem - Wikipedia, the free encyclopedia
		This constraint is equivalent to requiring that the system's Nyquist frequency (also known as critical frequency, and equal to half the sample rate) be strictly greater than the bandwidth of the 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.
		The sampling theorem, essentially a dual of Nyquist's result, was proved by Claude E. Shannon in 1949 ("Communication in the presence of noise").
	en.wikipedia.org /wiki/Nyquist-Shannon_sampling_theorem (5184 words)

	Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm
		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.
		As the frequency of each sinusoid approaches the folding frequency, the two mirror-image peaks corresponding to that sinusoid merge into a single peak with twice the height at the folding frequency.
	www.developer.com /java/other/article.php/3380031 (9896 words)

	Sub-Nyquist Distortions in Sampled One- and Two-Dimensional Signals Studied
		Put simply, the sampling frequency must be at least twice the frequency of any signal to be sampled, or vice versa; the signals must be filtered so that none of the signal frequencies are higher than one-half the sample rate (the Nyquist Limit).
		Input frequency was 6/53 of that, or 113.20754 kHz.
		The signal frequencies of concern are those that are a fraction of a harmonic of the sample rate, in which the numerical ratio in the fraction has all the common primes factored out.
	www.grc.nasa.gov /WWW/RT2000/7000/7715williams.html (512 words)

	Nyquist frequency (Site not responding. Last check: 2007-11-04)
		The Nyquist frequency is the bandwidth of a sampled signal, and is equal to half the sampling frequency of that signal.
		If the sampled signal should represent a continuous spectral range starting at 0 Hz (which is the most common case for speech recordings), the Nyquist frequency is the highest frequency that the sampled signal can unambiguously represent.
		This means that to heed this expectation, we should run the continuous signal through a low-pass filter with a cut-off frequency below 11025 Hz; otherwise, we would experience the phenomenon of aliasing.
	www.fon.hum.uva.nl /praat/manual/Nyquist_frequency.html (147 words)

	Experiment an Interactive Demonstration of the Art of Signal Sampling and Aliasing
		Nyquist frequency defined as maximum signal frequency that could be reliably measured to avoid aliasing, which is solely based on the sampling frequency, i.e.
		Nyquist frequency defined as minimum required sampling frequency for a given signal frequency to avoid aliasing.
		a half of the sampling frequency), and (2) based on a signal frequency (so the Nyquist frequency is the minimum sampling frequency required to avoid aliasing), thus the latter being twice the former.
	www.kostic.niu.edu /aliasing.htm (821 words)

	4200 - Conversion Principles - Sampling
		For a given sampling frequency, calculate the Nyquist frequency and the expected frequency response.
		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.
		Real-world filters cannot perfectly filter out frequencies at the exact edge of the desired program spectrum; therefore, Nyquist frequencies are set higher than the top program frequency to account for filter rolloff.
	www.mtsu.edu /~djbrown/4200_Site/Conversion_Sampling.html (923 words)

	Analog Devices: Analog to Digital Converters: Tutorial MT-002: What the Nyquist Criterion Means to Your Sampled Data ...
		Nyquist was working on the transmission of telegraph signals over a channel that was bandwidth limited.
		This implies any input frequency greater than 9.7 Hz is subject to conversion errors, even though a sampling frequency of 100 kSPS is possible with the 8-µs ADC (this allows an extra 2-µs interval for an external SHA to re-acquire the signal after coming out of the hold mode).
		In fact, the sampled signal frequencies may lie in any unique Nyquist zone, and the image falling into the first Nyquist zone is still an accurate representation (with the exception of the spectral reversal which occurs when the signals are located in even Nyquist zones).
	www.analog.com /en/content/0,2886,760__91249,00.html (3198 words)

	Systat Software Inc. - AutoSignal - Tutorials
		The upper graph confirms the amplitude and frequency of the three peaks isolated by the Lomb procedure.
		The lower graph plots the three sinusoidal components on the Y axis, and the model (the sum of the three components) and the prediction intervals in the upper graph.
		Although the lowest frequency peak at 2.0 is preserved, the remainder of the spectrum is nonsense.
	www.systat.com /products/AutoSignal/?sec=1037 (1396 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.
		As the square wave's period decreases, the negative frequency lines move to the left and the positive frequency ones to the right.
		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.
	cnx.org /content/m0090/latest (513 words)

	Comments on the Measurement of Power Spectra of the Interplanetary Magnetic Field
		The folding of power about the Nyquist frequency or aliasing can be a serious problem at times for many magnetometers, but it is not serious during typical solar wind conditions except near the Nyquist frequency.
		The Nyquist frequency (half the sampling frequency), the upper frequency cutoff of the instrument's passband, and the ratio of these two frequencies for spacecraft probing the interplanetary medium.
		Finally, at the highest frequencies we have used the OGO-5 power spectrum shown in Figure 7, which as suggested in the previous section, appears to be typical of average solar wind conditions since it joins smoothly with the intermediate activity spectrum of Mariner 4.
	www-ssc.igpp.ucla.edu /personnel/russell/papers/comment (4797 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 (1098 words)

	Scanners and sharpening: resolution and MTF
		The first sensor null (the frequency where a complete cycle of the signal covers one sample, hence must be zero regardless of phase) is twice the Nyquist frequency.
		By definition, the Nyquist frequency is 1 cycle in 2 pixels.
		Some of the problem is due to the Bayer sensor: the effective horizontal and vertical Nyquist frequency for red and blue pixels is half that of green.
	www.normankoren.com /Tutorials/MTF2.html (5419 words)

	Research Consulting Documents
		As in the question above, the bands are specified in terms of the Nyquist frequency, not the sampling frequency.
		Frequency represents a vector of frequencies specifying the start and end points for each band.
		The second is that extremely high frequencies (greater than 100MHz) are being specified in the frequency vector.
	www.utexas.edu /its/rc/answers/matlab/faq6.html (1994 words)

	Chapter 11 sampling
		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.
		If a frequency of A-14,080 Hz is to be recorded, a sample rate of 44.1 kHz would be the logical choice to use.
	csunix1.lvc.edu /~snyder/2ch11.html (1616 words)

	[Prosig.com] Data Decimation. What Do I Do ?
		The Nyquist frequency is simply the frequency which is half the sample rate.
		For instance, a common disturbance is the second harmonic of the mains frequency.
		Thus even for fatigue calculations when we are not looking at frequency analysed data we still have to obey the anti-aliasing rules.
	www.prosig.com /signal-processing/DataDecimation.html (1113 words)

	CTM: Function lnyquist1
		By taking the log of the magnitude, the magnitude scale is compressed and the overall shape of the Nyquist plot is easier to see on the screen.
		We use log base 2 and add one to the magnitude so as to preserve the key attributes of the -1 point for the Nyquist plot.
		vector W which must contain the frequencies, in radians/sec, % at which the Nyquist response is to be evaluated.
	www.engin.umich.edu /group/ctm/extras/lnyquist1.html (514 words)

	Folded-Frequency Calculator - Maxim/Dallas
		In the digital signal processing (DSP) domain, T/H processing is equivalent to convolution of the frequency spectrum of the impulse train (due to the sampling clock) with the frequency spectrum of the analog input.
		This convolution results in periodicity of the frequency spectrum that is observed over various Nyquist zones, as previously explained.
		ZOH processing in the DSP domain is equivalent to convolution of the sin(x)/x type of frequency spectrum (of the rectangular function appearing due to holding discrete time samples) with the DAC core’s output-impulse train frequency spectrum (of varying amplitude, in general).
	www.maxim-ic.com /appnotes.cfm/appnote_number/3716 (902 words)

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