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	Spectral density - Wikipedia, the free encyclopedia
		In applied mathematics and physics, the spectral density, power spectral density, or energy spectral density is a general concept applied to a signal which may have physical dimensions such as power per Hz, or energy per Hz, or none at all.
		The spectral density of f(t) and the autocorrelation of f(t) form a Fourier transform pair (for PSD versus ESD, different definitions of autocorrelation function are used).
		The spectral centroid of a signal is the midpoint of its spectral density function, i.e.
	en.wikipedia.org /wiki/Spectral_density (988 words)

	Window function - Wikipedia, the free encyclopedia
		In summary, spectral analysis involves a tradeoff between resolving comparable strength signals with similar frequencies and resolving disparate strength signals with dissimilar frequencies.
		Although we have depicted leakage as interference that one component imposes on other frequencies, the effect is reciprocal.
		When the signal is a sinusoid corrupted by additive random noise, spectral analysis distributes the signal and noise components differently, often making it easier to detect the signal's presence or measure certain characteristics, such as amplitude and frequency.
	en.wikipedia.org /wiki/Window_function (1463 words)

	Advanced DSP - FFT windows: Spectral leakage
		The amount of the contribution is proportional to the amplitude of the window function's kernel, centred at the FFT bin, measured at the interfering frequency.
		The effects of spectral leakage are worst when detecting small signals in the presence of nearby large signals.
		To minimise the effect of spectral leakage, a window function's kernel should have low amplitude sidelobes away from the centre: and the rate of fall off to the low sidelobes should be rapid.
	www.bores.com /courses/advanced/windows/10_leak.htm (160 words)

	Fourier Spectral Processing
		Spectral leakage is the term used to describe the loss of power of a given frequency to other frequency bins in the FFT.
		In fact, when a spectral component’s frequency is not centered in a bin, some portion of the variance due to this component may be accounted for by each bin in the spectrum.
		By having the data smoothly vary and decay to zero at the endpoints, spectral leakage is drastically reduced, so much so that a decibel (dB) scale, which is logarithmic, must be used to observe the spectral leakage across the bins in a meaningful way.
	www.clecom.co.uk /science/autosignal/help/Fourier_Spectral_Processing.htm (1509 words)

	week10notes
		Thus, spectral decomposition by fourier analysis provides us with a means of characterizing the relative importance of the multiple processes with different frequencies that contribute to the total variance of a time series.
		Leakage is the translation of power (variance) from a discrete spectral peak to adjacent frequencies above and below the true frequency of the process (see leakage figure).
		Like, leakage, this is a numerical consequence that is due to finte record length and arises during the transformation of the data from the time domain to the frequency domain.
	www.personal.kent.edu /~jortiz/earthstats/topic10notes.html (2797 words)

	5.3 Fabry-Pérot Overview (Site not responding. Last check: 2007-10-25)
		The spectral resolution decreases towards the short wavelength ends of the wavelength ranges covered by the two Fabry-Pérots, where the wavelengths corresponding to the resonances of the reflective meshes are approached.
		Large scale trends are determined by the counteracting effects of detector spectral response increasing with wavelength until close to the detector cut-off wavelength, and decreasing transmission of the Fabry-Pérot interferometer.
		Leakage has been quantified by analysis of the grating instrumental profile as seen by the F-P detectors in scans of solid state laser lines.
	www.iso.vilspa.esa.es /manuals/sws_idum4/sidm/node33.html (1289 words)

	Statistical Signal Processing (Signal Processing Toolbox)
		It is important to note that the effect of spectral leakage is contingent solely on the length of the data record.
		In order to resolve two sinusoids that are relatively close together in frequency, it is necessary for the difference between the two frequencies to be greater than the width of the mainlobe of the leaked spectra for either one of these sinusoids.
		As is the case for the correlation and covariance sequences, the toolbox estimates the PSD and CSD because signal lengths are finite.
	www-rohan.sdsu.edu /doc/matlab/toolbox/signal/spectra8.html (2677 words)

	Dynamic Testing of High-Speed ADCs, Part 2 - Maxim/Dallas
		To accurately determine spectral leakage, however, it may not be enough to use adequate signal-acquisition techniques, convert a two-sided power spectrum into a single-sided one, and rescale the result.
		Spectral leakage is the result of an assumption in the FFT algorithm that the time record is precisely repeated throughout all time and that all signals contained in this time record are periodic at intervals corresponding to the length of the time record.
		Spectral leakage distorts the measurement by spreading the energy of a given frequency component over the adjacent frequency lines or bins.
	www.maxim-ic.com /appnotes.cfm?an_pk=729 (4285 words)

	Lab 5
		The spectral components of the FFT are samples of the continuous DTFT of a signal.
		Another fundamental issue of the FFT is resolution and leakage which is determined by the choice of the truncating window.
		Leakage is when components at one frequency are spread into other frequencies and affect the components at those frequencies.
	www.eas.asu.edu /~eee407/labs03/node8.html (776 words)

	FFT Spectrum Analyser applet: guidance notes
		Spectral leakage occurs when a frequency component of a signal does not slot exactly into one of the frequency channels in the spectrum computed using the discrete Fourier transform.
		Spectral leakage is therefore almost certainly going to affect the spectrum of any signal of practical interest.
		Spectral leakage causes energy (amplitude) from distinct spectral features to "leak" into adjacent frequency channels, giving rise to spurious components in the frequency spectrum of the signal.
	www.dsptutor.freeuk.com /analyser/guidance.html (4439 words)

	Frequencies in the ``Cracks''
		This is sometimes called spectral leakage or cross-talk in the spectrum analysis.
		Note that peak spectral leakage is not reduced by increasing
		To reduce spectral leakage (cross-talk from far-away frequencies), we typically use a window function, such as a ``raised cosine'' window, to taper the data record gracefully to zero at both endpoints of the window.
	ccrma-www.stanford.edu /~jos/mdft/Frequencies_Cracks.html (612 words)

	Accelerometer Data Analysis and Presentation Techniques
		Spectral leakage will arise in the analysis of periodic data with period Tp if the length of the record being analyzed, T, is not an integer number of Tp periods as assumed in Fourier theory.
		In order to suppress spectral leakage, it is common to introduce a weighting function that tapers the time series data to eliminate discontinuities at the beginning and end of the record.
		Spectral averaging (point-by-point averaging of frequency domain spectra) is used to improve the estimation of the spectrum of interest [9].
	www.grc.nasa.gov /WWW/MMAP/PIMS/HTMLS/adapt.html (6777 words)

	Jesper Spetzler: The effect of small-scale heterogeneity on the propagation of waves : with applications to forward ...
		The term spectral leakage indicates that observed data affected by structures with a length-scale that is not account for in a given inverse can leak into the long-wavelength structures that are part of the estimated model.
		In the case of global surface wave tomography, surface wave scattering theory is used in an inversion including the spectral leakage correction of phase velocity measurements for Love waves at periods of 40 s and 150 s.
		The global phase velocity models from the spectral leakage inversion are obtained without applying any damping, but they show, however, a good correlation with tectonic features such as plate boundaries, ridges and trenches.
	igitur-archive.library.uu.nl /dissertations/1959646/inhoud.htm (825 words)

	SSA-MTM Toolkit User's Guide: MTM Theory
		The Multi-Taper method (MTM) of spectral analysis provides a novel means for spectral estimation (Thomson, 1982; Percival and Walden, 1993) and signal reconstruction (e.g., Park, 1992) of a time series which is believed to exhibit a spectrum containing both continuous and singular components.
		A set of independent estimates of the power spectrum is computed, by pre-multiplying the data by orthogonal tapers which are constructed to minimize the spectral leakage due to the finite length of the data set.
		Significance levels for harmonic or narrowband spectral features relative to the estimated noise background can be determined from the appropriate quantiles of the chi-squared distribution, approximating the spectrum as being distributed with 2K degrees of freedom (see Mann and Lees, 1996).
	www.atmos.ucla.edu /tcd/ssa/guide/mann/mann4.html (2880 words)

	Systat Software Inc. - AutoSignal - HTML Help
		option in the Spectral menu or the Spectral toolbar uses a series of orthogonal data tapers to generate a Fourier spectrum, utilizing the information at the edges of the data and reducing the variance of the spectral estimate.
		What is gained is a reduced-variance spectral estimator that retains a high dynamic range and which utilizes all of the data in the record.
		The spectral peaks in the averaged spectrum are identified by a local maxima detection algorithm in the F-ratio and averaged frequency spectrum.
	www.systat.com /products/AutoSignal/help?sec=1130 (1572 words)

	DSP Unit: Notes on Spectral Leakage (Site not responding. Last check: 2007-10-25)
		The amount of spectral leakage is related to the type of data window applied to the data samples before the DFT is calculated.
		The bottom plot used the same signal frequency as the middle plot, but a Hanning window was employed prior to the DFT (ie the N signal samples are multiplied by a N point Hanning window).
		In practice a data window (such as Hanning) is usually employed in Periodogram spectral estimates, and the relatively small leakage into adjacent bins is not a problem if N is large enough.
	www.itr.unisa.edu.au /cbt/dsp/leakage.html (265 words)

	Smoothing Windows for Spectral Leakage - Tutorial - Development Library - National Instruments
		These discontinuities produce leakage of spectral information, resulting in a discrete-time spectrum that is a smeared version of the original continuous-time spectrum.
		When performing Fourier or spectral analysis on finite-length data, you can use windows to minimize the transition edges of your truncated waveforms, thus reducing spectral leakage.
		Fortunately, another technique to reduce spectral leakage, known as windowing or smoothing windows, is available.
	zone.ni.com /devzone/conceptd.nsf/webmain/81E934672ABEB3D4862568C1006528F4?opendocument (444 words)

	Look Through Any Window (Site not responding. Last check: 2007-10-25)
		A spectral domain (or frequency domain) view of a wave shows amplitude as a function of frequency, meaning that frequencies are represented along the horizontal axis and their respective amplitudes are shown on the vertical axis (see Fig.
		This is called spectral “leakage” or “clutter.” The shorter the window, the fewer filters there are, and the more leakage they produce.
		The inaccuracies of spectral leakage and localization blur are minimized by “arithmetic preheating.” A set of samples is not simply lifted from the signal and then analyzed.
	emusician.com /mag/emusic_look_window (1795 words)

	Systat Software Inc. - AutoSignal - Tutorials
		The spectral peaks are now impulse functions, but the spectral leakage introduced by zero padding is sufficient to mask the three lower power components.
		Further, the first two spectral peaks are shown to be highly significant statistically relative to white noise having the same variance as this reconstructed signal.
		Absent the four major reference components, and their contributions to spectral leakage, the three lower power spectral peaks that comprise the filtered data are now recovered using a non-windowed FFT.
	www.systat.com /products/AutoSignal?sec=1035 (2764 words)

	Defining and Testing Dynamic Parameters in High-Speed ADCs, Part 1 - Maxim/Dallas
		The amplitudes of the nonaliased frequencies, which depend on the amplitude and the frequency of the applied input sine wave, are generally given as a dB-ratio with respect to the amplitude of the applied sine-wave input.
		Also known as spectral leakage, these components should be avoided because they mask spurious performance of the ADC itself.
		Noise-power ratio (NPR) is a figure of merit that defines the spectral power of contributed errors, such as IMD and THD, in a small frequency band within the baseband of the composite input signal being processed and analyzed.
	korea.maxim-ic.com /appnotes.cfm?an_pk=728 (3327 words)

	Spectral Leakage - Tutorial - Development Library - National Instruments
		In the figure below, you see the spectral representation when you sample a noninteger number of cycles of the time waveform (namely 10.5).
		Notice how the energy is now spread over a wide range of frequencies, so the relative height difference between the fft peak amplitude and the neighboring bins is reduced.
		This smearing of the energy is spectral leakage.
	zone.ni.com /devzone/conceptd.nsf/webmain/4D2F2B3C170CC02E862568C1006857EB (333 words)

	EDU» b = [
		This is referred to as the spectral leakage effect.
		Because the DFT operates on versions of signals having finite duration, it naturally causes spectral leakage to occur.
		However, spectral leakage may not be evident due to the discrete sampling introduced by X(k).
	www.ee.calpoly.edu /~fdepiero/curr/dsp/dsp1.htm (1164 words)

	baudline manual - equalization, windowing
		This will push the spectral energy up which could result in clamping at the 0 dB level and it might impair visualization resolution or scaling.
		This control reduces the post equalization spectral levels so that strongly equalized signals can be brought back into a usable zone.
		If the spectral windows are resized smaller than this value, the "extra" information is just discarded not rescaled unless a Hz zoom factor is selected.
	www.baudline.com /manual/equalization.html (1016 words)

	Martin Pessah's Home Page (Site not responding. Last check: 2007-10-25)
		A viable approach to addressing this problem is to assume an underlying power spectral density with a suitable mass dependence, derive the functional form of the relationship between fractional rms and mass for a given sampling pattern, and investigate whether the result is consistent with the observations.
		For a given model power spectral density one can ask how much of a difference does it make to consider or not to consider the spectral leakage the we mentioned above when associating the particular model with the corresponding fractional rms.
		By carefully accounting for sampling effects I derived equations that connect the model (underlying) power spectral density for a given AGN with the (observed) root mean square variability obtained from the time series representing the observed light curve.
	www.physics.arizona.edu /~mpessah/research/2005/agn-bhc (1101 words)

	Gut-Level Fourier Transforms - Part 5
		Spectral leakage can cause problems with digital spectrum analysis whenever the input data set doesn't hold an exact integer number of cycles of the signal.
		The situation is shown in Figure 4, with the input on top, then the lower and upper sidebands, and the signed sum of all these on the bottom trace.
		They all use the same idea of tapering the input data near the ends to reduce the splice that causes spectral leakage.
	www.daqarta.com /EEX05.HTM (1128 words)

	Aliasing and Leakage
		Another way of viewing the leakage is this: if we truncate a function then make it periodic, the resulting function is going to have additional frequency components in it that were not in the original function, due to the change from end to end.
		The only way this does not happen is if the the signal is periodic with respect to the number of samples already.
		Leakage can be reduced either by taking more samples (wider windows of data), i.e.
	www.engineering.usu.edu /classes/ece/3640/lecture9/node2.html (219 words)

	Zipper VDSL: A Solution for Robust Duplex Communication over Telephone Lines
		Zipper is characterized by high flexibility and high spectral compatibility with programmable spectrum usage, robustness against frequency-selective impairments such as radio frequency interference and bridge taps, interoperability with ADSL, and high spectral efficiency since no guard bands are needed.
		Spectrally compatible systems are those that can operate within the same cable binder without affecting each other's performance, for instance, by introducing NEXT.
		These discontinuities are the sources of spectral leakage between subcarriers in the FFT operation of the receiver.
	www.comsoc.org /ci/private/2000/may/Odling.html (4846 words)

	Fourier Preprocessing
		This effect is called spectral leakage and is typically observed as stripes along the x and y axes with a magnitude that decreases as a sin(x)/x function.
		To lower this spectral leakage effect Data Windows that lower the magnitude of the border data can be applied.
		It is also worth noting that a proper plane correction of the images can reduce the spectral leakage phenomenon dramatically.
	www.imagemet.com /WebHelp/idd_imfourier_dlg_preprocessing.htm (486 words)

	NZSA 2004 - Submitted Talks (Site not responding. Last check: 2007-10-25)
		Spatial spectral analysis is used to identify spatial structure in temperature measurements from a nuclear reactor core.
		The multi-taper spectrum estimation method of Thomson (1990) is adapted for spatial processes, to optimally minimise the bias due to spectral leakage and to improve the variance properties of the spectrum estimate.
		The results are used to construct a random effects model to predict the reactor temperatures and to improve the performance of a reactor physics model under development by the UK nuclear industry.
	www.mcs.vuw.ac.nz /events/NZSA2004/submitted/Carl-Scarrott.shtml (142 words)

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