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The peak is "well-sampled", so that less than 10% of the area or volume under the peak (area if a 1D Gaussian, volume if a 2D Gaussian) lies outside the measurement region. The width of the peak is much larger than the distance between sample locations (i.e. the detector pixels must be at least 5 times smaller than the Gaussian FWHM).
As the peaks at (x,y) in the 2D synchronous spectrum are a measure for the correlation between the intensity changes at x and y in the original data, these main diagonal peaks are also called autopeaks and the main diagonal signal is referred to as autocorrelation signal. The off-diagonal cross-peaks can be either positive or negative. On the ...
Some people use "spectral centroid" to refer to the median of the spectrum. This is a different statistic, the difference being essentially the same as the difference between the unweighted median and mean statistics.
To find the value of the energy spectral density ¯ at frequency , one could insert between the transmission line and the resistor a bandpass filter which passes only a narrow range of frequencies (, say) near the frequency of interest and then measure the total energy () dissipated across the resistor.
The Fourier transform of a function of time, s(t), is a complex-valued function of frequency, S(f), often referred to as a frequency spectrum.Any linear time-invariant operation on s(t) produces a new spectrum of the form H(f)•S(f), which changes the relative magnitudes and/or angles of the non-zero values of S(f).
This is also true of the third derivative; odd derivatives can be used to locate the position of a peak maximum. [22] The second derivatives, , of both Gaussian and Lorentzian functions have a reduced half-width. This can be used to apparently improve spectral resolution. The diagram shows the second derivative of the black curve in the diagram ...
Maximum entropy spectral estimation is a method of spectral density estimation.The goal is to improve the spectral quality based on the principle of maximum entropy.The method is based on choosing the spectrum which corresponds to the most random or the most unpredictable time series whose autocorrelation function agrees with the known values.
A series of mixed vertical oscillators A plot of the peak acceleration for the mixed vertical oscillators. A response spectrum is a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock.