Search results
Results from the WOW.Com Content Network
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.
Whereas the technique of the Fourier transform can be extended to obtain the frequency spectrum of any slowly growing locally integrable signal, this approach requires a complete description of the signal's behavior over all time. Indeed, one can think of points in the (spectral) frequency domain as smearing together information from across the ...
The coherence (sometimes called magnitude-squared coherence) between two signals x(t) and y(t) is a real-valued function that is defined as: [1] [2] = | | ()where G xy (f) is the Cross-spectral density between x and y, and G xx (f) and G yy (f) the auto spectral density of x and y respectively.
Welch's method is an improvement on the standard periodogram spectrum estimating method and on Bartlett's method, in that it reduces noise in the estimated power spectra in exchange for reducing the frequency resolution. Due to the noise caused by imperfect and finite data, the noise reduction from Welch's method is often desired.
The multitaper method overcomes some of the limitations of non-parametric Fourier analysis. When applying the Fourier transform to extract spectral information from a signal, we assume that each Fourier coefficient is a reliable representation of the amplitude and relative phase of the corresponding component frequency. This assumption, however ...
In many applications, phase information is not important. By discarding the phase information, it is possible to simplify the information in a frequency-domain representation to generate a frequency spectrum or spectral density. A spectrum analyzer is a device that displays the spectrum, while the time-domain signal can be seen on an oscilloscope.
A number of authors, notably Jean le Rond d'Alembert, and Carl Friedrich Gauss used trigonometric series to study the heat equation, [20] but the breakthrough development was the 1807 paper Mémoire sur la propagation de la chaleur dans les corps solides by Joseph Fourier, whose crucial insight was to model all functions by trigonometric series ...
A signal, as a function of time, may be considered as a representation with perfect time resolution.In contrast, the magnitude of the Fourier transform (FT) of the signal may be considered as a representation with perfect spectral resolution but with no time information because the magnitude of the FT conveys frequency content but it fails to convey when, in time, different events occur in the ...