Spectrum, Auto Spectrum, Power Spectral Density, Cross Spectrum
Spectrum
시간 영역의 함수를 Fourier Transform을 하면 주파수 스펙트럼(spectrum)이 생성되며, 이것은 각 주파수의 진폭과 위상의 복합으로 나타난다.
Plots the magnitude of a periodic frequency component at a discrete frequency. It is computed as the square root of the average auto spectrum. For an accelerometer, for example, the units for Spectrum are represented as g. Typically, Spectrum is best for narrowband, deterministic signals.
Auto Spectrum (Power Spectrum)
주로 랜덤한 신호에 대해서 각 주파수 영역상의 에너지 분포를 보기 위해 사용하는 방법이다.
A single-channel display function that plots the power of a periodic frequency component at a
discrete frequency. For an accelerometer, for example, the units for Auto Spectrum are
represented as g2. Typically, Auto Spectrum is best for narrowband, deterministic signals.
The Power Spectrum is simply the magnitude of the total spectrum.
The Power Spectrum is commonly used in many applications where phase information is not needed. This is similar to the information provided by swept spectrum analyzers which do not provide phase information.
Spectrum vs Auto Spectrum (Power Spectrum)
When performing a Fourier Transform, there are several types of spectral functions that can be computed. Two of these functions, Autopower and Spectrum can yield very different results.
Both the Spectrum and Autopower functions produce results of amplitude versus frequency.
The main difference between the two functions is in the handling of phase:
-Spectrum function includes phase
-Autopower function eliminates the phase
The only difference is that the Spectrum has phase, while the Autopower does not contain phase information (phase is zero at all frequencies)
Power Spectral Density (PSD)
The power of random vibration intensity as “mean-square acceleration per frequency unit.”
The spectrum is computed by squaring the magnitude of each frequency component in the FFT, and dividing this number by the change in frequency multiplied by the equivalent noise bandwidth of the windowing function (ENBW). For an accelerometer, for example, the units for PSD are represented as g2/Hz. Typically, PSD is best for wideband, continuous signals.
Auto Spectrum vs Power Spectral Density (PSD)
Autospectrum and power spectral density is same
Power spectral density (PSD) plots the power of each frequency component on the y-axis and the frequency on the x-axis
Auto spectrum is tool to get power related to each frequency whereas the Power Spectrum Density is tool to get power related to certain range of frequency and being range equal to frequency resolution.
However, they both looks same but their application varies.
The auto spectrum can only use for the signal which have specific frequency or frequencies also the signal should be perfectly acquire in time domain that is without leakag, as Auto Spectrum provides power related to each frequency On other hand, the Auto Spectrum failed to give same for continuously changing signal (Ex. reading of wind-force or White Noise ) if you get Auto spectrum of such signal it’s output is related to range of frequency. Thus, PSD is normalized with frequency to obtain results independent of frequency range.
PSD= (Auto-Spectrum)/(delta F)
Auto Spectrum – Discrete Signal
Power Spectrum Density - Continuously Changing Signal
Cross Spectrum
두 신호의 상호 스펙트럼이다. 주파수 영역에서 서로 공통적으로 같은 대역에 나타나는 성분을 계산한다. 두 신호 중 하나를 입력으로 취하고 나머지를 출력으로 취하여 입력으로부터 전달된 동일한 신호 성분이 출력에 전달되는 것을 확인할 수 있다.
Cross Spectrum Function
A two-channel display function of the frequency domain. It contains a building block that is used in FRF and other more advanced functions. It is the product of the complex Fourier spectrum of the response channel multiplied by the complex conjugate of the Fourier spectrum of the reference channel.
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