A&D RA3100 Omniace Instruction Manual page 131
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N
k
=
∑
1
N
−
W
) (
i
i
=
0
Amplitude
Logarithmic amplitude
Power Spectrum Density (One Signal Analysis)
Indicates the power spectrum by unit frequency ∆f.
R and I are the result of multiplying the window function peak compensation coefficient k.
N
k
=
∑
N
−
1
W
) (
i
0
i
=
Amplitude
Logarithmic amplitude
∆f = Fs/N; Fs: Sampling points; W (i): Window function
k1: Window function BW compensation coefficient
Rectangular
Hanning
Hamming
Cross Power Spectrum (Two Signal Analysis)
The cross power spectrum derives the power between two signals. It is derived as the product of the
linear spectrum Gx of the signal to compare and the complex conjugate Gx
of the base signal.
Linear spectrum of reference signal
Linear spectrum of comparison signal
Cross power spectrum
Cross power spectrum (real number part)
Cross power spectrum (imaginary number part)
Ryx and Iyx are the result of multiplying the window function peak compensation coefficient k.
N
k
=
∑
1
N
−
W
) (
i
i
=
0
Real number part
Imaginary number part
Amplitude
Logarithmic amplitude
Phase
1WMPD4004444
2
: Sampling points; W(i): Window function
Ｎ
Lin-Amp
Log-Amp
2
: Sampling points; W(i): Window function
Ｎ
Lin-Amp
Log-Amp
1
0.666
0.731
2
: Sampling points; W(i): Window function
Ｎ
Lin-Rel
Lin-Img
Lin-Amp
Log-Amp
Phase
R
+ I
2
2
10 × log(R
+ I
)
2
2
(R
+ I
)/∆���� × ����1
2
2
10 × log((R
+ I
)/∆���� × ����1)
2
2
Gx = Rx + jIx, Gx
Gy = Ry + jIy
Gyx = Gy x Gx
Ryx = (RyRx + IyIx) x k
Iyx = (RxIy – RyIx) x k
Ryx
Iyx
�(Ryx
+ Iyx
)
2
2
10 × log (������������
+ ���� ���� ����
)
2
2
tan
(Iyx/Ryx)
−1
131
10. 10Appendix - 10.4. FFT Analysis
*
of the linear spectrum Gy
*
= Rx – jIx
*
= (Ry + jIy)(Rx - jIx) = Ryx + jIyx
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