Fourier and Power Spectra

In this module, the Fourier Amplitude Spectrum and the Power Spectrum (or Power Spectral Density Function) are computed by means of Fast Fourier Transformation (FFT) of the input time-history. The Fourier amplitude spectrum shows how the amplitude of the ground motion is distributed with respect to frequency (or period), effectively meaning that the frequency content of the given accelerogram can be fully determined. The power spectral density function, on the other hand, may be used to estimate the statistical properties of the input ground motion and to compute stochastic response using random vibration techniques [e.g. Clough & Penzien, 1994; Vanmarcke, 1976; Yang, 1986].

In SeismoSignal:

• Fourier Amplitude is computed as the square root of the sum of the squares of the real and imaginary parts of the Fourier transform: SQRT (Re^2+Im^2)
• Fourier Phase (given only in table format) is computed as the angle given by the real and imaginary parts of the Fourier transform: ATAN (Re/Im)
• Power Spectral Amplitude is computed as FourierAmpl^2/(Pi*duration*RmsAcc^2), where duration is the time length of the record, RmsAcc is the acceleration RMS and Pi is 3.14159.

Note: Computation of Fourier and Power Spectra can be carried out only for records featuring not more that 2^15 data points (i.e. 32768 points).