INVPSD
IThe INVPSD (Inverse Power Spectral Density) function regenerates a time signal from a power spectral density description.
Format
INVPSD (x, id, fo, fi, nf, linlog, seed)
Arguments
x | The independent variable. |
id | The id number of the spline containing the PSD versus frequency data. |
f0 | A real variable that specifies the lowest frequency to be regenerated. |
f1 | A real variable that specifies the highest frequency to be regenerated. |
nf | An integer that specifies the number of frequencies. This number is supposed to be larger than 1 and less than 200. |
linlog | An integer variable that acts as a flag indicating whether the PSD data points are interpolated in the linear or logarithmic domain. The legal values are: ■yes (0) - linear domain ■no (1) - logarithmic domain |
seed | A real variable that specifies a seed for a random number generator, used to calculate the phase shifts. The seed is a real number that will be rounded to the nearest whole integer using the NINT FORTRAN function. During a simulation, INVPSD can be called with up to a maximum of 20 different integer seeds. |
Extended Definition
Mathematically, INVPSD is calculated as follows:
The regenerated signal consists of a series of sinusoidal functions where the amplitudes, Ai, are determined in such a way that the effective value for the PSD and the time signal are the same. The phase angle, 
, is calculated by a pseudo-random number generator.
, is calculated by a pseudo-random number generator.Using the same seed value will always result in the same set of phase angles.
Examples
For the power spectral density data shown in Figure 5, INVPSD(TIME, spline_1, 1, 10, 20, 0, 0) regenerates the time signal shown in Figure 6.
Figure 5 PSD vs. Frequency in Log-Log Scale
Figure 6 Regenerated Time Signal
See other General available.