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How to generate time series data from given PSD of random vibration input?
Repeat 1->4 multiple times concatenate each time domain sequence with the preceding one to get real random signal with the required PSD 1. take the square root of the PSD. 2. Generate random numbers with a variance of 1 with the length of the PSD pins 3. Take the FFT of this random sequence. 6. repeat 2->5 and concatenate the newer sequences.
What is the definition of power spectral density?
First we should return to the PSD definition. power spectral density is a representation of statistical power distribution across frequency range of a specific signal. Not an actual one to one representation of the signal in frequency domain as in FFT.
How to generate a new random time series?
You can always generate a new random time series by generating a new set of random phases PHI (f (k)) = random number, uniformly distributed between 0 and 360 degrees (or equivalently, between 0 and 2Pi radians), and then applying the iFFT once again.
Is the PSD of the given time series the same?
The PSD of this time series will be the same as your given PSD. You should check your result, of course, by taking the FFT of the resulting random time series in order to confirm that it is giving the same PSD as you given PSD.
Do you need a random generator for raw time domain signal?
Having a real random generator for the raw time domain signal provides a white noise with a variance equal to 1 (distributed equally across the whole frequency range, you might need to scale for that later) with random phases between +/- pi. So we don’t need two random generators for the amplitude and phase.
How to calculate PSD from a time history file?
The steps to calculating PSD are as follows: 1. Divide the time history file into frames of equal time length First, the time history file should be divided into frames of equal time length. The lines of resolution and sample rate determine the width of each frame. There are two samples per analysis line.
How do I enforce the time domain to be signal?
To enforce the time domain to be signal we need to have a DSB PSD signal and forcing a symmetry between the USB and the LSB before multiplying its square root by the fft of the white noise. Hello. In addition to the well thought out answers already given, I would add a couple of points.