Hi
Power Spectral Density (PSD) is Amplitude2/Hz.
PSD is the correct way to characterize stochastic processes as your values otherwise change with spectral resolution. [On the other hand, the PSD provides the wrong amplitude for ordered processes, i.e. tonal spectral components .] .
If you wish to look at amplitude at a specific frequency, you take the square root (SQRT) of the PSD and present a spectrum with the scaling Amplitude/SQRT(Hz).
If you want the RMS value, this is computed as RMS = SQRT(SUM(PSD*DF)) and, where DF is the spectral resolution, where you integarate from Fmin to Fmax, i.e. your lowest and highest analysis frequency of interest, respectively.
Sincerely
Claes
Hi
Power Spectral Density (PSD) is Amplitude2/Hz.
PSD is the correct way to characterize stochastic processes as your values otherwise change with spectral resolution. [On the other hand, the PSD provides the wrong amplitude for ordered processes, i.e. tonal spectral components .] .
If you wish to look at amplitude at a specific frequency, you take the square root (SQRT) of the PSD and present a spectrum with the scaling Amplitude/SQRT(Hz).
If you want the RMS value, this is computed as RMS = SQRT(SUM(PSD*DF)) and, where DF is the spectral resolution, where you integarate from Fmin to Fmax, i.e. your lowest and highest analysis frequency of interest, respectively.
Sincerely
Claes
Hi
Power spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function and then transforming it.
I advice you to see the document. You will find what you need.
Best regards
http://www.cygres.com/OcnPageE/Glosry/SpecE.html
Hi
Power Spectral Density (PSD) is a measure of a signal's power intensity in the frequency domain.In practice, the PSD is computed from the FFT spectrum of a signal. The PSD provides a useful way to characterize the amplitude versus frequency content of a random signal. In the Random Control System, PSDs are used to represent the control and input channel signals.
Random vibration is experienced everyday in the real world. The motions experienced, on the back of a truck, the hold of an airplane or ship, the bed of a flatcar during travel are all random vibration. It is motion at many frequencies at the same time. The amplitude at these frequencies varies randomly with time. The usual way to describe random motion is in terms of its Power Spectral Density. The plot below shows random vibration in the time domain and in the frequency domain in the form of a PSD.
Best regards
Hi
If you want to attach physical meaning to your analysis, then go with the power spectral density, (PSD). This is because this will simply give you the power of your signal, in each frequency band. On the other hand if you do not want/care about a physical meaning, but want to know how the fourier amplitudes of each band vary relative to each other, you can stick to absolute magnitude.
In practice, you can compute the PSD as simply the absolute magnitude of the fourier transform squared. For example, if your signal is x[n], and its DFT is X(f), then the absolute magnitude of the DFT is |X(f)|, while the PSD is |X(f)|2.
I hope that I helped you, let us know if you have another questions or you need more details.
Best regards
Regarding to this question, I'm trying out to calculate RMS value of a certain frequency bandwith FROM FFT. I solved how to calculate RMS from FFT of all spectrum using Parseval's Theorem as follows: (I got an array of data named "data")
N= lenght(data);
NFFT = 2^(nextpow2(N);
dt = 1 / fs;
df = fs / NFFT;
ScalingFactor = fs;
Parseval = sum( abs(fft(data, NFFT)/ScalingFactor).^2 )*df
RMS_Total = sqrt(Parseval);
Theorem is holded wit hrms calculation from time domain
OK. I got an spectrum with 3 bins (3 KHz, 10 KHz AND 21 kHz) so I suppose the sum of each RMS bandwidth is the total RMS previously calculated. Now, What if had I to calculate the RMS between e.g. 9.8 KHz and 10.2 KHz?
Firstly I have to calculate my data indexes corresponding to 9800 and 10200 frequencies:
k = nFFT / fs;
f0Index = k * F0;
f1Index = k * F1;
Now I could follow 2 ways:
A) Applying Parseval's theorem again between these 2 limits (Wrong results):
Parseval_partial = sum( abs(fft(data, NFFT)/ScalingFactor).^2 )*df(f0Index:f1Index);
RMS_Partial = RMS_Total = sqrt(Parseval);
B) Filling in the array with zeros out of these limits to focus on the bandwith desired. But it also doesn't work. How could I calculated this problem? Why Parseval's theorem seems not to be holded in a certain bandwith?
Thank you
Hello I would like to know if my way of expressing RMS doppler spectral density is good or not
Dear. Claes Richard Fredö
Long time no see. How are you?
I have some problem relative with RMS value. Could you explain to me?
I have been reading a book on noise and vibration analysis. But, in this book, author wrote:
scaled DFT of windowed signal to RMS value, Xw(k) = Aw/(N*sqrt(2)*sum(x(n)w(n)e^-j2pikn/N)
where, Aw is the amplitude correction factor of the window, w(n)
x(n) is sampled signal,
and sqrt(2) scales to RMS value.
So, i don't understand, "sqrt(2) scales to RMS value". what does this mean?
Thank you.
I want to calculate the amplitude of specific frequency from psd. I took the resolution and multyply by the psd value and then take the sqrt. Now my unit conversion is ok. am i correct?
This article:
http://www.schmid-werren.ch/hanspeter/publications/2012fftnoise.pdf
explains how to use MATLAB's pwelch function and the normalized PSD to actual signal amplitudes and/or to the RMS amplitude. These methods are explained clearly with MATLAB examples for various window functions. I hope this helps.
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