Psd Definition and 24 Threads

Hi, I was looking at the following example, and I cannot really understand the justification for why this function is positive semi-definite. Example Problem: We are looking at the function: ## f(x, y) = \frac{x^2}{y}, x \in \mathbb{R} , y > 0 ##. Is this function positive semi-definite...

I have a question related to linearity of power spectral density calculation. Suppose I have a time series, divided into some epochs. If I compute PSD by Welch's method with a time window equal to the length of an epoch and without any overlap, I obtain this result: If I calculate the...

(Just as clarification on what I am doing, I am attempting to use MATLAB to create PSD plots of time series from pressure and accelerometer sensors. Wave gauge sensors might still be helpful for me. I did not discuss accelerometer sensors in the post but maybe I could figure it out if I get the...

I am starting work on structural durability area for after treatment systems and deal with Random Vibration and PSD profiles quite often. However there are few fundamental questions about PSD profiles that I could not get answer to after a lot of search on internet. So finally decided to write...

I have a question regarding transient vibration data I received that was processed into a peak-hold equivalent amplitude (units = g). I have come across peak-hold before which is a type of "averaging" that retains the highest values from each estimate in random vibration overlap processing and...

Homework Statement Let K and L be symmetric PSD matrices of size N*N, with all entries in [0,1]. Let i be any number in 1...N and K’, L’ be two new symmetric PSD matrices, each with only row i and column i different from K and L. I would like to obtain an upper bound of the equation below...

In the analysis of Random vibration, we use the PSD curves as the input, I am confused as to why we simply don't use acceleration versus time graph but instead convert it into g^2/Hz and Hz.

Hi, I am working on a project and came across a conceptual roadblock. I am working with a PSD, let's say the units are V^2/Hz. I choose a dF based on how many sine tones I want in the time signal I am going to create. I sample the PSD curve at my frequency bin locations; so I have both my...

I would be grateful for some direction on this. I wish to implement the following - Given a deterministic signal (the feedback signal of a closed-loop stable system) I would like to plot the power spectral density. The definition I am working with is this: Implementation (MATLAB): %...

Hello everybody , I am student in mechanical enginnering. I have to evaluate the solution Fe-Safe. i am working on two subjects: Harmonic and PSD Vibrations. The modal analysis are done in Abaqus. I would like to understand how Fe-Safe computes Life Fatigue in case of harmonic analysis. What...

I know the power spectral density, PSD, of noise is: \frac{N_{0}}{2} from where do we get N_{0} ? Is that the RMS value of the noise? Is it related to noise power and noise temperature as in the following: N=kTB, where k = Boltzmann’s constant, T is noise temperature, and B is...

Homework Statement Ok So this is an example from my text. I am having trouble following a portion of it and was curious if anyone could shed some light on it. I've typed most of it and posted a screen shot of the second portion since there is a table involved. Determine the PSD of the...

Hi all, I have a vehicle multibody model and I want to excite it in different conditions. So I'm thinking to use the PSD or road roughness as reported in the ISO 8608. What I don't understand is, how can I get an equivalent time history of the vertical road displacement from the PSD? thanks

I am confused a bit :confused:. I read in a paper that the following property holds, but can't find where it comes from. \mathsf{E}\left[X(\omega)X^*(\omega')\right]=2\pi\delta(\omega-\omega')S_{XX}(\omega) it says that the expected value of the Fourier transformed signal is proportional...

This might not be in the right place but here it goes: Homework Statement A given periodic function in time is given u(t). I must compute the probability density function that describes u. u(t) = A sin (2π / T t + ψ) A and ψ are constants. T is the period. t is time. Homework EquationsThe...

First question: If A is pd, then A^-1 is pd. Outline of answer: If A is pd, then there exists a nonsingular matrix P st A=P'P Then A^-1 = (P'P)^-1 = (P^-1) * (P^-1)' = (P^-1)' * (P^-1) 3. If (P^-1)' * (P^-1), then there exists a A^-1 that is positive definite Second question: If...

I'm trying to plot the PSD of a signal, I did it using the fft function but I was wondering if there is another direct method?

Hi all, I have a suspension system that is mounted in a vehicle and I must evaluate its behaviour. So I have measured the acceleration at the suspended mass and at the base. Since I haven't a bench I was obbliged to test it during vehicle driving. All signal are sampled at 500Hz. In the next...

Is it possible to express a n-by-n positive semi-definite matrix (A) in terms of a sum of n terms of something, i.e. A = B1+B2+...+Bn, where each Bi has similar structure? Thanks!

Please help me to solve this question: Let A=\left[\begin{array}{ccccccc} |a_0|^2 &a_0\bar{a}_1 &a_0\bar{a}_2 &0 &a_0\bar{a}_3 &0&0\\ \bar{a}_0a_1 &|a_1|^2 & c &0 &a_1\bar{a}_3 &0&0\\ \bar{a}_0a_2 &\bar{c} &|a_2|^2...

Hi everyone, Let A=(a_{ij}) be a symmetric (i.e., over reals) PSD matrix. Then is the following correct? "If any principle minor ( \ne A ) be zero, then all principle minor contained in this minor should also be zero". I can not prove or disprove it..any help? By the way how...

I have the intrinsic noise PSD spec for Honeywell's QA3000 accels, and I need to find the velocity random walk due to noise to show that I'm within my allowable. The PSD is given in units of g^2/Hz vs Hz. I'm given a velocity random walk due to noise spec of 15 (micro-m/s)/rt(s) that I must be...

As stated in title: I have full knowledge of the 2 signals. They have the same Power Spectral Density. However, only certain components of the 2 signals have the same phase. Is there any way of extracting these components, or at least their PSD functions? Is this doable at all? The phase I...

Hi everyone, I know that for a hermitian matrix to be PSD it is necessary that every principal minor [i.e, the minors obtained by deleting all the last i rows and columns for all i=(n-1)(-1)0]. I want to know if it is necessary that all minors of order>=2 be non-negative. Particularly, for...