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Questions tagged [power-spectral-density]

The Power Spectral Density (PSD) is the distribution of signal power over frequencies.

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Physical meaning of cross spectral matrix in a microphone array

Currently I am processing data from a 64 microphone array to identify noise source locations on an airfoil. I am using the simple sum and delay beamforming algorithm. I get good results, however in ...
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Example of non-equivalence of the two PSD definitions

According to the book Introduction to Spectral Analysis by P. Stoica and R. Moses, the power spectral density (PSD) $P(\omega)$ can either be defined as the discrete-time Fourier transform (DTFT) of ...
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retrieving complete 2d autocorrelation function from 2d power spectral density function (numpy.fft.ifft2)

My question is at the boundary between signal processing and python. I have a 2d power spectral density function (PSDF) constructed on Nx/2 + 1 and ...
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25 views

What is wrong with my PSD computation?

I'm trying to calibrate the RX of my SDR Board to become a measuring receiver. I.e, by connecting it to a known source of power (in my case, a frequency generator), at a fixed frequency, I'm trying to ...
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PSD Periodogram smaller segments compared to larger segment

I am calculating the power spectrum of a heart rate variability via FFT and a Welch window. I have a sample of 500 points as the input signal. The signal was broken up into two 128 point segments. ...
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9 views

Correct way to calibrate RX into a measuring receiver

While playing with my SDR (Software Defined Radio) Board, I was interested in performing a TX output power table at different center frequencies and TX antenna gains. I have an RF frequency generator....
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23 views

Power Spectral Density of discrete White Gaussian Noise defined with variance and sampling interval

From Creighton and Anderson Chapter 7 on Gravitational Wave data analysis: Please explain where the delta t and the limit came from in this derivation.
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Random sampling Bartlett spectrum estimation vs Welch

I'm trying to estimate the spectrum of a noisy time series and considering two approaches and their relative correctness. Let's say the time series is 800s long. Option 1 is to do a Welch spectrum ...
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55 views

How to calculate the PSD from the complex calculated STFT?

I have calculated the STFT with scipy python library: ...
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62 views

Spectrum estimation

When calculating the spectrum estimation of a signal $x(t)$ with random noise, why do we use ($E$ for expectation) $$E[|X(\omega)|^2]$$ but not $$E[|X(\omega)|] $$ If it is because the random ...
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How does discrete spectral moment relate to continuous spectral moment?

It is said in discrete/digital signal processing that $r$th spectral moment of signal $x[n]$ is defined as: $$\sum_{n=-\infty}^{\infty}n^r x[n]$$ But how does this relate to usual continuous $r$th ...
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Can spectral density be a complex quantity?

I have a signal ($S(t)$) which is product of a Gaussian ($G(t)$) and a random phase function ($e^{i\theta(t)}$, here $\theta(t)$ is a random function), as shown below $S(t)=G(t).e^{i\theta(t)}$ If I ...
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About the power spectrum and confidence upper limit of a time-series data

For now, I have a coupled system with 5 variables and use the Runge-Kutta method to integrate. ...
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33 views

Number of discrete samples required for the longest wavelength

I am trying to understand the effect of the critical Nyquist frequency when applying the Goertzel algorithm for estimating the power spectrum of a discrete signal. (Goertzel doesn't really matter, ...
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3answers
60 views

Band-limited random signal with arbitrary distribution?

I'd like to generate a random discrete-time signal that is band-limited to some bandwidth B (by means of a digital filter, ie in MATLAB). The catch is that I'd like this signal to have an arbitrary ...
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28 views

What's the maximum energy for a finite signal?

I'm trying to calculate the spectral density of a signal. What I'm expecting is a scale in dbFS where 0 dbFS would be the maximal theorical energy if all my signal is concentrated in a single ...
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PSD of randomly positioned dirac delta train

Let $s(t)= \sum_{i=0}^{T} \delta(t-\tau_i)$, where $ \{ \tau_{i} \}$ are random integers between $0,1,\cdots, T-1$. What is the power spectral density of the signal $s(t)$?
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How to window a time domain signal for 6 symbols with cyclic prefix length of 512 samples?

Based on LTE stds. I am running a simulation for 6 symbols (each having 1200 central subcarriers) each in a 2048 FFT/IFFT bin. To these symbols are appended 512 samples as cyclic prefixes. I have to ...
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Same PSD from different FFTs

Is it possible to obtain same PSD from different FFTs? Can anyone explain it mathematically?
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Proof that the Lomb-Scargle periodogram reduces to the classical periodogram when the sample is equally spaced

If we have a equally spaced sample, we can use the conventionally used periodogram: $$P_x(\omega) = \frac{1}{N_0}\left[\left(\sum_j X_j\cos \omega t_j\right)^2+\left(\sum_j X_j\sin \omega t_j\right)^...
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Converting a non-stationary random process into a WSS process by adding a random phase

Here is an example where this method has been implemented. We were trying to calculate the spectrum of a transmitted signal(Random signal/weighted pulse) The auto correlation function of the pulse ...
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1answer
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When does a color channel such as RGB carry more info than a grayscale channel or image?

Typically a gray-scale image gives us more information about an image in terms of a signal processing problem. But when does a color channel carry more info than a gray-scale channel? I understand ...
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finding energy content of signal from “energy spectral density” function

from "Signals and Systems Demystified", 2006, page 142, Example 6-3: (http://www.gatestudymaterial.com/study-material/signals%20and%20systems/text%20books/SIGNALS%20AND%20SYSTEMS%20BY%20DAVID%...
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31 views

How to make a Power Spectral Density Plot in R

I have a time series point process representing neuron spikes. I have computed and plotted autocovariance using acf but now I need to plot the Power Spectral ...
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33 views

Why is the sound field intensity due to $K$ point sources given by $ I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)$?

I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below. Statement: 1. We ...
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217 views

Power Spectral Density From Variance

For an exercise, we made a noise signal by generating a normally-distributed random vector in MATLAB. The mean is defined to be equal to zero and the variance is set to 0.5. I know that the power ...
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70 views

Spectrogram Interpretation

I collected vibration data (amplitude and time) on a component that was attached to an engine. Using MATLAB I plotted a spectrogram to see what frequencies it vibrated at. The code: ...
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51 views

Modified Periodogram function in MATLAB

Given below is a function written in MATLAB for computing the modified periodogram, taken from Hayes, Statistical Digital Signal Processing and Modeling ...
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50 views

Physical significance of Power spectral density of sum of correlated random processes

For two processes $X(t)$ and $Y(t)$, PSD of $Z(t) = X(t) + Y(t)$ is $S_Z(\omega) =S_x(\omega)+ S_Y(\omega) + S_{XY}(\omega)+S_{YX}(\omega) $. If $X(t)$ and $Y(t)$ are orthogonal, PSD of the sum ...
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60 views

Question based on scaling the FFT for obtaining PSD

Following is the code given in MATLAB's site to estimate PSD using FFT. ...
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49 views

Why do we need the power spectral density?

Since the power spectral density is just the squared of the fourier transform, why is it useful ? Can't I just replace every solution that requires the psd with the fourier transform ?
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Difference between power spectrum of NR signal as seen in Vector Signal Analyser and MATLAB pwelch method

My setup is as follows: I have an R&S SMW signal generator which generates a 100 MHz 5G New Radio signal. The signal is passed through a channel emulator which has components like Digital-To-...
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1answer
23 views

Cross power spectral matrix from PSDs and coherence using matrix notation

I have a vector containing all the PSD of a series of signals $\underline{s} = \left[ |S_{x_1x_1}| |S_{x_2x_2}| |S_{x_3x_3}| ...\right]^T$ I also have a matrix $\gamma^2$ containing all the ...
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118 views

What is an “innovation filter”?

I'm a math postgrad student working through a paper on eigenvalue decompositions of matrices of FIR filters (used for stuff like total decorrelation, convolutive mixing, MIMO). Towards the beginning, ...
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38 views

Efficient audio power spectrum estimation

I am working on a small personal project where I want to control a matrix of roughly 100 actuators with an audio stream. The goal would be that the user can see/feel the music features in the movement ...
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1answer
143 views

Confusion about PSD and RMS

Let's say I have a noise power-spectral-density (PSD) which is not flat and ranges from 0 to $f_1$ Hz in frequency. As we know, the total area under the PSD is equal to the total average power of the ...
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73 views

Wiener Filter in Frequency Domain: What it does to a specific Frequency?

As I understand Wiener filter in time domain tries to estimate a signal as close as possible to its (original) non-degraded signal using the degraded signal by white noise. $$H(\omega)=\frac{\Phi_{...
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85 views

Do energy of signal and power spectrum (in db/hz) indicate towards same signal property?

If I calculate energy of signal by squaring the magnitude of signal sample and power spectrum using spectrogram (db/hz) what kind of property of signal do they indicate and are they point towards same ...
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2answers
187 views

Properties of Up- and Downsampling

Given a gaussian white noise with mean 0 and $\sigma = 1$. I'm interested in the PSD (power spectral density), when the signal is plain up- or downsampled. No interpolation, no filtering nothing. ...
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1answer
59 views

Application of Parsevals theorem with Welch method

For my project I had to manually code the welch method using the code below. Pretty much it involves finding the spectral density through fft and incorporating windowing and segmenting with overlap. ...
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72 views

While finding the ESD/PSD of a signal why we always prefer to find it via Auto-correlation function then the square of the FT of the signal? [closed]

In a video i saw that while calculating ESD or PSD of a signal time auto correlation function was used when it can be also done by the square of FT of the signal.Why we followed that approach even ...
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1answer
235 views

Computing the Power Spectrum Density (PSD) on a CSV File in Python

im quit new with signal processing and im trying to calculate the PSD of a signal im sampling. the signal is an output of a DC buck converter this is the code im using and this is the plot im getting ...
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27 views

Remove artefact in signal, and then look at the PSD?

To note, I am using Matlab R2017a for my signal processing. I have filtered my EEG signal according to the frequencies I am interested in using butterworth (2Hz-30Hz). But there are some large ...
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72 views

Noise PSD and sampling rate relation

Let's consider generating samples of a random process like white Gaussian noise (AWGN). Let's assume I am generating $N$ samples of AWGN with variance $\sigma ^2$ in MATLAB by using randn() funtion i....
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22 views

How to extract desired frequencies from a spectrum using e.g. a Parzen window?

Disclaimer: I am a geophysicist working with time-domain data which needs to be converted to the frequency domain evaluated at a specific set of logarithmically-spaced frequencies. The textbooks I am ...
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1answer
66 views

Small shift in frequency in FFT

I'm trying to compare the estimation of the power spectral density (in this case of a fake cosine signal) by two different methods: 1st, MATLAB's fft function, and 2nd, a direct calculation from the ...
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1answer
557 views

How to calculate the power of a discrete signal? / Clarification on PSD estimates

I want to calculate the channel power $ P_\mathrm{x}$ of a given discrete and complex signal $x[n]$ (with a length of N) in a given bandwidth $B$. I'm aware, that I could probably apply a sharp ...
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1answer
68 views

Phase and Amplitude estimation

Context: I have used FFT many times, but for real, non-periodic signals I consider it a poor estimator. For most of my applications I am only interested on the power spectrum, so I use the Welch's ...
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29 views

find power of recieved signal of usrp b200 in gnu radio companion

how to find power of recieved signal of usrp b200 in gnu radio companion from frequency sink block (the frequency plot) or any other block available in gnu radio. I am transmitting and receiving ofdm ...
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33 views

power spectral density window function gaussian

I'm using psd in python using mlab library ...