Questions tagged [power-spectral-density]

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

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Power spectral density of a simple continuous cosine and checking the correct average power can be recovered, as it should according to Parseval

I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice, and would be very grateful if someone could check my ...
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Using the log power spectrum as features for a Classifier

I have a set of time series signals for which I have to develop a anomaly detection algorithm. I am considering using classifiers like SVM to do this. However I am confused about how to properly ...
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Proof that spectrum analyzer measures mathematical Power Spectral Density

It seems to me the power spectral density (PSD) is defined as follows. Consider a signal $X(t)$ The windowed version of this signal is Consider a signal $X(t)$. We defined a time-windowed version of $...
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Power Spectrum Density and Frequency

if i have some random signals (sampling rate = 10Hz, 0.1s per data) Using python library i transformed it to power spectral density power spectral density forms = f, psd (using mlab.psd) I'm really ...
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Power Spectrum and Power Spectral Density

From signal theory we know that a very useful representation of some power signals is that of its power spectral density, whose curve represents how the total power of the signal is distributed at all ...
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Power spectrum of uniform white noise

Given a white noise image $W_{i,j} \sim U[a,b]$ where each pixel is distributed uniformly in $[a,b]$, how would I go about computing its power spectral density? That is, I want to find $E[|\hat{W}_{i,...
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Converting PSD to Time Domain Signal

I am currently using MATLAB and I'm thinking if I can reconstruct PSD back to time domain signal using MATLAB's ifft. I found a link in solving this problem but it's in Phyton and when I tried it in ...
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Power spectral density: where does the difference from decibel and regular representation come from?

I am generating a simple DC signal with noise. As expected the fft shows that there is one peak at 0Hz and some noise. I am also trying to get the spectral power density representation of that signal, ...
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How to create a wide-sense stationary time series with a frequency of 40 Hz?

I want to create a time series in MATLAB which has a peak frequency of 40 Hz but is also a wide-sense stationary random process. I then want to use power spectral density estimation to recover the ...
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Relation between Gaussian and bi-Gaussian distribution

A Gaussian Doppler Spectrum can be seen as a bi-Gaussian Doppler spectrum in wich only one Gaussian function is present ( the second having a zero power gain) ? any help will be really appreciated
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HF ionospheric Channel Model Example in matlab : Watterson model

In the example file in matlab HFIonosphericChannelModelExample.m, the watterson model is simulated. In this model the channel is represented as one tap (for the sake of simplification) delay channel. ...
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Can someone explain me what is the doppler spectrum?

I have a signal generated in matlab, with Rayleigh Fading, how can I add a given type of Doppler spectrum ( Gaussian for instance) to that signal ? Any help will be really appreciated
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MATLAB's $\tt cpsd$ and $\tt pwelch$ - different results for cross spectral power density

I am wondering why the following code does not yield the same results for Sxy1 and Sxy2, where ...
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How to simulate (in matlab or c) power spectrum of random brownian noise signal?

I have a semi random noise signal, it does have some periodicity however. I can estimate the power spectrum (of the blue signal, I thought that it would be more clear, because white noise is flat, ...
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Cross power spectral density (CPSD) comparison between signals

I want to compare various signals with Matlab's CPSD to identify shared frequency components. (If there's a better method, I would like to know!) I have 3 signals, A, B, and C. B is pure noise while ...
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SNR Signal to noise ratio of Pseudo random bit sequence (PRBS)

How should I estimate the Signal to noise ratio of a 20 Gbps NRZ PRBS pattern from power spectral density--where should I take the noise floor if I can assume well the noise is AWGN? I know roughly ...
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How do I find variance from the PSD of a stochastic process?

I have a time series that consists of noise and a signal, shown here windowed and Wiener filtered: and the PSD of just the noise (used in filtering): I want to find the variance of the noise using ...
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Why are the Fourier transforms of autocorrelation and cross-correlation different?

I'm almost definitely misunderstanding this, but as far as I can tell we can equate the Fourier transform of the auto-correlation function $R_{xx}(\tau)$ with power spectral density (PSD) like so: $\...
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867 views

PSD using MATLAB's $\tt pwelch$ algorithm window length and measure units

When using pwelch algorithm in MATLAB for a signal with $N$ samples, Is there a good rule of thumb for determining the length $L$ of the sections (second variable ...
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288 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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Why am I not getting a flat phase for a Gaussian pulse when doing a Fourier transform in Python?

I have been trying to obtain a spectrum and a spectral phase of a Gaussian pulse using the Fast Fourier Transform provided with numpy library in Python. Here are ...
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1answer
99 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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Power Spectral Density (PSD) from autocorrelation

I have a 1D fractional Brownian motion (fBm) signal, $u(x)$, of size $N$, generated through a random number generator with a gaussian mean, $\mu=0$, and standard deviation, $\sigma=\sqrt{N}$. I want ...
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25 views

Harmonics below oscillation frequency in the brain

Apologies if this question is trivial, I'm a neuroscientist and would hugely appreciate your help to correctly interpret my analysis. I am recording EEG signals and am manipulating the brain using ...
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Subtract background from 2D signal using spectral methods

I have a 2D signal, with intensity as a function of two angles (alpha and beta), as shown below. This contains a background, which makes the signal's base-surface locally convex-concave. I would like ...
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What are some of the disadvantages of parametric PSD estimation methods?

Roughly speaking, the methods of power-spectra estimation can be divided in two categories : parametric and non-parametric. From what I understood, parametric methods assumes that the signal can be ...
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Get autocorrelation function from the power-spectrum (python)

I am trying to compute the autocorrelation function of a signal for which I only know the power-spectrum. In order to test my approach I wanted to try it out on the spectrum of $1/f^2$ noise for ...
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205 views

Correct comparison of FFT noise with FFT signal

I have a sensor which I am using to track a strong but noisy varying signal. When the signal is present there is a lot of energy in the FFT bins, when there is no signal the is much less energy - but ...
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How to create a synthetic time series where power spectral density estimation is achieves better results than a direct Fourier transform?

I am trying to create a synthetic time series where PSD estimation is necessary and useful to recover the correct spectral information of the time series. But so far I can only create a time series ...
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Calculating the power spectral density on a different bandwidth

Let us say I have the power spectral density for a given bandwidth F1 at a transmit power T. I would like to calculate the power spectral density for bandwidth F2 for 1) the same transmit power T 2) ...
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Power spectral density vs. Fourier Transform

I am trying to understand the difference between the Power Spectral Density and the Fourier transform. Specifically, I am trying to understand why the power spectral density is useful and in what ...
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47 views

Autocorrelation to diagnose faults

I'm attending a very practical course on signals and i have some doubts, i hope to receive answers in layman terms. 1) My prof said i can use the autocorrelation of the output of a process to ...
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Removing DC Offset (via removing mean) of input and output signals affects their coherence

I have input $x$ and output $y$ signals (fs=10 Hz, length N=10800). I have removed DC offset via the following equation: $x_{normalized} = 100 \frac{(x-\bar x)} {\bar x }$ where $\bar x$ is the mean ...
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Can't seem to get welch function in scipy work correctly

I'm trying to learn DSP through using Python's scipy package. I have measure some 200Hz signal from a machine. Now I want to inspect the spectral density of the signal. Here's the signal plotted out: ...
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MATLAB & Power Spectral Density - Error - Getting the same range of values regardless of sound type?

I wrote code [attached at end of question] to take .wav files of child vocalizations and tried to see if there are valid ranges for the formants F1:F2:F3 for the 5 ...
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1answer
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SDR spectrum anomalies

Is it normal to see periodic peaks going from 48.75 - 90 MHz? Also i was checking on my SDR dongle once and the whole band was raised above background offset for like a whole 50 MHz bandwidth and then ...
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Calculating the Spectral Centroid of a Signal

Here is the equation: $$C_i=\frac{\displaystyle \sum_{k=1}^{W_{f_L}}kX_i(k)}{\displaystyle\sum_{k=1}^{W_{f_L}}X_i(k)} $$ The MATLAB code for the equation is: ...
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Scaling of the PWELCH function in MATLAB

I am trying to compute the power spectral density of a random signal using the PWELCH function in MATLAB. Since I think have not understood properly how Pwelch scales the PSD, I wrote a sample ...
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What is the unit for power spectrum of acceleration signals in log scale

I have a signal recorded by an accelerometer in m/s^2. It is basically accelerations over a period of time. I have calculated the power spectrum of the signal over in a certain frequency band and then ...
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1answer
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Proof that module of FT of 2 independent signals is sum of modules

I found on these posts (PSD subtraction and PSD of a sum of two stationary real signals) what I expected : that, just like the variance of the sum of 2 independent signals is the sum of the variances ...
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47 views

The expectation in power spectral density

I'm a bit confused with the definition of the power spectral density (PSD). From Wiki https://en.wikipedia.org/wiki/Spectral_density , I found the definition is: $$ S_{xx}(\omega) = \lim_{T\...
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835 views

Quantify the difference between two audio spectrograms

I have two speech signals of the same length. They contain the exact same speech content but are recorded from two different microphones. I want to compare the differences between them. 1) Assuming ...
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Normalizing white noise to match pink noise's amplitude at a given frequency?

I have a pinking filter which I am running white noise through to get pink noise. I would like to then mix the white noise with this pink noise, where the amplitude of the white noise will match the ...
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73 views

Normalizing vectors to be the same size to retain PSD data

Context: PSD=periodogram(y) in MATLAB gives the PSD (power spectral density) estimate of a sound-source signal. I want to find the local maximum within 3 different ...
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302 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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403 views

How to Estimate a Normalized PSD Using the Burg’s Method in MATLAB?

I'll try to be most sintetic as I can. I'm using an EEG system and I want perform an frequency analisys of the brain waves. I found this interesting article which describe how is possible to discern ...
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How Exactly Does MATLAB Zero Pad Signal?

I am doing some massive number crunching in MATLAB which involves millions of PSD estimations. Each data segment has length 41. So I have been using the multi-taper method with ...
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1answer
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Implementing Welch's method for Power Spectral Density

I want to implement Welch's method for PSD calculation in MATLAB. I do not want to use built in MATLAB cpsd function, such that I can change the FFT implementation ...
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Comparing Welch and FFT power spectrum density

Based on previous answers from the forum, I implemented a function to compute the Power Spectrum of a 1D time series. ...
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218 views

Frequency response of a microphone using a sine sweep

I want to determine the frequency response (magnitude, phase) of a microphone. I have another "good" reference microphone whose frequency response I know. I understand that I can use a good speaker ...

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