Questions tagged [power-spectral-density]

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

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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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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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50 views

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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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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23 views

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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1answer
30 views

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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1answer
179 views

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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47 views

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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23 views

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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22 views

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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45 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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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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1answer
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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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1answer
39 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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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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How to find the solution of nonlinear least square (NLS) equation for freqeuncy estimation

I am struggling to understand the theory of parametric methods for power spectral estimations of line spectra. And I want to find the solution of nonlinear least square (NLS) method for estimating ...
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Formula for PSD across an axis of a 2D output

Consider a 2D stationary input $e(x,y)$ and a 2D real convolution function $h(x,y)$. Let $S=h*e$ be the result of the convolution of $e$ by $h$. If needed, we may assume $e$ is isotropic (spectrum ...
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PSD graph of GPS L1 Signal on MATLAB

I'm trying to analyze GPS L1 C/A signal on MATLAB. I could generate the PRN codes(binary signals). After I add NAV Data to the PRN code using modulo 2, I need to modulate it using BPSK. I also could ...
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14 views

Normalize a Mel-Spec over which axis?

I have to find out: how to normalize a Mel-spectrogram.(for mashine-learning purpose) However, I don't know which axis has to be transformed. The spectrogram S is of shape (m x n) where n are the ...
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1answer
32 views

Analytically determine a PSD from a transient function

This question is related to a series of questions I have asked about the units of PSD and ESDs. I include it as a separate question as it may have worth in isolation. As I understand it to compute ...
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The Fourier transform of a damped cosine and the units of the result

If I take a simple transient voltage signal of the form $$f(t) = V_p e^{-t/\tau} \cos(\omega_0 t)$$ and take the Fourier transform in the normal way $$F(\omega) = \frac{V_p}{\sqrt{2 \pi}} \int^{+\...
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Power spectral density of surface roughness

I am currently working on understanding how visually and intuitively the power spectral density is the fourier transform of the autocorrelation of a signal. I was wondering if anyone had a good ...
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1answer
38 views

Peak to Average Power Ratio of an exponentially increasing signal

I am having an exponentially increasing sinusoidal signal. After sampling, I am dividing the signal into frames of length 128 and doing windowing operation with a hanning window of length 128. Then ...
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How to applying window function to get same result with pwelch in MATLAB

I'm trying to calculate the power spectral density (PSD) to analyze signal power. To do so, I wrote a MATLAB code with the great help of others and below is my code. ...
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Integral over power spectral density

The wikipedia entry on PSD has one confusing line: Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process) But ...
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1answer
179 views

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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how to calculate power spectrum of Gaussian noise from the known variance of it?

can someone explain me the following paragraph, i tried to understand it but i am not getting it exactly, Thank you ! Since you know the variance, you can predict the energy of the noise image, ∑x∑y|...
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69 views

How to implement Matlab welch in python with the same result?

I want to implement Matlab pwelch function in python. The Matlab code is shown blew: [PSD,f] = pwelch(data,length(data),[],[],2000); which data is a row vector ...
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1answer
58 views

Plotting curved peaks on PSD graph

I am a PhD student with little engineering experience, currently attempting to recreate the signal processing techniques used in this paper: Monitoring Vital Signs and Postures During Sleep Using WiFi ...
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why a limit on passband in spectral masks?

I was wondering why there is a usually flat limit on passband of every spectral masks. For sidebands it makes sense but for passband not so much.
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Definitions of PSD, ESD and Autocorrelation

This question is going to encompass multiple areas and may not have a single answer but here it goes. I'm trying to conceptualize 3 different concepts and how they relate to each other. These 3 ...
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1answer
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Difference of doing a PSD estimate of data and logarithmic transformed data?

What is the difference between doing a PSD estimate with data and the same data but which is logarithmically transformed before the estimate? Does it make the data more sinusoidal in nature? An ...
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Relating Fourier and power-law descriptions of noise

I'm trying to understand this PDF, which is in English but has Polish authors, so there may be translation issues confusing me. The subject is the frequencies of sentence lengths in novels. Eq. (1), ...
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Spectral density functions in NMR

A spectral density function (three of them depicted below) is 'power' vs frequency. These functions apparently inform us on the dynamics of spins in a protein somehow but I'm having the hardest time ...
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Fluctuations of spectral density estimates

I have seen in a few papers things like : or Without ever seeing the assumptions which are made, and of course no justifications. Does somebody know why it is a valid approximation to make ?
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Test of statistical significance of power-spectrum against red-noise

I have a process which is most probably red-noise and my goal is to know if the peaks or pits are "real" or just due to random fluctuations. I would like to know if there is exists a test of ...
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132 views

Prefactors computing PSD of a signal with numpy.fft VS. scipy.signal.welch

The power spectral density St of a signal u may be computed as the product of the FFT of the signal, ...
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power systems database

I'm having a hard time searching for a power systems database. I need some samples of a real wave form from a power source, like a residential power plug or an industrial one.
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Is there a version of Welch's method that doesn't look for power?

Welch's method splits a time signal, $x(n)$ into $M$ periodograms $P_m$, $P_{x_m,M }(k) = \frac{1}{M}|F_k(x_m)|^2$ and averages them to give the Power Spectral Density (PSD), $S_{x}(k) = \frac{1}{K}...
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Power Spectral Density of Finite Signals

I have a basic confusion which I hope someone can help clear. Say I have two signals: $S_1=\sin(2\pi t) \forall t\in[0,+\infty]$ $S_2=\sin(2\pi t) \forall t\in[2,5]$, $S_2=0$ otherwise Now let's ...
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179 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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Clip wav by PSD

I have the following two things. sequence_1: Sound file in the wave format. PSD_1: Some PSD (Power Spectral Density). I want that the PSD(sequence_1) < PSD_1 for all indices. How I think about ...
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1answer
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Calculate Frequency/Period from Output of a Maximum Entropy Spectrum MATLAB function

When I plot said function output, "p," it looks like a typical spectrum with an easily identifiable peak at a given ix on the x axis. The help rubric from the function is ...
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1answer
28 views

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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STFT on time varying signal with good time and frequency resolution

I am trying to determine the main frequency of a noisy signal that varies in frequency over time. Ideally I want to detect changes in the frequency as rapidly as possible - say 50Hz update rate, but I ...
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Estimate peak bandwidth from adjacent STFT bins for notch filter

I am using STFT to extract a strong, frequency varying signal from a continuous set of digital samples. I am able to do this very successfully and am determining the peak bin using PSD and 50% overlap ...
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1answer
268 views

PSD from autocorrelation in MATLAB

I am trying to simulate a simple stochastic process defined by the equation: \begin{equation} \frac{1}{v}\frac{db}{dt} +\Gamma_0 b= \sqrt{\sigma}R(t), \end{equation} where $R(t)$ is a zero-mean white ...
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Computing differences between dynamic power spectrums to identify transient features

I have a few minutes of magnetic field data with a lot of noise and unwanted frequencies, and I'd like to be able to identify any transient waves that may appear in my data. To do this, I'm dividing ...

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