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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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Causal Part of an Expression

I try to find the causal part of $$H(z) = \frac{{\sigma_a}^2 z}{{\sigma_a}^2 + {\sigma_w}^2 (1-3z^{-1})(1-3z)}.$$ In order to find the causal part of a transfer function, the expression must be put in ...
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Spectrum in real life with Spectrum in theory

as you know it is possible to measure the power spectral density ($|X(f)|^2$) of a certain voltage signal $x(t)$ through a Spectrum Analyzer. As far as I'm concerned, the simplest spectrum analyzer ...
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Why are some Shannon's limit plots exponential rather than logarithmic?

This diagram again. This is clearly not the shape of $\log_2(1+SNR)$ but I very frequently see this instead of this: But this is also a stupid diagram because it doesn't cross at the origin. Also why ...
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Why do we need to 'estimate' the PSD

I've read about the PSD of one OFDM symbol for instance being an estimate of the PSD, but how can it be an 'estimate', when it literally is the PSD of that OFDM symbol. What is actually being ...
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Estimating Average HR from PPG sensor

I am reading Smartphone based Blood Pressure Monitoring via the Oscillometric Finger Pressing Method, which is trying to estimate blood pressure from a PPG sensor and a small applied force finger ...
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Coherence of a signal with itself to assess the PSD increase due to device turning on

I have a sensor that acquires data in the form of a time series, which I can model as a (mostly Gaussian) stationary stochastic process. I can study it in the frequency domain through its Power ...
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1answer
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Obtaining real numbers from FFT with same length as original signal

In this article the real valued time domain signal is transformed to the frequency domain to extract some features like mean or variance. But after transform to the frequency domain I calculate ...
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29 views

Calculating total power for the signal

In my previous question I asked about calculating a single number as "Spectral Density" feature from signal data. We concluded that it is really a total power and article (link) authors ...
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Power Spectral Density as a single number confusion

I'm trying to recreate the results of a machine learning applied to the DSP classification in the article: link. I have a signal (activity measurements from a smartwatch) per patient, so about 30 ...
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Trying to implement matlab pwelch function in python using scipy welch

I am trying to port the statistics toolbox function pwelch from matlab into python, but when I am trying to implement it using scipy.signals.welch, it does not return the same results as it does in ...
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Why is Power spectral density of random walk noise defined despite it being non-stationary? [duplicate]

While reading up on oscillator stability, I noticed that authors characterize random walk noise (Brownian noise) as having a PSD of $S_y(f) = h_{-2} f^{-2} $ where $h_{-2}$ is some constant. This is ...
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Allan Variance vs Autocorrelation - Advantages

I am currently studying oscillator stability and have come across the Allan variance. I gather that it was developed as an alternative to the standard variance as it doesn't necessarily converge for ...
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Relation between probability of a signal and its magnitude spectrum

I am a newbie. In these days I am searching if there are reference about properties that can relate the probability of the signal and the magnitude spectrum. I know what are both. But I was curious ...
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What are the kernels that are used in the Smooted Psuedo Wigner-Ville distribution?

Defined in Matlab's docs for WVD, SPWVD is given by: $\int_{-\infty}^\infty g(t) * H(f) x(t + \frac{\tau}{2}) x^*(t - \frac{\tau}{2}) e^{-j2\pi\tau\,f} \, d\tau$ H(f) and g(t) are the smoothing ...
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Given the Power Spectral Density of a random process determin if it is stationary in a wide sense

I am studying a Communication Systems course and have trouble figuring out how to tell and prove if a random process is stationary in a wide sense while only having it's power spectral density. some ...
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signal of $\frac{1}{f}$ Noise

I am working on kind of signals that can be classified as 1/f Noise. In this article is explained that the time history of 1/f noise follows a power law proportional to $t^{-\alpha}$. I am very ...
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Does a power spectral density that follow a power law imply that the time hisory follows a power law?

This is a question related to this previous question "I cannot find reference (paper) of this relation $u(t)t^{α} ↔^{FT} f^{-(α+1)}$". The signal that I work with g(t), is the time history ...
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Periodogram/PSD from FFT amplitude

I have performed a STFT for signals and obtained the amplitude through ...
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1answer
35 views

Power Spectral Density of a Filter

I need to calculate the output power spectral density of the following digital filter My calculations are as follows: $y\left(n\right)\:=\:x\left(n-1\right)+d\left[x\left(n-1\right)+x\left(n\right)\...
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61 views

Calculate average from a power spectrum

I want to calculate the average of a power spectrum in the complete frequency range. I have done a stft and want to calculate power in dB and then the average. Please let me know from the code below ...
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1answer
28 views

How to calculate mean and Variance of Gaussian-distributed random noise?

I have been given a Gaussian-distributed random noise n(t) which has an average power of 5 mW. How can I calculate the mean and variance of noise n(t)? Any suggestions? Thanks!
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How to get velocity from PSD graph

Hello everyone! I have a graph, which is Spectra inside cavity. PSD vs. frequency. I need to get velocity [m/s] from PSD [dB/Hz]. Does anyone know how to do that?
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The plot of instantaneous power of the Dirac function

I am very confused. I have tried researching this question for the last two weeks and I cannot get a conclusive answer. I was wondering how would I go about plotting the instantaneous power in the ...
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81 views

Windowing of signal before FFT

I am facing an interesting problem: I have a signal in the time domain. In order to avoid discontinuities at the edges of the signal --- which would lead to artifacts when calculating the FFT --- I ...
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Generating new 2D data using power spectrum density function from spatial frequency domain via ifft?

This is my first post so apologies for any formatting related issues. I also tried posting in stackoverflow but I'm more optimistic that I might get a response here. So I have a dataset which was ...
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Can I simplify $x=\frac{\ln(|\mathcal F((\mathcal F^{-1}(\sqrt{(f^{-5/3})}))^{2})|)}{\ln(f)}$

Given a variable in time $u_{k}$, and an other variable f which represents the frequencies in a range [a,b]: $$|\mathcal F \left \lbrace u_{k}\right \rbrace |^{2}=f^{-5/3}\tag{1}$$ where $\mathcal F$ ...
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difference beetween decimate an array and decimate function

i'am actually comparing data and i got a question that i cannot anwser, here is what i understand. nanometrique move X[::256] : decimate and take 1/256 point in the vector (blue) decimate(X, 256, ...
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Coherence for order spectra

The scipy signal coherence function computes for two time series the coherence as a function of the frequency. For rotating systems however, it is sometimes meaningful to analyze the two recorded ...
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Ringing/Oscillation in the reconstructed Periodogram

I have an original periodogram that I need to model with autoregressive process. However the model isn't right as it is not fitted well to the original periodogram. I am suspecting I am doing ...
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Power Spectral Density vs Frequency Domain separation

I am just starting to learn about Power Spectral Density (PSD). What I'm reading is that it is possible to separate PSD masks if they are isolated, even if the frequencies do overlap. My understanding ...
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Calculating SNR & Es/No and placing noise onto a signal

I have a signal power of -12 dBW from a 16 QAM signal after the first RRC. I want to create a channel SNR of 30 dB I calculate my noise power from this, i.e. its -42 dBW and make the noise to add to ...
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Processes/Transforms involved to get brainwave data from raw EEG? (Autocorrelation confusion)

Not clear on what the autocorrelation function of raw EEG means physically why can't you take the FT of a the EEG itself and get frequency data? With BCI & basic electrode setups you can ...
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Use of spectrograms in using deep learning on EEG related problems

I am currently working on a classification problem related to EEG signals. My professor asked me to convert those signals into their spectrograms and try various convolutional neural networks on them. ...
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Is there a relation between abs(fft(u.^2)) and abs((fft(u)).^2

Is there a relation between (1) abs(fft(u.^2)) (2) abs((fft(u)).^2 where u is a general variable. I have accidentaly found that if (1) has a power law +2, (2) has a power law +1. Can someone help me? ...
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Cross-correlation estimation in MATLAB using a method similar to pwelch for the PSD

Is there a function in MATLAB to estimate the cross correlation function of two wide-sense stationary signals (or the autocorrelation of the signal with itself) in a way similar to the estimation of ...
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How to find Integration of sinc function and then it's infinite summation?

I was doing this problem,i got answers of (a) and (b) by going following way, first i computed F.T. of x(t) as follows which in turn will be used to estimate it's bandwidth which will come as 2Hz and ...
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Response of an unstable LTI system to random signals

A convenient approach for studying the response of a stable LTI system with impulse response $h(t)$ to a WSS stochastic input $X(t)$ is to look at the power spectral density (PSD) of the output $Y(t)$ ...
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Calculating transmitter power from spectral density

I want to find out what is the real transmit power of my USRP 2922, unfortunately the only results I get when looking at the spectrum analyzer is the spectral power density. These are the results of ...
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How to compare PSD methods?

I am trying to compare several PSD methods to determine the most suitable method for my application. Does anyone know a good approach to start with? I am relatively new to this field of topic. I could ...
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Allan variance vs power spectrum density for noise estimation

I know than we can estimate noise level (and noise colors) from power spectrum density function OR from Allan variance. Why do we need Allan variance at all for such estimation? In my opinion PSD ...
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Spectral decomposition of the DC part of the signal

The title of the question might be misleading, but it shows how clueless I am about this problem. I have a time series of some quantity $X(t)$. I can calculate autocorrelation of this quantity $Y(\tau)...
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Noise removal where gains are >1

I am currently working on some noise removal algorithms and have come across what seems to be an oversight in the design of some of these algorithms. Two of the algorithms I am looking at use the PSD ...
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117 views

Is spectral density conserved after aliasing?

Will the integral of the PSD of a down-sampled signal still equal the variance in all cases
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Should we divide the power at 0Hz by two for Single-Sided Power Spectrum with FFT?

To make my question as clear as possible I will go through an example. I want to plot one sided power spectrum of a signal. As an example my signal is sum of "50Hz sine with and amplitude of 1V&...
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Constrained filter design

I have a desired filter magnitude response, i.e. $|H(j\omega)|$. How can I find the time-domain coefficients of a filter $h=[h_0, h_1, ..., h_{L-1}]$ that has a similar magnitude response such that $...
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39 views

What is the relation between input and output PSDs given system transfer function $H(s)$

If I have the system transfer function $H(s)$ in the complex frequency domain, how would I relate the input/output power spectral densities? I have come across the relation $P_{out}(f) = |H(f)|^2P_{in}...
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Male and female voice spectrum

I have a set of data which consists of male and female voices. They are pronunciation of a same sentence. What's the appropriate method for getting an average spectrum for the male and female voices ...
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translating 1 dB increase in thermal noise to interference to noise ratio (I/N)

I often see statements like "1 dB increase in the receiver thermal noise density results in an interference-to-noise density ratio of -6 dB". How can I obtain this result mathematically? ...
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1answer
54 views

Power Spectral Density Reconstruction

I am from an ML background and I am working on MP3 audio reconstruction and I have managed some amount of spectrogram reconstruction but I have noticed that the higher frequency end of the generated ...
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Help with denoising signal and periodogram analysis resources

This is a cross posting from the crossvalidated stack exchange as I thought this may be a better forum to ask. I have a dataset consisting of respiratory time series signals of different lengths ...

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