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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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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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power spectral density estimation

I have an audio signal carols.wav. How do I obtain the PSD in Matlab using the inbuild pwelch function and also to write my own code.
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23 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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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
25 views

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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36 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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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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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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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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62 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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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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Should PSD be smoothed for SNR computation in frequency domain?

When taking the Power Spectral Density of a short duration signal (say 1 second, sampled at 4096 Hz), should it be smoothed to compute SNR? I want to computed the matched filter SNR, perfectly knowing ...
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Relation between $X(f)$ and $S_x(f)$

We know that for a signal $x(t)$, it is related to $R_x(\tau)$ as, $$R_x(\tau) = \int_{-\infty}^{\infty}x(t)x(t-\tau)dt$$. $\\$We also know that $$R_x(\tau) \rightleftharpoons S_x(f)$$ $\\$How do we ...
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FFT and Power Spectrum Normalization

On many websites, including MathWorks, it was suggested to normalize the fft spectrum (MATLAB or numpy) by dividing it by the total number of samples ($N$). For a sinusoidal signal, for example: $$x(...
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Over-the-air (OTA) BER measurement

I'm in the process of evaluating BER performance for a GNU Radio BPSK receiver. The setup for the experiment is illustrated below. Using a spectrum analyzer just before the USRP, the average channel ...
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psd in matlab, problem with the coefficient $\frac{1}{2\pi}$

Using the fft to mimic the Fourier Transform I have this question. The definition that I use for the PSD $S(f)$ is: $S(f)=\frac{1}{2\pi}\int_{\infty}^{\infty}exp(-i\tau2\pi f)r(\tau)d\tau$ where r(t)...
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How can we prove that Spectral density of In-Phase component and Quad-Phase component of a sample function of narrow-band noise have same definition?

Suppose we have a narrow-band noise $N(t)$. We analyse this to In-Phase and Quad phase components by the equation: $$N(t) = N_I(t) \cos(2\pi f_c t) - N_Q(t) \sin(2\pi f_c t)$$ Now a book (by Simon ...
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Question regarding AC power of ergodic process

We know Ergodic process is the subset of Weakly stationary process which permits us to substitute time average for ensemble Average My teacher said If $X(t)$ is Ergodic random process then following ...
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limit of the integral in the anti-transform

if I have an autocorrelation on a limited domain r($\tau$)=$\lim_{T \to \infty}\frac{1}{T} \int_{0}^{T} u(t)u(t+\tau)dt$ The power spectral density, obviously will have an infinitive domain: S(f)=...
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how to cut off frequencies above 10 Hz with Welch method

This is the first time I have worked with any code so I am rather unfamiliar with all the lingo and processes involved. I am trying to convert a signal to the frequency domain and want to find the ...
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36 views

demonstration using parseval

I have to do a demonstration. If we do the Parseval identity of the signals $x(t)$, $y(t)$ and $z(t)$ that go from $0$ to $T$ and that are real, we have: $\int_{0}^{T} x(t)^2dt=\int_{-\infty}^{\...
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Power Spectral Density vs Energy Spectral Density for Discrete Signal

I'm sure this is a silly question but reading a bit about the PSD vs ESD for continuous signals, I'm a bit confused how that applies to discrete signals. Usually people seem to be using the PSD when ...
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what is equal to the FT of the Autocorrelation function

I am trying to make my own demonstration in order to find what is equal to the FT of the Autocorrelation function. The autocorrelation function in some book about turbulence is defined as: r($\tau$)=...
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63 views

Filter before or after multiplication of two signals?

I have two signals and want to multiply them, e.g. voltage and current are multiplied to get power. The result (e.g. power) shall be a filtered result, e.g. to see the average. Is it better to filter ...
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40 views

power spectrum -PSD

I was wandering if someone can help me to understand if there is difference between power spectrum and power spectral density. Looking here I found that there are differences https://www.quora.com/...
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66 views

Power contained in a random process $X(t)$

How do we calculate the AC and DC power of random process $X(t)$ , provided we have $R_x (\tau)$, and $S_x(f)$ ?
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the demonstration that states that the FT of the ACF function is the square of the DTFT of the signal

I am following the book The Intuitive Guide to Fourier Analysis & Spectral Estimation with MATLAB. I am trying to selflearn the fourier analysis in matlab. I got lost in one passage in the ...
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Power spectral density: why this 2 method are equal

the Power spectral density can be calculated in two way: by doing the fourier transform of the autocorrelation by doing (abs(X(f)).^2 where X(f)=fft(x(t)) Can you explain me passage by passage why ...
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How does spectral density of a power signal change when it is multiplied by $\cos(2\pi f_ct)$?

Suppose we have a power signal $n(t)$ whose power- auto-correlation function is: $R_{n}(\tau)$. Now we multiply the signal by a cosine as $$\cos(2\pi f_ct) \cdot n(t)$$ whose auto-correlation is $R_{...
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Expectation of power spectrum for nonorthogonal wavelets

I'm working through "A Practical Guide to Wavelet Analysis" by Torrence and Compo, and I am confused about section 3d ("Wavelet Power Spectrum"). Let $x_n$ denote the signal, sampled at increments $\...
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Changing power of an audio signal to a specific dB

Suppose I have an audio signal with power 31dB. I want to change the signal power to 24dB. How can I change the power of that signal from 31dB to 24dB?
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47 views

Fourier transforms and time shift

There is probably something trivial behind this, but I am missing something. I need to create a stationary random time series data v(t) which is the the sum of another time series u(t) and u(t) with a ...
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Time derivative of signal - effect on noise distribution

I have an angular velocity measurement that has a certain amount of ripple that yields an histogram shaped like a gaussian curve. I quantify that ripple using a standard deviation. I am interested in ...
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163 views

Comparison of results own implementation and python signal.welch

I am trying to replicate the output of Python's signal.welch function to make an estimate of the PSD from an FFT calculation. I don't want to use the built-in function to understand better what is ...
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101 views

How to normalize PSD to get the same magnitude as FFT peak

I am trying to use FFT and power spectra density estimation with python (np.fft.fftand scipy.signal.periodogram). And trying to ...
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32 views

Correlation/anticorrelation as a function of frequency

I am tracking the values of two fluctuating quantities as a function of time and am trying to analyze possible correlations between the two as a function of frequency. The application is experimental ...
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Morlet-based Cross Spectral Density vs Wavelet Transform

I am interested in the frequency distribution and power of neural alpha waves (8-12Hz), and have been using WT to examine them. I am quite new to the techniques involved, however, and have noticed ...