Questions tagged [power-spectral-density]

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

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442 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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51 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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456 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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296 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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2answers
304 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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878 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
182 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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301 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
2k 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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266 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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1answer
116 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
4k 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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125 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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2answers
156 views

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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Is there a criterion that says at what point you can distinguish 2 partially overlapping Lorentzian peaks?

If you have 2 Lorentzian peaks that partially overlap and you have some frequency resolution df (your points in frequency space are separated by df) and both Lorentzian peaks have FWHM $\Gamma$ is ...
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142 views

How to choose the right segment length for a given signal?

Im working on plotting the power spectral density of a random time series measured. I know the target spectrum.The idea is check the measurement vis-a-vis the target spectrum. However, I get slightly ...
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174 views

Correctly scaling Power Spectrum and Correlation Function of Galaxies from Mock Catalogues

I'm currently writing a code to compute the two-point correlation function of a set of galaxies. As I work with a loooot of galaxies, it was suggested to me not to do it in real space, but to compute ...
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2answers
294 views

Understanding PSD: Why Does Power at High Frequencies Affect Low Frequencies?

I'm trying to wrap my head around power spectral density on a conceptual level, but I am having some difficulty. Suppose I have a communication system where I am receiving and sampling white Gaussian ...
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100 views

non-negative FFT spectrum, subtlety

definations $x(t)$ is a function of time. Physically, it can be voltage, displacement, magnetization and so on. It can be real, complex, vectors or more fancy numbers. $C(t)$ is the auto correlation ...
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336 views

frequency spectrum of a sampled signal, PSD and power discussion

Before I go into my question, I first want to review the basics of sampling a signal and at the same time I build the basics of my questions so that they make more sense. I know I have asked couple of ...
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1answer
1k views

How Does the RMS of White Noise Change with Sampling Frequency?

There is an analog system which includes the continuous-time linear equalizer (CTLE). With some .noise analysis the power-spectral density (PSD) of the noise in that system is provided. So let's not ...
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90 views

How to generate the amplitude of a signal with a certain power spectral density?

I am a newbie. If I posted a question someone else already asked, please forgive me. Thank you! Now, I have a power spectral density named $P(f)$ as a function of $f$. Let's say this function is ...
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1answer
56 views

Isolating frequency-specific oscillation from transient

I am performing time-frequency analysis on electrophysiological data with complex morlet wavelets. Each decomposition in the attached figure shows total power following the onset of a stimulus (top ...
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92 views

psd of an ac voltage signal

In an lab class experiment who's subject of interest was Johnson's noise I measured the ac voltage of a battery. Now I wish to find the psd of the measurement and show that it is constant. 1.Is such ...
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1answer
438 views

Should scipy.signal.coherence be 1 for single input and output signals?

I am trying to calculate the coherence between input and output signals. I thought I could work with a single input and a single output time series and calculate the coherence $\gamma^2$ between them. ...
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484 views

Condition for modelling noise as white noise

I am reading a book on Communication System by Simon Haykin. In the topic of white noise there is a paragraph "We may state that as long as the bandwidth of noise process at input of a system is ...
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657 views

Amplitude of signal and PSD peak height

So, suppose you have a superposition of cosines of the same magnitude: $\sum_{i}\cos[\omega_i t]$ When you take the Fourier transform, theoretically you'd expect to find $\delta$-like peaks of the ...
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Octaves vs Decades Fractions

At this USGS very good site about rms noise in sensors, a phrase regarding third octave bands (the original topic) appeared. The figure displays the minimum vertical seismic noise directly as rms ...
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319 views

Applications of Power Spectral Density [closed]

I have a class covering Power Spectral Density but I have no idea why it matters. Could someone provide some examples of its use? Thanks
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844 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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2k views

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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410 views

Why look at power spectral density for stochastic processes?

I have been told that for deterministic signals, it makes sense to look at their respective Fourier transforms/spectra. For stochastic processes on the other hand, I am supposed to work with power ...
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185 views

Phase information from product of complex conjugate transfer functions

For an input signal $x(t)$ and output signal $y(t)$ through an LTI system I $H(t)$ I have found and interesting property that concerns signals' power spectral densities: $${\lvert H(\omega)\rvert}^2 =...
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144 views

Estimating number of sinusoid from spectral estimation

Suppose I am given a data X0 that have 50 realizations of a sum of an unknown number of sinusoids in additive white Gaussian noise. I plotted the Spectral estimate as attached. How do I estimate the ...
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1answer
367 views

What is the relationship between image spatial domain and FFT powerspectrum?

I am trying to perform contrast-transfer-function for pictures which were recorded in defocus. To do so, I have to calculate the contrast-transfer function from the Thon rings and fit the function to ...
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3answers
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Generating a timeseries with an arbitrary power spectrum

I need to generate random numbers with a given PSD. To do so, I found this recipe. In case it's behind a paywall, here's now it works: Given your power spectrum $P_k$ with $0\leq k<N$ points ...
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1answer
4k views

Converting PSD to dB scale

I am taking the PSD of the output of an RTL-SDR with Welch's method. The output is an array like: [1.34225796e-07 1.37964799e-07 1.24558405e-07, ....]. I'd like to convert this array to dB, so ...
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1answer
223 views

Wiener Filter Additive Noise Uncorrelated

I have been trying to understand for a while now why a non-causal Wiener filter that has a frequency response of the type H(jω)=S_yx(ω)/S_xx(ω) where ...
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1answer
386 views

Estimating the bandwidth of various signals

I am trying to estimate the bandwidth of different signals, with different modulations, as seen in a PSD graph. I've heard about a "$3\ \rm dB$ rule" in this context. I don't need extreme accuracy. ...
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Calculating SPL from pressure signal - Amplitude vs Power method

I have a pressure signal from a Fluent FFowcs-Williams Hawkings acoustics analysis. I converted this pressure signal into the frequency domain in order to get SPL values, using Matlab. I used the ...
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2answers
659 views

Why averaging in Spectral magnitude domain not in complex domain to estimate spectrum of a process

Consider we need the magnitude spectrum of the signal. Signal is recorded in $N$ trials to a certain stimuli. Signal varies from each trial because of noise. So, to estimate the actual magnitude ...
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5k views

variance in the time domain versus variance in frequency domain

Hi All: I'm trying to better understand the connection between variance of a time series and the integral of the spectral density over all frequencies. Rather than going through all of the relations, ...
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100 views

Approximate the change in perceived gain from applying transfer function to audio signal

I have an audio signal that I am applying an analogue transfer function $H(s)$ to. I would like to approximate the change in gain ($\Delta \text{ Gain}$) as perceived by the listener for an arbitrary ...
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Definition of average power?

There are two kind of average power I encountered in random signal class and textbook: definition 1: average power =$$E[|x(t)|^2]=R_{xx}(0)=\int^\infty_{-\infty} S_{xx}(f)\,df$$ definition 2: average ...
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289 views

Autocorrelation and PSD

Let $X(t)$ and $Y(t)$ be two orthogonal processes with power spectral densities $$S_{xx}(f) = S_{yy}(f)=\begin{cases} 1-\lvert f\rvert, & \lvert f\rvert<1 \\[1ex] 0,& \text{otherwise} \end{...
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1answer
721 views

Question on the definition of one-sided PSD in AWGN channel

I am currently simulating the following in a telecommunications exercise in Python: Consider a binary sequence $m[n]$ that is being modulated with QPSK (Gray-mapped) that is being transmitted via ...
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2answers
198 views

Filter away sinusoidal noise properly

I have a stereo music signal corrupted by strong sinusoidal noise that varies over time. Here is the spectrogram of Left channel I plotted with Matlab. As you can see there are 3 or 4 strong ...
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1answer
845 views

Power Spectral Density of Digital Modulations

I want to simulate the power spectral densities of different modulations in MATLAB (without Simulink). Unfortunately I have only very basic understanding of signal processing, hence I struggle with ...
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1answer
137 views

Spectral density interpolation: Applications?

Let $\Phi_1$ and $\Phi_2$ be two matrix-valued power spectral densities. I wonder whether the problem of interpolating $\Phi_1$ and $\Phi_2$ has been studied in the literature and/or applied in ...
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543 views

What is the difference between the PSD of a deterministic and stochastic signal?

I am learning about stochastic processes and I don't get one thing: What is the advantage of calculating the PSD of a signal using the Wiener-Khinchin theorem $\Phi(\omega) =\mathcal{F}\{R_{xx}\}$ ...

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