Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [power-spectral-density]

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

5
votes
0answers
549 views

fit theoretical spectrum to simulated one

I have a bunch of simulated time series, for which I can compute the power spectrum. Generally, the simulated power spectrum can be sketched as follows: I now aim to calculate the features of the ...
3
votes
0answers
78 views

Example of non-equivalence of the two PSD definitions

According to the book Introduction to Spectral Analysis by P. Stoica and R. Moses, the power spectral density (PSD) $P(\omega)$ can either be defined as the discrete-time Fourier transform (DTFT) of ...
3
votes
0answers
50 views

Physical significance of Power spectral density of sum of correlated random processes

For two processes $X(t)$ and $Y(t)$, PSD of $Z(t) = X(t) + Y(t)$ is $S_Z(\omega) =S_x(\omega)+ S_Y(\omega) + S_{XY}(\omega)+S_{YX}(\omega) $. If $X(t)$ and $Y(t)$ are orthogonal, PSD of the sum ...
3
votes
0answers
550 views

Power Spectral Density of Brownian Motion despite non-stationary

Note: I originally asked this on Physics Stack Exchange but haven't attracted any interest there so I'm asking here where it may be more relevant. A white noise process, $\xi(t)$ with delta ...
2
votes
0answers
12 views

Proof that the Lomb-Scargle periodogram reduces to the classical periodogram when the sample is equally spaced

If we have a equally spaced sample, we can use the conventionally used periodogram: $$P_x(\omega) = \frac{1}{N_0}\left[\left(\sum_j X_j\cos \omega t_j\right)^2+\left(\sum_j X_j\sin \omega t_j\right)^...
2
votes
0answers
72 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....
2
votes
0answers
696 views

Yule-Walker PSD Estimate of an AR Process

I am trying to implement a Yule-Walker PSD estimation in Python but my results are not up to the expectations. In MATLAB, I would normally implement my functionality as follows: ...
2
votes
0answers
35 views

Determining the point in a temporal signal when a periodic behavior begins to occur

I'm a newcomer to digital signal processing, so I'm looking for some general advice and direction on this problem I have. I have a signal like that shown below. Starting around x=40000, you can see a ...
2
votes
0answers
175 views

Noise analysis with periodogram. problem with different resolutions

I don't understand what happened in my simulation. I would like to perform a trade off between 2 ways to estimate power in frequency bands. I want to detect spurious frequencies. First method: I ...
2
votes
0answers
122 views

How to properly express periodogram over analog frequency?

Assume a signal $x[n]$ with $N$ samples and its $N$-point FFT $X[k]$. Assume also the simplest power spectral density estimator: $$ S_x[k] = \frac{\left| X[k] \right|^2}{N} $$ With this estimator, ...
2
votes
0answers
53 views

Stationary processes and their power

The top answer to this question: Power spectral density vs Energy spectral density states: However if random process is stationary, then it is for sure that it has some finite power over some ...
2
votes
0answers
855 views

Matlab: Estimating power spectral density of an experimental data?

How do I estimate PSD in matlab ? There are lots of methods to estimate, depending on application. I am using an experimental data to identify faults ( e.g. interturn fault of electric motor), which ...
2
votes
0answers
241 views

Is there any problem with my FFT method?

I am trying to analysis a system by Fourier Transform. my system has 3 dominant modes. (1,0.05) (0.51,0.01),(0.46,0.01) the pairs are defined as (freq,damping_ratio) I've got those result with ...
2
votes
0answers
811 views

difference (or relationship ?) between power spectral density, power density function and periodogram

What exactly is the difference or relationship between power spectral density and power density function? I thought they referred to the same thing but one article I need says to calculate both of ...
1
vote
0answers
23 views

PSD of randomly positioned dirac delta train

Let $s(t)= \sum_{i=0}^{T} \delta(t-\tau_i)$, where $ \{ \tau_{i} \}$ are random integers between $0,1,\cdots, T-1$. What is the power spectral density of the signal $s(t)$?
1
vote
0answers
38 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 ...
1
vote
0answers
77 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 ...
1
vote
0answers
59 views

Synthesizing a band limited noise from time samples of white noise and the relation to sampling frequency

I wan't to synthesize a colored noise of Bandwidth of 40Mhz around some carrier (say 2.5Ghz) from samples of WGN. So, I sample in matlab using randn(1,10000) samples of normal distribution. Now, ...
1
vote
0answers
39 views

Is power density invariant to Fourier Transform? Does it hold through derivation?

Assumptions We have a finite discrete measurement. Introduction I had some troubles determining a power spectral densities needed for Wiener deconvolution. Looking through the continuous equations ...
1
vote
0answers
124 views

What is the power spectral density after filtering?

Consider a signal $x(t)$, which is input to a pulse shaping filter with transfer function $g_t(t)$: $$x(t) = \sum_n d_n \delta(t-nT_s)$$ with $n$ an index from negative to positive infinity and $...
1
vote
0answers
228 views

Power Spectral Density of a WSS Random Process with 2D Discrete Fourier Transform

I'm trying to understand how the random process (RP) signal in discrete time domain is related to its power spectral density (PSD) in frequency domain if the signal is wide sense stationary (WSS). If ...
1
vote
0answers
35 views

Interpretation of steady state sensor signal

I try to understand some measurement results of an accelerometer MEMS sensor. I used a mikrocontroller which is sampling an accelerometer's analog signal with the built in analog-digital-converter. ...
1
vote
0answers
122 views

AWGN Build vs Randn noise do not match

I am generating noise in two different cases with the same SNR once using AWGN command which is a built in command and second time using randn function with the correct scaling however I am getting ...
1
vote
0answers
51 views

Epoching Data with no Events in mne?

I am new to Python and signal processsing, and I'm trying to create a spectrogram of EEG data taken during a course of general anesthesia. I would like to use MNE's ...
1
vote
0answers
482 views

Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
1
vote
0answers
23 views

Appropriate model for IIR filter to compare with spectral ratios

A quick, basic question. I have measured spectral ratios - comparing a measured signal to an 'ideal' signal. I am fitting a specific, simple IIR filter to that data for transfer functions. So, if I'...
1
vote
0answers
20 views

Power Spectral Density Via Rank 1 Update

I know that I can find the autocorrelation matrix of a series of finite length sequences via rank-1 updates using the relation: $\mathbf{R}[k] = \frac{1}{k}\mathbf{R}[k-1] + \frac{1}{k+1}\mathbf{r}[k]...
1
vote
0answers
1k views

1/f noise parameter characterization

I would like to characterize 1/f noise in some time series data. I would like to estimate the 1/f noise corner, and the standard deviation of the 1/f noise component and white noise component. The ...
1
vote
0answers
35 views

Generating 3-dimension $1/f^\alpha$ noise

I'm stumped trying to find a way to generate a 3-dimensional $1/f^\alpha$ noise time series. Basically I want simulate a forcing that is $1/f^\alpha$ in the 2 space dimensions and $1/f^\beta$ in time, ...
1
vote
0answers
210 views

How do I perform a spectral averaging? Amplitude spectral density

I haven't been doing much signal processing over the years and I'm wondering if my logic is sound. I'd appreciate any input. So, I have a data set with independent variable ($A$) in Frequency ($1\...
1
vote
0answers
61 views

Quantifying how good I'm producing a spectral density

I recently asked a question here on how to create noise with a specific spectral density $S_{xx}(f)$. The helpful people of this stack exchange told me one way to do it was filtering white noise with ...
1
vote
0answers
195 views

Why is it better to sample white noise in frequency domain here?

We have a channel $c(t)$ that we want to sample. It can be expressed as $ c(t)= g\ast x(t)$ where $x(t)$ is white complex Gaussian noise and $g(t)$ is a function that we know the PSD of, let's call it ...
1
vote
0answers
1k views

How do we calculate Power Spectrum Density (PSD) which is given in dB/Hz and not just dB?

I found many definitions for this quantity, PSD. In a document on signal analysis by National Instruments say that it is the amount of power in a unit bandwidth. Let's say P(f) is the power of the ...
1
vote
0answers
17 views

What spectral estimation technique to use for finding sharp spectral lines?

At the moment, I am using the Welch's averaged modified periogram method for spectral estimation, which has the frequency resolution $f_s/N$ where $f_s$ is the sampling frequency and $N$ the window ...
1
vote
0answers
12 views

Temporal window $\{v(t)\}$ of Welch estimator

The Welch estimate [1] of PSD (power spectral density) is determined as: $$\hat{\phi}_W(\omega)=\frac{1}{S}\sum_{j=1}^S \hat{\phi}_j(\omega)$$ where $$\hat{\phi}_j(\omega)=\frac{1}{MP}\left|\sum_{t=1}^...
1
vote
0answers
126 views

Why is generating $1/f^\alpha$ noise so complicated?

Why can't I just take the square root of the power spectrum $P(f) = Cf^{-\alpha}$, multiply with $e^{i\theta_n}$ ($\theta_n$ being $N/2$ random phases in $[0, 2\pi]$), and then do an inverse Fourier ...
1
vote
0answers
99 views

Removing the mean in finding PSD

Does removing the mean value of the signal effect the estimation of power spectral density(PSD)? If it effects, how? What is the advantage we can get by removing the mean of the signal in estimating ...
1
vote
0answers
713 views

What is the best method to estimate the frequency(PSD) for noise signal

I’ve been trying to estimate the frequency of a signal I obtained at 1000Hz sampling frequency. The dominant frequency is expected to be not more than 4 or 5 Hz. I’ve estimated the PSD using ...
1
vote
0answers
50 views

Power contained in a signal

Given a signal $$x(t)=16\cos(20\pi t+\frac\pi 4)+6\cos(30\pi t+\frac\pi 6)+4\cos(40\pi t+\frac\pi 3)$$how can I calculate the power contained in a frequency interval, say 12Hz to 22Hz. The total power ...
1
vote
0answers
372 views

What is OSNR in Fiber Optics?

I have seen that the SNR is measured for optical fibers "OSNR". What is the difference? Is there any equivalent?
1
vote
0answers
100 views

Spectral estimation from noisy time-series data

This is the first time I'm posting a question on here so I hope I'm doing it right. I've tried searching on here for an answer but haven't found anything particularly relevant. I have some data ...
1
vote
0answers
136 views

Importance of phase of time-series for PSD

I have $m$ complex-valued time-series $z_m(t_n)$, which I am currently analyzing. I started by calculating their PSDs and CSDs. These exhibit an unexpected peak at a given frequency, which is present ...
1
vote
0answers
179 views

when trying to nomalize a power plot , do we normalize it after converting it to db scale or before it?

I have two power plots. I am trying to normalize it for comparing them . So , do we normalize it after converting to db scale? or do we normalize the power as such?
0
votes
0answers
25 views

retrieving complete 2d autocorrelation function from 2d power spectral density function (numpy.fft.ifft2)

My question is at the boundary between signal processing and python. I have a 2d power spectral density function (PSDF) constructed on Nx/2 + 1 and ...
0
votes
0answers
25 views

What is wrong with my PSD computation?

I'm trying to calibrate the RX of my SDR Board to become a measuring receiver. I.e, by connecting it to a known source of power (in my case, a frequency generator), at a fixed frequency, I'm trying to ...
0
votes
0answers
20 views

PSD Periodogram smaller segments compared to larger segment

I am calculating the power spectrum of a heart rate variability via FFT and a Welch window. I have a sample of 500 points as the input signal. The signal was broken up into two 128 point segments. ...
0
votes
0answers
9 views

Correct way to calibrate RX into a measuring receiver

While playing with my SDR (Software Defined Radio) Board, I was interested in performing a TX output power table at different center frequencies and TX antenna gains. I have an RF frequency generator....
0
votes
0answers
23 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.
0
votes
0answers
7 views

Random sampling Bartlett spectrum estimation vs Welch

I'm trying to estimate the spectrum of a noisy time series and considering two approaches and their relative correctness. Let's say the time series is 800s long. Option 1 is to do a Welch spectrum ...
0
votes
0answers
15 views

How does discrete spectral moment relate to continuous spectral moment?

It is said in discrete/digital signal processing that $r$th spectral moment of signal $x[n]$ is defined as: $$\sum_{n=-\infty}^{\infty}n^r x[n]$$ But how does this relate to usual continuous $r$th ...