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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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What is the physical meaning of the cross-spectrum of two signals measured at two locations and different moment?

I am working with steady state pressure field measurement where sound pressure at multiple locations in the field needs to be measured. In my case, more than one microphone existing in the field at ...
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How to find spectral density of a signal whose correlation depends on time?

Suppose we have two uncorrelated, real white noise $\xi_1(t)$ and $\xi_2(t)$, with zero mean, and equal variance. Now, I create the signal $\xi(t) = a\xi_1(t)\cos(\omega_0 t) + b\xi_2(t) \sin(\...
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What kind of power spectrum implies uncorrelation in time?

I am new in signal processing field, and actually I just need some basic tools for what I am working on. I've learnt that the autocorrelation function is the inverse Fourier transform of the signal's ...
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Calculating Data Rate using Bandwidth, Transmission Power, Noise Power Spectrum Density and Channel Gain

I'm a Software Engineering student researching on Load Balancing in IoT and I need to calculate data rate. However, I don't know how to use these values to attain data rate despite searching on the ...
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Relation between power spectral density and mean absolute value

The root mean square $$\sigma_{x} = \sqrt{\frac{1}{T}\int_0^T x^2(t) \, \mathrm{d}t}$$ of a finite zero-mean random signal $x(t)$ in the range $0 < t < T$ is related to the signal's power ...
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How exactly does one apply a Hanning Window for a spectral estimate?

PREAMBLE I am a graduate student researching evolutionary ecology. My supervisor and I have been trying to learn how to simulate colored noise, discretely, by the $\frac{1}{f^\alpha}$ power law for $\...
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Analytical spectral density of a On/Off modulation defined by a Bernoulli process

Consider a narrow band signal (laser) that I can modulate digitally with a on/off switch controlled by a digital pseudo random number generator. The resulting signal features a linewidth broadened by ...
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How to choose the order of the filter - Capon's method

I am studying power-spectra and I want to find the best estimation method for my problem. I stumbled upon Capon's method (sometimes also called minimum variance), which on paper looks very nice. On ...
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What are some of the disadvantages of parametric PSD estimation methods?

Roughly speaking, the methods of power-spectra estimation can be divided in two categories : parametric and non-parametric. From what I understood, parametric methods assumes that the signal can be ...
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Binary vs 4-PAM PSD

I'm struggling to understand how you would form an expression for the PSD of a 4-PAM signal which is using rectangular pulse shaping. I understand for binary the likelihood of +/1 is equal so the ...
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How to get PSD from frequency domain representation of time-series data [duplicate]

Let's say we have a realization (time-series data) of a random process. I take fft() of that to get its frequency domain representation. Then how can I estimate the PSD of this random process by ...
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Units for a PSD from square of FT?

If I am looking to do a PSD plot on a signal $x(t)$ with units $m$ then the units I am expecting in the PSD would be $\frac{m^2}{Hz}$ but I can't seem to get this result from the following reasoning: ...
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Losing lowest Frequencies in frequency modulated signal, rest of spectrum is fine

For several reasons I am attempting to re-modulate a de-modulated FM (as in WFM Radio) signal using python. Demodulating the initial signal goes well, it produces the PSD chart below which looks just ...
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MATLAB & Power Spectral Density - Error - Getting the same range of values regardless of sound type?

I wrote code [attached at end of question] to take .wav files of child vocalizations and tried to see if there are valid ranges for the formants F1:F2:F3 for the 5 ...
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Is it possible to approximate given skewness and kurtosis values using an IFFT?

I have time domain data for a signal that behaves randomly but has non-random (non-Gaussian?) skewness and kurtosis values of ~0.9 and ~7.4, respectively. The FFT of the signal shows that it's not ...
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QPSK Data Rate vs Bandwidth at Passband: Why can it only transmit 1 bit per Hz and not 2 bits per Hz?

1) This is a follow up question to the most up-voted answer to this question. 2) The accepted answer is that "QPSK transmits 1 bit per Hz at passband". 3) The theory found in books seems to agree ...
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PSD subtraction

I am interested seeing the difference between two power spectral densities (PSD) as a noise reduction exercise The blue line is the psd of my signal, and the the orange line is the psd of the ...
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How to relate power spectral density with the number of resource blocks in LTE?

I am running a simulation with 100 Resource blocks for LTE OFDM and I plotted a PSD for it. Now I am able to bring down the out of band emissions when I perform an algorithm on it. Based on the ...
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Why does power spectral density of OFDM signal changes with number of zero subcarriers

I am trying to plot the power spectral density (PSD) of an OFDM signal with $N_{dsc}$ subcarriers and $N_{zeros} = N_{fft}-N_{dsc}$ zero subcarriers. I am using the matlab function pwelch() to plot ...
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Normalizing vectors to be the same size to retain PSD data

Context: PSD=periodogram(y) in MATLAB gives the PSD (power spectral density) estimate of a sound-source signal. I want to find the local maximum within 3 different ...
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Help obtaining the variance of a signal from a power spectrum?

I have been reading this. The paper presents a power spectrum (attached). The power spectrum shows the power spectrum of velocity perturbations, $v$, in the solar atmosphere. If I want to obtain the ...
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Equivalence of the Power Spectral Density definitions

I am trying to show the equivalence of the following Power Spectral Density definitions in Matlab: Definition 1: $$ P(\omega) = \sum_{k=-\infty}^{\infty} r(k)e^{-j\omega k} $$ Definition 2: $$ P(\...
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Chi-squared distribution variable spectral analysis

I an interested in spectral analysis of a random signal. Assume the signal $n(t)\sim\mathcal{N}(0,\sigma^2)$ is followed by the white Gaussian noise with zero mean and $\sigma^2$ variance. The test ...
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1answer
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When a stochastic process would be a beneficial model in terms of noise

Let's say we have an image/signal with some noise in it. When would it be beneficial to model the signal as an outcome of a stochastic process? More specifically: How significant would noise have to ...
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Interpreting Auto correlation results

I used xcorr function in Matlab to compute the autocorrelation of my signal. I obtained a graph, which is shown below. How to interpret this? I read that autocorrelation helps in finding the patterns ...
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Power spectral density of a pulse

A little background: I am simulating the response of an antenna to a pulse. The pulse has a wide frequency range, but the antenna only responds to a fairly narrow frequency. I can extract voltage and ...
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How to find mean value of a random process from power spectral density?

I have a periodic function that is given as x(t). I found out the power spectral density. How do I find out the mean value from the power spectral density. I know how to find out the mean square ...
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On the spectral representation of deterministic and random signals

I went back to many references in order to fix some of the confusions that I have on many concepts in signal spectral representation. I concluded that: 1) Deterministic signals may be represented ...
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Attempting to remove the 60Hz frequency out of a noisy ECG signal

load eeg_plus_noise Fs=200; Fn=Fs/2; b = fir1(64,[59.8 60.2]/Fn,'stop'); figure(3) freqz(b,1,512,Fs); y = filter(b,1,eeg_plus_noise); I am then using the ...
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196 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 ...
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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 ...
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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 ...
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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. ...
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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....
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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.
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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 ...
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How to calculate the PSD from the complex calculated STFT?

I have calculated the STFT with scipy python library: ...
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Spectrum estimation

When calculating the spectrum estimation of a signal $x(t)$ with random noise, why do we use ($E$ for expectation) $$E[|X(\omega)|^2]$$ but not $$E[|X(\omega)|] $$ If it is because the random ...
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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 ...
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Can spectral density be a complex quantity?

I have a signal ($S(t)$) which is product of a Gaussian ($G(t)$) and a random phase function ($e^{i\theta(t)}$, here $\theta(t)$ is a random function), as shown below $S(t)=G(t).e^{i\theta(t)}$ If I ...
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About the power spectrum and confidence upper limit of a time-series data

For now, I have a coupled system with 5 variables and use the Runge-Kutta method to integrate. ...
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40 views

Number of discrete samples required for the longest wavelength

I am trying to understand the effect of the critical Nyquist frequency when applying the Goertzel algorithm for estimating the power spectrum of a discrete signal. (Goertzel doesn't really matter, ...
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108 views

Band-limited random signal with arbitrary distribution?

I'd like to generate a random discrete-time signal that is band-limited to some bandwidth B (by means of a digital filter, ie in MATLAB). The catch is that I'd like this signal to have an arbitrary ...
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What's the maximum energy for a finite signal?

I'm trying to calculate the spectral density of a signal. What I'm expecting is a scale in dbFS where 0 dbFS would be the maximal theorical energy if all my signal is concentrated in a single ...
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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 $s(t)$?
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How to window a time domain signal for 6 symbols with cyclic prefix length of 512 samples?

Based on LTE stds. I am running a simulation for 6 symbols (each having 1200 central subcarriers) each in a 2048 FFT/IFFT bin. To these symbols are appended 512 samples as cyclic prefixes. I have to ...
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Same PSD from different FFTs

Is it possible to obtain same PSD from different FFTs? Can anyone explain it mathematically?
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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)^...
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Converting a non-stationary random process into a WSS process by adding a random phase

Here is an example where this method has been implemented. We were trying to calculate the spectrum of a transmitted signal(Random signal/weighted pulse) The auto correlation function of the pulse ...
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When does a color channel such as RGB carry more info than a grayscale channel or image?

Typically a gray-scale image gives us more information about an image in terms of a signal processing problem. But when does a color channel carry more info than a gray-scale channel? I understand ...