Questions tagged [power-spectral-density]
The Power Spectral Density (PSD) is the distribution of signal power over frequencies.
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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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23 views
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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18 views
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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15 views
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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10 views
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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2answers
22 views
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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21 views
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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18 views
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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1answer
45 views
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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18 views
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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1answer
13 views
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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44 views
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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1answer
59 views
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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1answer
53 views
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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7 views
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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49 views
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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1answer
33 views
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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40 views
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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30 views
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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0answers
18 views
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
42 views
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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0answers
36 views
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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0answers
54 views
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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1answer
74 views
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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55 views
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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35 views
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 ...
3
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1answer
193 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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72 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 ...
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0answers
28 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 ...
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0answers
27 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. ...
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0answers
11 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....
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43 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.
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18 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 ...
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2answers
157 views
How to calculate the PSD from the complex calculated STFT?
I have calculated the STFT with scipy python library:
...
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4answers
71 views
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)|] $$
If it is because the random ...
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0answers
17 views
How does discrete spectral moment relate to continuous spectral moment?
It is said in discrete/digital signal processing that $r$th spectral moment of signal $x[n]$ is defined as:
$$\sum_{n=-\infty}^{\infty}n^r x[n]$$
But how does this relate to usual continuous $r$th ...
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1answer
40 views
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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0answers
33 views
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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1answer
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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2answers
92 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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1answer
28 views
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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0answers
32 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)$?
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1answer
28 views
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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1answer
30 views
Same PSD from different FFTs
Is it possible to obtain same PSD from different FFTs?
Can anyone explain it mathematically?
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0answers
13 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)^...
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1answer
49 views
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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1answer
18 views
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 ...
2
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1answer
59 views
finding energy content of signal from “energy spectral density” function
from "Signals and Systems Demystified", 2006, page 142, Example 6-3: (http://www.gatestudymaterial.com/study-material/signals%20and%20systems/text%20books/SIGNALS%20AND%20SYSTEMS%20BY%20DAVID%...
2
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1answer
165 views
How to make a Power Spectral Density Plot in R
I have a time series point process representing neuron spikes. I have computed and plotted autocovariance using acf but now I need to plot the Power Spectral ...
2
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1answer
35 views
Why is the sound field intensity due to $K$ point sources given by $ I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)$?
I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below.
Statement: 1.
We ...
