Questions tagged [power-spectral-density]

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

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Signal Timing Recovery, Loop Bandwidth and SNR

As explained in the answer here, for the symbol timing recovery loop we need to keep loop bandwidth sufficiently below the modulation bandwidth of the signal so as to avoid the filtering of the signal ...
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How to separate EEG frequency band in python?

Sorry for stupid question! I am very new in EEG signal processing and python environment.I have started my a project work related to EEG signal analysis using MNE. I would like to separate EEG Bands ...
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MATLAB: Generating a random bit stream in a frequency Band for PSK Modulation

I want to generate a pseudo-random bit stream in MATLAB in a given frequency band for PSK Modulation. I am using the idinput function to generate the bit stream: <...
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124 views

High Pass Filtering and Noise

I have the following code: ...
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DFT for signals of different length and sampling rate

I would like to compare oscillations of biological object. I have multiple datasets which are taken with different sampling rate and have different length. My current workflow: Take derivative, ...
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Am I supposed to normalize FFT in Python?

I'm sorry if this question is posed often, I can't seem to understand the answers already out there. I'm working with several forms of the Fourier transform, including the FFT, PSD, and spectrograms. ...
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Help with finishing this integral, to obtain the power spectral density of a pure cosine wave

I am trying to evaluate the power spectral density $S_{xx}(f)$ of a cosine signal $x(t) = A\cos(2\pi f_0t)$, by starting from its definition for deterministic power signals $$S_{xx}(f) = \lim_{T\...
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Gaussian signal generation

Edit: Could the following be the answer? Generate WGN-like-signal which is centered around a set dBm value. Treat that signal like it was a frequency domain representation of an unknown X time-domain ...
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Inconsistency with the units of power spectral density and the definition the people often give

Perhaps someone can help me resolve something - this is my understanding: In deterministic signal analysis, for a signal $x(t)$ the signal energy (as opposed to the real physical energy) is given by $...
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Interest in adapting signal processing for reverse engineering principally from a biogenomic standpoint [closed]

NB: Cross-post to this post on reverseengineering.stackexchange.com. I am seeking any possible help for a problem I have devoted a quite protracted period of time exploring. I am total perm disabled, ...
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Help with obtaining the power spectral density of a simple continuous cosine (using both forms of the definition for PSD)

I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice and would be very grateful if someone could check my ...
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Using the log power spectrum as features for a Classifier

I have a set of time series signals for which I have to develop a anomaly detection algorithm. I am considering using classifiers like SVM to do this. However I am confused about how to properly ...
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Proof that spectrum analyzer measures mathematical Power Spectral Density

It seems to me the power spectral density (PSD) is defined as follows. Consider a signal $X(t)$ The windowed version of this signal is Consider a signal $X(t)$. We defined a time-windowed version of $...
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Power Spectrum and Power Spectral Density

From signal theory we know that a very useful representation of some power signals is that of its power spectral density, whose curve represents how the total power of the signal is distributed at all ...
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1answer
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Power spectrum of uniform white noise

Given a white noise image $W_{i,j} \sim U[a,b]$ where each pixel is distributed uniformly in $[a,b]$, how would I go about computing its power spectral density? That is, I want to find $E[|\hat{W}_{i,...
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Converting PSD to Time Domain Signal

I am currently using MATLAB and I'm thinking if I can reconstruct PSD back to time domain signal using MATLAB's ifft. I found a link in solving this problem but it's in Phyton and when I tried it in ...
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Relation between Gaussian and bi-Gaussian distribution

A Gaussian Doppler Spectrum can be seen as a bi-Gaussian Doppler spectrum in wich only one Gaussian function is present ( the second having a zero power gain) ? any help will be really appreciated
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HF ionospheric Channel Model Example in matlab : Watterson model

In the example file in matlab HFIonosphericChannelModelExample.m, the watterson model is simulated. In this model the channel is represented as one tap (for the sake of simplification) delay channel. ...
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1answer
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Power spectral density: where does the difference from decibel and regular representation come from?

I am generating a simple DC signal with noise. As expected the fft shows that there is one peak at 0Hz and some noise. I am also trying to get the spectral power density representation of that signal, ...
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Can someone explain me what is the doppler spectrum?

I have a signal generated in matlab, with Rayleigh Fading, how can I add a given type of Doppler spectrum ( Gaussian for instance) to that signal ? Any help will be really appreciated
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How to simulate (in matlab or c) power spectrum of random brownian noise signal?

I have a semi random noise signal, it does have some periodicity however. I can estimate the power spectrum (of the blue signal, I thought that it would be more clear, because white noise is flat, ...
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Cross power spectral density (CPSD) comparison between signals

I want to compare various signals with Matlab's CPSD to identify shared frequency components. (If there's a better method, I would like to know!) I have 3 signals, A, B, and C. B is pure noise while ...
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1answer
25 views

How do I find variance from the PSD of a stochastic process?

I have a time series that consists of noise and a signal, shown here windowed and Wiener filtered: and the PSD of just the noise (used in filtering): I want to find the variance of the noise using ...
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Why are the Fourier transforms of autocorrelation and cross-correlation different?

I'm almost definitely misunderstanding this, but as far as I can tell we can equate the Fourier transform of the auto-correlation function $R_{xx}(\tau)$ with power spectral density (PSD) like so: $\...
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Why am I not getting a flat phase for a Gaussian pulse when doing a Fourier transform in Python?

I have been trying to obtain a spectrum and a spectral phase of a Gaussian pulse using the Fast Fourier Transform provided with numpy library in Python. Here are ...
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Harmonics below oscillation frequency in the brain

Apologies if this question is trivial, I'm a neuroscientist and would hugely appreciate your help to correctly interpret my analysis. I am recording EEG signals and am manipulating the brain using ...
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1answer
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Subtract background from 2D signal using spectral methods

I have a 2D signal, with intensity as a function of two angles (alpha and beta), as shown below. This contains a background, which makes the signal's base-surface locally convex-concave. I would like ...
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How to create a synthetic time series where power spectral density estimation is achieves better results than a direct Fourier transform?

I am trying to create a synthetic time series where PSD estimation is necessary and useful to recover the correct spectral information of the time series. But so far I can only create a time series ...
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Get autocorrelation function from the power-spectrum (python)

I am trying to compute the autocorrelation function of a signal for which I only know the power-spectrum. In order to test my approach I wanted to try it out on the spectrum of $1/f^2$ noise for ...
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How to create a wide-sense stationary time series with a frequency of 40 Hz?

I want to create a time series in MATLAB which has a peak frequency of 40 Hz but is also a wide-sense stationary random process. I then want to use power spectral density estimation to recover the ...
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197 views

Power Spectral Density (PSD) from autocorrelation

I have a 1D fractional Brownian motion (fBm) signal, $u(x)$, of size $N$, generated through a random number generator with a gaussian mean, $\mu=0$, and standard deviation, $\sigma=\sqrt{N}$. I want ...
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Power spectral density vs. Fourier Transform

I am trying to understand the difference between the Power Spectral Density and the Fourier transform. Specifically, I am trying to understand why the power spectral density is useful and in what ...
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Calculating the power spectral density on a different bandwidth

Let us say I have the power spectral density for a given bandwidth F1 at a transmit power T. I would like to calculate the power spectral density for bandwidth F2 for 1) the same transmit power T 2) ...
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SNR Signal to noise ratio of Pseudo random bit sequence (PRBS)

How should I estimate the Signal to noise ratio of a 20 Gbps NRZ PRBS pattern from power spectral density--where should I take the noise floor if I can assume well the noise is AWGN? I know roughly ...
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Autocorrelation to diagnose faults

I'm attending a very practical course on signals and i have some doubts, i hope to receive answers in layman terms. 1) My prof said i can use the autocorrelation of the output of a process to ...
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Removing DC Offset (via removing mean) of input and output signals affects their coherence

I have input $x$ and output $y$ signals (fs=10 Hz, length N=10800). I have removed DC offset via the following equation: $x_{normalized} = 100 \frac{(x-\bar x)} {\bar x }$ where $\bar x$ is the mean ...
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What is the unit for power spectrum of acceleration signals in log scale

I have a signal recorded by an accelerometer in m/s^2. It is basically accelerations over a period of time. I have calculated the power spectrum of the signal over in a certain frequency band and then ...
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Proof that module of FT of 2 independent signals is sum of modules

I found on these posts (PSD subtraction and PSD of a sum of two stationary real signals) what I expected : that, just like the variance of the sum of 2 independent signals is the sum of the variances ...
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Normalizing white noise to match pink noise's amplitude at a given frequency?

I have a pinking filter which I am running white noise through to get pink noise. I would like to then mix the white noise with this pink noise, where the amplitude of the white noise will match the ...
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1answer
57 views

The expectation in power spectral density

I'm a bit confused with the definition of the power spectral density (PSD). From Wiki https://en.wikipedia.org/wiki/Spectral_density , I found the definition is: $$ S_{xx}(\omega) = \lim_{T\...
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SDR spectrum anomalies

Is it normal to see periodic peaks going from 48.75 - 90 MHz? Also i was checking on my SDR dongle once and the whole band was raised above background offset for like a whole 50 MHz bandwidth and then ...
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How to find the solution of nonlinear least square (NLS) equation for freqeuncy estimation

I am struggling to understand the theory of parametric methods for power spectral estimations of line spectra. And I want to find the solution of nonlinear least square (NLS) method for estimating ...
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Formula for PSD across an axis of a 2D output

Consider a 2D stationary input $e(x,y)$ and a 2D real convolution function $h(x,y)$. Let $S=h*e$ be the result of the convolution of $e$ by $h$. If needed, we may assume $e$ is isotropic (spectrum ...
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PSD graph of GPS L1 Signal on MATLAB

I'm trying to analyze GPS L1 C/A signal on MATLAB. I could generate the PRN codes(binary signals). After I add NAV Data to the PRN code using modulo 2, I need to modulate it using BPSK. I also could ...
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Normalize a Mel-Spec over which axis?

I have to find out: how to normalize a Mel-spectrogram.(for mashine-learning purpose) However, I don't know which axis has to be transformed. The spectrogram S is of shape (m x n) where n are the ...
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1answer
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Analytically determine a PSD from a transient function

This question is related to a series of questions I have asked about the units of PSD and ESDs. I include it as a separate question as it may have worth in isolation. As I understand it to compute ...
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140 views

The Fourier transform of a damped cosine and the units of the result

If I take a simple transient voltage signal of the form $$f(t) = V_p e^{-t/\tau} \cos(\omega_0 t)$$ and take the Fourier transform in the normal way $$F(\omega) = \frac{V_p}{\sqrt{2 \pi}} \int^{+\...
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Power spectral density of surface roughness

I am currently working on understanding how visually and intuitively the power spectral density is the fourier transform of the autocorrelation of a signal. I was wondering if anyone had a good ...
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1answer
44 views

Peak to Average Power Ratio of an exponentially increasing signal

I am having an exponentially increasing sinusoidal signal. After sampling, I am dividing the signal into frames of length 128 and doing windowing operation with a hanning window of length 128. Then ...
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How to applying window function to get same result with pwelch in MATLAB

I'm trying to calculate the power spectral density (PSD) to analyze signal power. To do so, I wrote a MATLAB code with the great help of others and below is my code. ...

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