Questions tagged [spectrum-estimation]
The spectrum-estimation tag has no usage guidance.
59
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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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Calculate 1D Power Spectrum from 2D Images
Imagine satellite images, these are irregularly sampled in the X and Y directions, and the shapes are, of course are oddly off.
We now want to estimate a 1D power spectrum from the whole image to ...
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How Are MATLAB's `cpsd()` and SciPy's `csd()` Related?
I am trying to determine an estimate of the H1 transfer function between two acceleration signals in Python. To do this, I am calculating Pyx using ...
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5
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2
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Detecting Pattern from Signal Data by Gaussian Mixture Model?
I'm a machine learning newbie.
I have sensor data which is generated by several sensors.
The data is a series of 'time's. (it is not labeled, in other words, I cannot know which sensor generates ...
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1
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Understanding the Windowing Method in PSD Calculation
I have some issues understanding the use of a window (it doesn't matter which one) to calculate the Power Spectral Density of a signal.
For example say I want to use the hann window, with $N = 1024$,...
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2
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An explanation of parts of the MUSIC Algorithm for someone without a background in signal processing?
I've been looking at every tutorial and paper I can find, but I keep losing the intuition behind what's going on when they get into the matrix operations.
There is a step in which the signal vector ...
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4
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1
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813
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Practical cross-spectrum estimation using Blackman-Tukey approach
I would like to estimate the cross-spectrum of two signals using the (lag-windowed) Blackman-Tukey approach but I'm having difficulties with proper practical implementation. As defined in equation 2.8....
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Estimation / Reconstruction of an Image from Its Missing Data 2D DFT
Given the 2D DFT of an image i.e. a NxM matrix of complex numbers, with some missing lines (or even partial lines), considering we have zeros in the missing positions.
Any suggestions for an ...
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Are there algorithms to invert a magnitude spectrum?
I have a speech signal and have calculated the magnitude spectrum for the signal. Is it possible to get a good estimate of the original signal from the magnitude spectrum, seeing that phase ...
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0
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Running window design for irregular or nonuniform time series
I have to deal with multiple time series $X_n$ that are non-uniformly or irregularly sampled at increasing times $\Theta=\{t_k\}_{k\in \mathbb{Z}}$ ($ t_k<t_{k+1}$). In case this could help, this ...
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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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A few questions about the output value of dsp.SpectrumAnalyzer
I am testing the output values of dsp.SpectrumAnalyzer for a sine wave mixed with white noise. The $\sigma^2$ of the white noise is 1e-4, so I use 0.01*randn(1024,1)...
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Is there an efficient algorithm to precisely find the spectrum of a finite discrete signal consisting of incommensurable frequencies?
If we periodically sample a continuous band-limited signal at a sufficient sampling rate, we can estimate its spectrum by using Discrete Fourier transform (DFT). DFT of a finite discrete signal sample ...
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2
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Computable Time-Frequency Distribution without Cross-Terms
Context:
I have a single receiver that is receiving multiple signals. Each signal has a few strong harmonics, but I don't know the fundamental frequency. I would like to display them on a spectrogram ...
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Simplest way to generate AR(2) process on MATLAB
As part of a project I need to use autocorrelation method of estimating model paramters of an autoregressive process on MATLAB.
Can anyone tell me the simplest way to generate an AR(2) process on ...
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Estimating the PSD (Periodogram): How do you find the Expected Value
The periodogram $\widehat{P_x}(e^{jω})$ is an estimate of PSD $P_x(e^{jω})$ and for mean-square convergence -
$\lim_{N \rightarrow \infty}E\left\{\widehat{P_x}(e^{jω})\right\}=P_x(e^{jω})$
My ...
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What is the computational complexity of Spectrum Estimation Algorthms and What they depend upon?
There are lots of spectrum estimation techniques, each with some pros and cons.
Algorithms like:
Music
Welch's method
Yule-Walker AR method
Periodogram
modified covariance method
multitaper method (...
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2
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392
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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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Analysing mp3 quality with spectrum, how to interpret the results?
When comparing spectrum images between two different audio sources in order to determine which has better quality, I sometimes come to an impasse. For example, consider the following images from two ...
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Estimation of occupied frequency bins (location of non-zero fourier coefficients)
I'm working in circuits fields and I am not very familiar with spectrum sensing techniques.
Is there a method to identify location of non-zero Fourier coefficients of a signal (just locations, not ...
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0
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765
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Welch Method FFT Python - Scaling factor?
I've been implementing a Welch method FFT and I am trying to work out the correct scaling factor that should be applied to the output of the function so the PSD is accurate because at the moment it's ...
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0
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340
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How to derivate in the frequency domain
I have two Time Domain functions, $f_1(t)$ and $f_2(t)$.
I have both Fourier Transforms, $F_1(\omega)$ and $F_2(\omega)$. Functions $f_1$ and $f_2$ are not independent and, in fact, $f_1$ is also a ...
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possible spectral leakage
If I perform a FFT of a real signal which is limited on time (for example the atmospheric pressure in time from 0s to 5000s), is it possible that the fact that is limited on time can affect the FFT ...
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2
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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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1
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233
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Power Spectrum Estimation of three sinusoids in white noise
Let's assume we have a random process consisting of three sinusoids in white noise:
$$x[n] = 3 \cdot \sin(ω_1 \cdot n + ϕ_1) + 5 \cdot \cos(ω_2 \cdot n + ϕ_2) + 2 \cdot \sin(ω_3 \cdot n + ϕ_3) + v[n]$$...
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1
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An equality in DOA estimation
Suppose we use a uniform linear array for DOA estimation. Assuming neither of the signals and noise are correlated, and the noise power on each sensor is equal, it's well known that the covariance of ...
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2
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141
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The frequency spectrum of a static non-linearity driven by colored noise
Does there exist any straight-forward theory that can explain what happens to colored noise that passes through a static non-linearity? That is, if you have colored noise
$$v = H u \, , \; u \sim N(0,\...
- 1,035
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1
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148
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Accurate frequency estimation with closely-spaced tones
I have a MIPs-limited DSP platform where I am taking an FFT of a streaming audio signal at regular intervals. I need to find the top 4 amplitude peaks and their corresponding frequency for every frame....
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What is the best way to decide whether a periodic signal is present in a noisy environment with a limited number of samples?
Suppose I have few samples (e.g. 20) of a decaying sinusoidal function and I am heavily noise-dominated (SNR ~1, noise is Gaussian or Poissonian). Let's think of e.g.
\begin{equation}
y(t) = A \, \sin(...
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How to eliminate a cyclic spectrum estimation window artifact?
I am using an implementation of the averaged cyclic periodogram (section 3.2.4 in Antoni, Jérôme. "Cyclic spectral analysis in practice." Mechanical Systems and Signal Processing 21.2 (2007):...
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Power Spectral Density units
I am trying to compare power spectral density values (obtained from dsp.SpectrumAnalyzer) with PSD values obtained from hardware which has a VSA.
MATLAB's documentation says that " The power spectral ...
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Explanation of Spectral Line Splitting when AR process is overmodeled
In the book Statistical Digital Signal Processing and Modeling by Monson Hayes, it is shown (in section 8.5.1) that when an AR(2) process described by the following difference equation
$$x(n) = 0.9x(n-...
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Periodogram Averaging
FOR CONSISTENT ESTIMATION OF PSD
Let, $x_i(n)$ be a sequence of random variables for $i=1,2, ... , K$ uncorrelated realizations and $\widehat{P}_{(i)}^{per}(e^{jω})$ is their corresponding ...
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Anyone know what algorithm the Spice AC Noise Analysis uses?
Anyone know what algorithm the Spice AC Noise Analysis uses?
http://vision.lakeheadu.ca/eng4136/spice/noise_analysis.html
Is it some spectral modeling synthesis? I.e. that it estimates the main ...
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Proving Convergence of a limit related to Cross-Spectrum Estimation
Proving asymptotic covariance of Cross-Spectrum Estimation I came across this mathematical problem:
Consider two constants $M,L$ such that $M\to \infty, L \to \infty \hbox{ and } \frac{L}{M} \to 0$, ...
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0
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How do I convert the Amplitude from Power/Amplitude spectral density?
I recently started working on PSD of seismic signals. PSD signal can be expressed in 2 ways. One in ($PSD=g^2/Hz$) and other in $PSD=((meter/sec.^2)^2/Hz)$ and $ASD = \sqrt(PSD)$.
More details have ...
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Wrong amplitude in the FFT for 10 seconds measured signal
I measured a signal with the Osziliscope that I generated with a signal generator. The signal is a pure sine wave with a frequency of 1 kHz and a peak amplitude of 2.5 V, I measured the signal for ...
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0
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Interpreting scipy spectrum from audio signal
I have recorded some audio and would like to obtain a spectrum from it. As the audio is a real valued signal, I figure that I could perform a FFT with some window and obtain a spectrum for that period....
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0
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Complex Spectral Phase Evolution (CSPE) Performance depending on signal windowing?
I am look into CSPE. "Signal Analysis Using the Complex Spectral Phase Evolution (CSPE) Method"
The method is simple. It compares the original signal's FFT and shifted signal FFT in phase domain so ...
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Second moment properties (covariance) of lag window estimator
We know that the lag window estimator of the spectral density is defined as:
$$S^{(lw)}(f)=\int_{-f_{(N)}}^{f_{(N)}}W_m(f-\phi)\hat{S}^{p}(\phi)d\phi=\sum\limits_{\tau=-(N-1)}^{\tau=N-1}w_{\tau,m}s^{(...
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Spectral peak location estimation using complex DFT
In this paper a simple method to estimate a spectral peak is proposed, by using quadratic interpolation between three samples of the DFT of the signal. Namely, the position of the peak relative to the ...
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Finding the phase and frequency of a tone with Doppler. What is wrong in the code?
I am trying to find the phase and frequency of a single tone having a small Doppler (10 Hz). I have the following code. The integration time for the operation (the length of the time vector) is ...
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Spectrum Inversion Problem
For a signal with $f_c$ (Centre Frequency) $=1200MHz \,\,$ and $BW= 100MHz$ ,which of the following Sampling Frequency ($f_s$) will cause spectrum inversion:
A)$\, 287.5MHz \quad$ B)$\,575MHz \quad$...
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Accurate estimate of the power spectrum at frequencies of with very low power
I am wondering if anyone knows of situations where one would need to accurately estimate the power spectrum of a signal at a frequency where the power is known to be very low, much lower than at other ...
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1
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233
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Number of antenna to perform MUSIC algorithm
When the MUSIC algorithm is used for direction of arrival (DOA) estimation it can identify up M-1 signals, where M is the number of array elements. MUSIC can also be used for spectral frequency ...
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141
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Sub-Band Extraction Techniques for Complex (I/Q) Signal
There is an application which processes Complex I/Q signal of 100 MHz bandwidth and it is required to extract independent sub-bands from this bandwidth at different center frequencies and bandwidths. ...
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what is the best technique to detect a given signal : energy detection, autocorrelation, and matched filter based sensing, CRC?
In order to detect the presence of a signal impaired by noise, what is the best technique (best metrics) one can use ?
energy detection,
autocorrelation,
matched filter based sensing,
CRC
data ...
user47976
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1
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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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1
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395
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Defining frequency axis for periodogram
I am trying to simulate example 8.2.2 from Hayes, Statistical Digital Signal Processing and Modelling, on MATLAB.
Let $x(n)$ be a WSS process consisting of random phase sinusoid in unit variance.
$$ ...
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1
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171
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Welch's overlapped method for amplitude by frequency estimation
pwelch is a useful matlab function for computing real/magnitudes for power using WOSA method, but I'd like to apply the same thinking in order to output complex pairs for amplitude (not power) ...
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