Questions tagged [coherence]
Coherence is a stastic to examine the relation between two signals.
65
questions
3
votes
0
answers
132
views
Emergence - what constitutes a minimally coherent source that "just begins" to produce stationary interference patterns?
A superposition of two signals with different frequencies will never produce visible (i.e. stationary) interference patterns. Such waveforms will produce spatiotemporal beat patterns, but they rapidly ...
- 131
2
votes
0
answers
96
views
Coherence between two signals at a particular frequency is less than one, yet the corresponding frequency components differ by a scalar multiple
I'm sampling from the functions $x(t)=\cos(2\pi f_0t)$ and $y(t)=\cos(2\pi f_0t^{1.005})$, for one second, where $f_0=300$ and my sampling rate is
$f_s=1000$. ($N=1000$).
A plot of the coherence ...
- 261
2
votes
1
answer
66
views
Is the coherence between two signals defined at frequencies above the Nyquist frequency?
Suppose I sample from two continuous signals, $x$ and $y$, with sampling rate $f_s=1000$ Hz yielding $N$ samples.
A plot using coherence from ...
- 261
0
votes
1
answer
77
views
What is the actual coherence value between two simple signals, one a cosine and the other a sine?
Suppose $f=300$ and I sample from $x=\cos(2\pi f t)$ and $y=\sin(2\pi f t)$ for a period of one second with sampling frequency $f_s=1000$. Then the number of samples is $N=1000$ and the DFT's for $x$ ...
- 261
2
votes
0
answers
101
views
Coherence between two signals: How to convey the underlying idea using spectral decomposition and orthogonal projections?
My question is somewhat similar to one I posted previously
I understand how coherence is defined in terms of spectral densities, but I would be elated if I could explain the basic concept of coherence,...
- 261
1
vote
1
answer
85
views
Constructing spectral components of signals using the Fourier matrix and interpreting coherence using the results
I have an EEG signal of length 2 sec. sampled at a rate of 200 Hz. If $\vec{x}$ denotes my signal in $\mathbb{R}^{400}$, then I can obtain the DFT by computing $W\vec{x}$,
where $W$ denotes the 400-by-...
- 261
1
vote
0
answers
27
views
Is it possible to explicitly express a simple coherence calculation in terms of linear regression?
I'm a mathematician seeking to improve my conceptual understanding of what the coherence between two signals, $x$ and $y$, represents. I know it's analogous to a linear regression coefficient, in that ...
- 261
2
votes
3
answers
93
views
For two signals having a common frequency, w, and differing by a fixed phase shift, why is the coherence even defined at frequencies other than w?
This question is related to one posted a couple years ago at (Why the spectral coherence is unity for all frequencies between single-frequency time series and itself).
Suppose two signals have common ...
- 261
2
votes
3
answers
90
views
For two sinusoidal waves, what does the magnitude of their coherence tell us, and why do the periodogram and csd commands yield incorrect results?
Suppose I have 2 seconds of data sampled at 1000 Hz., and two sinusoids differing only in amplitude and phase shift:
...
- 261
0
votes
0
answers
85
views
Why is there coherence below the cutoff frequency of two high-pass filtered signals?
I record surface EMG signals from two muscles at 1500 Hz. The following preprocessing steps are performed using basic MATLAB commands.
First, I decimate both signals to 500 Hz (Lowpass filtering ...
- 1
0
votes
0
answers
84
views
Coherent detection in fading channel
I want to design an optimum receiver for a fading AWGN channel for ML Detection. I know that in the case of non-coherent communication we have to use an energy detector(even when the fading channel is ...
- 23
1
vote
1
answer
350
views
Magnitude-squared coherence using pwelch function yields different results than mscohere
I am trying to reproduce mscohere function from Matlab.
$$C_{xy}(f) = \frac{\left\lvert P_{xy}(f)\right\rvert^2}{P_{xx}(f)P_{yy}(f)}$$
This is inside Algorithm section in docs for mscohere:
mscohere ...
- 111
2
votes
3
answers
104
views
Identify which of the three signals is closest to a sinusoidal curve
I have some acceleration values from a sensor. These values are reported as x, y and z components of the acceleration. As can be seen in the attached figure, it is clear that the z signal has a clear ...
- 21
0
votes
0
answers
67
views
From Delay Spread to Coherence Bandwidth?
The phase difference of two sinusoids is given as:
| TX --(r)--->RX <------- (Reflection)|
d: whole path from sender to reflecting object
$ \Delta \theta = 2 \pi \cdot \frac{(2d - r)-r}{c} f + \...
- 49
0
votes
0
answers
31
views
the amplitude-frequency spectrum and the phase-frequency spectrum of a coherent packet of radio pulse
Who can tell you how to draw the amplitude-frequency spectrum and the phase-frequency spectrum of a coherent packet of radio pulses?
- 1
0
votes
1
answer
123
views
Coherence for order spectra
The scipy signal coherence function computes for two time series the coherence as a function of the frequency. For rotating systems however, it is sometimes meaningful to analyze the two recorded ...
- 101
1
vote
1
answer
703
views
Fast/Slow Fading: How are doppler shift and coherence time related?
In the literature I've read that fast fading happens if the bit duration is larger than the coherence time of the channel.
The coherence time of a channel is proportional to $\frac{1}{f_{Doppler}}$. ...
- 11
0
votes
0
answers
36
views
Changing Coherence function from float to fixed point
I want to calculate the coherence between two audio signals. After referring a few websites, I found that the coherence is calculated by using the equation $(1)$ which is as follows
$$\rm Coherence = \...
- 59
2
votes
1
answer
394
views
Why coherence function calculation needs averaging of different segments of the signal?
I am trying to understand coherence function calculation. I am working with a non-linear system without any noise. Coherence function is defined as:
I understand that coherence is 1 for N=1, but I ...
- 21
0
votes
0
answers
75
views
Probability of similarity for two random white noises
I'm looking for the method to calculate theoretical similarity of two random noises $x$ and $y$ with mean $0$ and standard deviation $1$, I've got also $12500$ samples of signal, sampled $2.5$ Ga/s.
...
2
votes
3
answers
132
views
What is the physical meaning of coherence bandwidth in mmWave massive MIMO channel?
I am doing some research about millimeter wave massive MIMO channel now.
We first take account about static MIMO channel, cause we only have SISO measurement system now.
We use scanner to move our ...
- 57
6
votes
5
answers
4k
views
Intuitive explanation of coherence
I am a biologist so apologies for the basic question.
I am trying to get an intuitive understanding of what the coherence between 2 signals actually means. I have read a couple of introductory texts ...
- 61
0
votes
2
answers
363
views
Coherent detection in radar and radio signals
Coherent demodulation\detection is usually done via matched filtering in RF signal processing. In radar signals, coherent integration can be done if the phases of the returns are known. In terms of ...
- 131
0
votes
0
answers
517
views
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 ...
- 1
-1
votes
1
answer
194
views
Coherent Radar -- How do we justify it?
How can we justify doing coherent radar when the phase of the return is unknown?
For instance, after a reflection, assuming a stationary target, we should get something akin to:
$$ x_{rx}(t) = |\...
- 29
1
vote
0
answers
43
views
Time spans in coherence computation
Currently I'm writing my master thesis and I'm having troubles with coherence definition. My question is similar to https://stats.stackexchange.com/questions/92412/clear-steps-to-calculate-coherence-...
1
vote
1
answer
323
views
Why is the coherence function unity at all frequencies when only one reading is done?
Several papers on the internet states that the coherence function is unity for all frequencies if only one reading is done, and that the coherence function requires an average of two or more readings ...
3
votes
0
answers
277
views
How to compare imaginary coherence values?
High, I am currently writing my Master's thesis on susceptibility for hypnosis. I am comparing EGG signals of lowly and highly susceptible individuals.
The imaginary coherence is given by:
$$ \...
- 31
1
vote
0
answers
228
views
Mscohere in Matlab-why would the coherence tends to 1 as nfft increases?
Does anyone have a clue as to why -using mscohere- the coherence becomes exactly one for all frequencies if nfft is set to about 190-200. I know it's standard practice to set it to a number that is a ...
- 11
1
vote
0
answers
106
views
Coherence and non-linear interactions
Reportedly, coherence-based metrics are primarily influenced by linearity in phase. However, Klein et al report that coherence is also:
... very sensitive to fluctuations of linearity in ...
- 21
1
vote
2
answers
233
views
Why Coherence is not a valid metric when performing impact excitation?
INTRODUCTION
I have understood that Coherence is a function that explains the linear relationship between an excitation signal and a response signal. I know how it is calculated and why it is bounded ...
- 209
-1
votes
1
answer
79
views
Is it possible to zero-pad series when using MSCOHERE in matlab?
The function fft allows one to zero-pad, and mscohere, after all works with auto and cross spectra, which, presumably, have all been calculated with fft. I haven't found any mention on zero-padding in ...
- 11
2
votes
1
answer
165
views
Cross power spectral matrix from PSDs and coherence using matrix notation
I have a vector containing all the PSD of a series of signals
$\underline{s} = \left[ |S_{x_1x_1}| |S_{x_2x_2}| |S_{x_3x_3}| ...\right]^T$
I also have a matrix $\gamma^2$ containing all the ...
- 141
1
vote
0
answers
88
views
Simulating two signals with a desired coherence
I'm trying to simulate two frequency-domain signals with a desired coherence, and I'd like to check if my idea is right.
To simulate two time-domain signals with a desired correlation, we can use the ...
- 11
1
vote
2
answers
963
views
Why does the addition of noise improve coherence between two signals?
Taking a simple example of the coherence between two signals, each composed of two sinusoids of frequency 100 and 200 Hz, I expect the coherence to show two peaks in the spectrum located at precisely ...
- 255
0
votes
1
answer
1k
views
Should scipy.signal.coherence be 1 for single input and output signals?
I am trying to calculate the coherence between input and output signals. I thought I could work with a single input and a single output time series and calculate the coherence $\gamma^2$ between them. ...
- 13
2
votes
2
answers
316
views
Optimal segment length for coherence estimation
I have a question about the computation of coherence between two signals with Welch's method.
The two signals are relatively short (e.g. 256 samples) and I would like as correct an estimate of shared ...
1
vote
1
answer
374
views
Averaging magnitude squared coherence across multiple time series
In a previous post, A. Donda had suggested that, in order to calculate the average magnitude squared coherence of more than one pair of time series (e.g. y1 and x1, and y2 and x2), one ought to follow ...
- 49
3
votes
1
answer
1k
views
Deciding for the correct way to calculate coherence time
I have to calculate the coherence time of an indoor environment. The signal I am sending is modulated with GFSK, the carrier frequency is about 2.4 GHz and my symbol time is 1 microsecond.
During my ...
- 195
1
vote
1
answer
382
views
confidence interval estimate for coherence
Is there any solution for estimating Confidence interval of coherence derived by Welch method with overlapping segments?
Moreover, the window length is not same for all the observations, only the ...
- 121
2
votes
1
answer
214
views
Multi-taper Coherence, With Tapers=1
I had a question regarding multi-taper estimated coherence. It appears when the number of tapers is set to 1, all coherency values, per frequency, are always 1. It's obvious solving for autospectra $...
- 23
0
votes
1
answer
3k
views
Compute phase coherence between two eeg signals
I have two EEG signals/channels and I would like to compute phase coherence in MATLAB. I have this paper: https://www.nature.com/npp/journal/v39/n5/full/npp2013330a.html but it does not say what Sij ...
- 1
1
vote
1
answer
160
views
Is Spectral Coherence (MSC) dependent to the initial amplitude of the comparing signals?
Given the signals
\begin{align}
x(t) &= A_1\sin(\omega t)\\
y(t) &= A_2\sin(\omega t)
\end{align}
Do $A_1$ and $A_2$ play a role in the $C_{xy}$ coherence estimator? MATLAB's ...
- 13
2
votes
3
answers
3k
views
What is meant by "correlation" when referring to spectral coherence
I've been reading that coherence measures the correlation between two waves as a function of frequency. I also read that difference in phase does not mean less coherence at a given frequency, and that ...
- 23
1
vote
1
answer
560
views
Calculating spectral coherence coefficient (scc) - implementation help
I am trying to calculate the SCC of a cyclostationary signal. I have estimated the Spectral Correlation Function (scf) of the signal using FFT Accumulation Method (FAM). I implemented the following ...
- 15
-1
votes
1
answer
344
views
How to implement Cross Spectral Density [duplicate]
I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image.
Reading wiki1,wiki2,wiki3 from wikipedia, and ...
0
votes
1
answer
256
views
Calculating incoherency in compressive sensing
CS is based on a choice of a sensing basis $\Phi$ relative to a representation basis $\Psi$. There are many well known pair matrices for $\Phi$ and $\Psi$ like random Gaussian and FFT, and also they ...
0
votes
3
answers
6k
views
Phase locking value / phase synchronization
I have pairs of EEG signals filtered to give me just alpha bands. For a machine learning problem I have found that calculating the phase locking value between the alpha signals of these 2 channels ...
- 305
0
votes
4
answers
3k
views
Coherence vs. Magnitude Squared Coherence
currently I am writing my masther thesis. The theory part is about the turbulent wind field generation, where the coherence (not magnitude squared) is used:
$$\text{coh}(f) = \frac{|P_{xy}|}{\sqrt{P_{...
- 101
0
votes
3
answers
459
views
Synchronicity of two signals
I am trying to determine the synchronicity between two oscillating signals. I was attempting to do this by making use of the cross correlation between the two signals and looking at the maximum value. ...
- 51