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# Questions tagged [coherence]

Coherence is a stastic to examine the relation between two signals.

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1 vote
2 answers
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### DFT Matrix Oversampled In Frequency?

Edit 2: I am trying to replicate results from this paper Compressed Sensing with Coherent and Redundant Dictionaries. On page 3 the "oversampled DFT" is mentioned as an example of an "...
• 13
0 votes
1 answer
76 views

### Difference between Coherent and Non-Coherent in Fibre Optics?

I have been given the following equation to show the difference between coherence and non-coherence in optics and how the third term represents the interference between two optical pulses. Can someone ...
0 votes
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44 views

### Is it possible to use np.fft.fft to pick out the Fourier coefficients from one timepoint, at a specific frequency?

I am trying to apply np.fft.fft on a 2D array of data of shape (98, 1024), where 98 is the number of trials and 1024 is the sampling rate in Hz. I am trying to find ...
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 ...
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2 votes
0 answers
99 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
74 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
91 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
124 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
89 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-...
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1 vote
0 answers
32 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
121 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
110 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
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95 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 ...
0 votes
0 answers
101 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 ...
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1 vote
1 answer
425 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 ...
2 votes
3 answers
105 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 ...
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0 votes
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77 views

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 vote
1 answer
175 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 ...
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 ...
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1 vote
1 answer
573 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 ...
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-1 votes
1 answer
358 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 ...
1 vote
1 answer
268 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 ...