# Questions tagged [coherence]

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

65 questions
Filter by
Sorted by
Tagged with
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 ...
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 ...
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 ...
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 $x$ ...
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,...
1 vote
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-...
1 vote
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 ...
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 ...
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: ...
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 ...
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 ...
1 vote
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 ...
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 ...
67 views

1 vote
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
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 ...