Questions tagged [cross-correlation]

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1answer
57 views

finding the audio pulse compression peak in extra-low SNR scenario?

I just want to obtain some general ideas for such a scenario: if the environmental noise is extremely strong and the audio signal at the receiver is extremely weak(for instance, low range propagation),...
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1answer
258 views

Wiener Filter in Frequency Domain: What it does to a specific Frequency?

As I understand Wiener filter in time domain tries to estimate a signal as close as possible to its (original) non-degraded signal using the degraded signal by white noise. $$H(\omega)=\frac{\Phi_{...
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1answer
91 views

Maximum of cross-correlation not moving

I already asked this question here yesterday, but it was very poorly worded I think. I made a much more detailled post explaining my problem of stackoverflow, as it might also be a code problem. Here ...
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0answers
89 views

Common mode signal cancellation on multi-channel system

I have a system consisting of 32 horizontal plus 32 vertical charge sensitive wires. They are part of a particle detector and each one is coupled to a charge amplifier consisting of preamp stage ...
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1answer
511 views

How to find shift between two signals with Cross correlation?

I have calculated the cross-correlation function between to waveforms. I would like to find the shift between the two waveforms from the peak of the cross-correlation function. I am not really sure ...
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2answers
415 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 ...
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0answers
105 views

Subtracting audio signal emitted - trying to use spectral subtraction to localize moving objects

I am a Software Engineer without much signal processing background and currently spending and experimenting to get use to it. My scenario: Assume a speaker and a microphone array. A speaker emits an ...
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1answer
42 views

Why is the correlation of two random markov chains so large?

A very simple python code shows that the correlation coefficient and spearmann rank between two datasets of uniform random numbers drops proportionally to the square root of the number of points in ...
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2answers
642 views

How can I align these two signals? Cross correlation isn't working properly

I have two radios sampling simultaneously, and I am trying to time-align their two signals (they will always start sampling at slightly different times with random delays due to hardware differences). ...
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3answers
242 views

The explanation of $|R_{XY}(\tau)| \le \sqrt{R_{XX}(0)R_{YY}(0)}$

If i said the explanation of $|R_{XX}(\tau)| \le R_{XX}(0)$ is that in the time domain,any signal wave are the same as itself when it doesn't shift.Then what is the explanation of $|R_{XY}(\tau)| \le ...
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1answer
220 views

No cross-correlation between same signal recorded using two different microphones

I've recorded the same audio signal using two microphones located at the same approximate location. However, when checking the cross-correlation using MATLAB (using the xcorr function) it is ...
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0answers
306 views

PHAT filtering for cross-correlation yields wrong results while simple cross-correlation does OK (Python)

I work with two signals, the second being perfectly delayed and attenuated, with no reverberation. I implemented cross-correlation algorithm, which yields me these results: Here is my code for these ...
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1answer
467 views

Autocorrelation of Addition of Two Independent Signals

Given a random signal $ Z \left( t \right) $ which is addition of two independent signals $ X \left( t \right) $ and $ Y \left( t \right) $ with constant parameters $ a $ and $ b $: $$ Z (t) = aX(t) +...
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1answer
26 views

Investigating correlation for unequal signal lengths

I have measurements from two tablet sensors. The first sensor measures the touch pressure applied to the tablet and the second sensor is the acceleration of the tablet (in z direction). The sensor ...
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2answers
146 views

How to calculate time of arrival using room impulse response

I need to find the timestamp of arrival of a particular signal at a receiver location within a room. The known parameters are the room impulse response h for a ...
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4answers
4k views

How to calculate a delay (correlation peak) between two signals with a precision smaller than the sampling period?

I would like to calculate a delay between two signals in MATLAB. Normally, I would do this with a cross-correlation (xcorr), and then calculate the position of the ...
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1answer
64 views

Parabolic fiting for sub-sample precision

I am performing cross-correlation between two double[1024] arrays. I want to track the correlation's maximum with sub-sample accuracy, so I decided to implement parabolic fitting to my code. I used ...
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1answer
342 views

Windowing a signal for FFT

I am actually working on a project involving the cross-correlation of two signals. My cross-correlation code is working fine, but I suspect that I should apply a window to my data set in order to ...
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1answer
344 views

Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
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1answer
513 views

How to calculate a delay between two signals in frequency domain?

Calculation of a delay between two signals is generally done by finding the maximum in the cross-correlation of the two signals (in time domain): $$ \tau_{delay} = \arg\max_\limits{t}(f(t) \star g(t)) ...
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1answer
423 views

Is there any relationship between the convolution and cross-correlation of two signals? [duplicate]

There are two square 2-D signals with the same size $m \times m$, if the result of convolution of those two signals is first picture, And the result of cross-correlation of those two signals is second ...
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0answers
204 views

Frequency Domain Variant of Pearson's Sample Correlation Coefficient?

Suppose that you need to find (i.e. acquire) $x_1$, a short data packet with a known bit sequence preamble (i.e. a PRBS BPSK), in $x_2$, quantized samples recorded from the output of an ADC. You don'...
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2answers
107 views

How to estimate ALL time-delays across MULTIPLE signals?

Imagine there are 100 recordings of the same signal or pattern, but those recordings are not properly aligned with each other in time. In other words, each sample has some unknown time delay in ...
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1answer
501 views

DoA estimation using microphone array

I am using an array of 4 microphones in a square formation. My goal is to estimate the direction (azimuth only) of incoming speech sound. The array looks like this: I have recordings from the array ...
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3answers
8k views

How do I get the phase angle from Cross Correlation?

Im trying to cross correlate two signals in matlab and get the phase difference between the signals. For cross correlation (the idea is to do it without xcorr) I used: ...
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3answers
2k views

Cross correlation, when two signals are “uncorrelated”?

Definition of cross correlation is $$ \int_{\mathbb{R}}s_1^*(\tau)s_2(t+\tau)d\tau $$ I wonder using such definition, when two signals are not correlated? My guess is the following... defining $$ s_{...
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0answers
73 views

Minimum time delay that can be estimated between two sensors

Consider a 1-dimensional toy problem. I have two sensors at different points along the $x$-axis. Somewhere away from the sensors, a disturbance is created which travels towards the sensors, first ...
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1answer
297 views

Cross-correlation - Why is there a complex part after FFT/IFFT when deleting the mirrored part of the spectrum?

I want to detect a special shape in my time series and I apply an matched filter using cross-correlation to increase the SNR. ...
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1answer
1k views

Image Cross-Correlation interpretation

I'm working on this idea of choosing best cover image from given db for image steganography(hiding secret image inside cover). I've started with calculating cross-correlation matrix between images in ...
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1answer
204 views

Finding audio signal time delay: cross-correlation vs. impulse response?

I need to find a time delay between the two audio signals, one comming from one set of speakers, and the other being the source signal that is initialy sent to speakers. I send some noise through ...
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1answer
178 views

Why MATLAB only allows cpsd and mscohere between vectors with the same length?

I am studying the applications of finding coherence in the frequency spectrum between two signals for pattern recognition. I have a recording that is way longer than the sampled signal that I want to ...
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2answers
691 views

Interpolating the peak of a cross-correlation using a centroid

Forgive me if this question is poorly worded, I'm not sure if centroid is the word to use here. Say I want to interpolate the peak of a cross-correlation function in order to get sub-sample delays. I ...
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2answers
365 views

Why do we use white noise to estimate echoes?

I'm interested in the case where I have received a signal as a composition of three echoes of the transmitted signal $x[n]$ (each echo has its amplitude and time delay). I know that in order to ...
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1answer
256 views

Synchronizing 2 seperate speech audio signals

I have two speech signals: one with a man reading a passage, and one with a woman reading the same passage. I want to synchronize these signals so that, for each word, their readings line up. The ...
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1answer
415 views

Finding autocorrelation matrix of an autoregressive process AR(1)

Having that $\ v(n) = [x(n),x(n-1),x(n-2))]^T $, and being $\ x(n) $ an autoregressive process AR(1) with known variance $\ \sigma_v^2 $ and transfer function $\ H(z) ={ 1 \over {1-0.7z^-1}}$, how ...
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1answer
129 views

Calculation of cross-correlation of a system with noise

Having the following system: I'd like to know how to obtain the cross-correlation between$\ w(n) $ and$\ y(n) $ having the following conditions: $\ w(n) $ is a zero-mean white noise with power$\ P_w ...
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1answer
1k views

Obtaining impulse response by means of cross-correlation between input and output

Having a system with an input (sound emitter) that is defined as a unit-variance white noise sequence, and I get the output (sound receiver) so I can measure cross-correlation functions between them, ...
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2answers
982 views

How to preprocess signals prior cross-correlation?

Problem Description I have two devices which are measuring the same inputs and are using them to calculate the same (non-periodic) output signal. The process generating the inputs is deterministic. ...
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2answers
215 views

Autocorrelation function $R_{yy}(t_1,t_2)$?

If $x(t)$ is a zero mean stationary Gaussian process and if $y(t)=x^2(t)$,then $\{y(t)\}$ is called a square law detector process. Now i want to find autocorrelation function $R_{yy}(t_1,t_2)$,that is ...
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0answers
113 views

Choice of axes in 1D cross-correlation of a signal in a 2D space

I am working on a research project in which we present an observer with a target moving in a random walk in a plane in front of them, and record the eye movements they make to track it. We cross-...
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1answer
420 views

Maximum likelihood estimator of active time delay and passive time delay

A typical time delay estimation problem has the model: $$ \begin{align} x_1(t) &= s(t)+ n_1(t) \\ x_2(t) &= a s(t-D) + n_2(t) \end{align} $$ Where $n_1$ and $n_2$ are considered to be ...
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1answer
103 views

perfect sequences

I have heard somewhere that sequences with perfect autocorrelations and crosscorrelations do not exist. I have been searching for an insight into this claim, but have not been successful. Can anyone ...
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1answer
163 views

Response of Linear System to Stochastic Process

Somehow I am getting the variance{u(n)} equal to '0' !! This is the case when I take the coefficient 'a' as real. As it is not mentioned in the question I need to find the solution to this question ...
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1answer
47 views

Can cross-c.(x,y) be positive if signals x and y do not share frequencies?

The question is if the cross-correlation of two signals $x$ and $y$ can be non-zero even if $x$ and $y$ do not share frequencies. My approach is the following: The cross-correlation $\rho_{xy}\left(\...
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1answer
1k views

Efficient Marker Detection for Images

I need to detect a known number of simple markers (chessboard patterns) in a color image efficiently. I implemented normalized cross correlation (NCC) as a pixel shader via WebGL since I need this to ...
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1answer
2k views

Cross-correlation of two signals using matlab

I am trying to measure the similarity between two signals and I am using cross-correlation to achieve this. Following the matlab example, I seem to have accomplished that, however, I do not ...
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1answer
2k views

Correlation as measure of similarity

Normalized correlation is used to measure how similar are two signals. I can understand similarity visually but I haven't seen a mathematical definition for the similarity of 2 signals anywhere. So I ...
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0answers
654 views

Synchronizing signals with different sample rates

I am relatively new to signal processing, so I am still missing some basic knowledge, but I am trying to improve as much as I can. I am trying to synchronize two signals with matlab using cross-...
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2answers
424 views

Why use cross-spectral density to calculate frequency response?

I am taking a class about system identification and currently learning about cross-spectral density. My textbook says that the frequency response, G, of a system can be determined as $$G=\frac{S_{uy}}...
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2answers
638 views

Cross-Correlation of two signals each with independent complex Gaussian noise

The nearest question I can find is here, but it does not have an answer. Say I want to correlate the following two noisy channels: $x_1 = s_1 + n_1$ and $x_2 = s_2 + n_2$, where $s_1$ and $s_2$ are ...