Questions tagged [cross-correlation]

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331 views

What is the meaning of positive and negative shift in signal correlation?

If $x(t)$ and $y(t)$ are real valued signal then from this page cross correlation between them is defined as \begin{align} R_{XY}(\tau) &= \int_{-\infty}^{\infty}x(t)y(t-\tau) dt\quad\text{+ve ...
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0answers
784 views

Basics of Normalizing Cross-Correlation with a View to Comparing Signals

I'm trying to understand how cross-correlation is used determine the similarity of two signals. This tutorial offers a very clear explanation of the basics, but I still don't understand how to use ...
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1answer
3k views

Comparing multiple signals for similarity

I have multiple (between 2 and 100) signals and need to determine when a significant number diverge from the rest. We're exploring machine learning techniques, but we also want tackle this as a signal ...
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1answer
75 views

Cramér-Rao lower bound

I have been trying to implement the Cramér-Rao lower bound from the paper - A reference-free time difference of arrival source localization using a passive sensor array (eq. 6 and eq. 7). $$ \...
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2answers
260 views

Interpolation of audio for new frames

I am trying to upsample a video by existing frame interpolation techniques. In the process, I realize that I also need to interpolate the audio signal for the new frames so that the audio signal is in ...
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1answer
142 views

Findin the source direction using cross-correlation function

I am new to DSP and I'm working on the following problem. We have a sound source in the far field and a microphone array consisting of two microphones with distance d. We want to determine the source ...
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2answers
113 views

Two different definitions of cross-correlation

I have come across two different definitions of the cross-correlation function: $$ R_{XY}(\tau) = \int_{-\infty}^{+\infty} x(t) y(t+ \tau) dt $$ and $$ R_{XY}(\tau) = \int_{-\infty}^{+\infty} x(t)...
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2answers
96 views

Interpolation of missing audio signal in a video sequence

Suppose there is a video sequence and there are some frames for which the audio data is missing. I want to interpolate the missing audio data on the basis of the correlation of the audio signal with ...
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1answer
35 views

Why is the sound field intensity due to $K$ point sources given by $ I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)$?

I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below. Statement: 1. We ...
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1answer
348 views

Problem understanding the Expectation Operator

I know that the Expectation Operator $E\{x\}$ four discrete values is $$ \sum_k \alpha Pr(x = \alpha_k)$$ and its very intuitive when speaking out a formula which contains the Expectation Operator. ...
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1answer
1k views

GPS Coarse Acquisition PRN Codes

Are the actual 1023 bit sequences for each of the 32 GPS satellites available to consumers? I found the IS GPS 200 but it doesn't list the entire sequences. Are verified sequences available for ...
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2answers
166 views

Cross-correlation peaks in acoustic multi-path conditions

Consider a speaker and a microphone are placed in a multi-path environment and the audio signal to be transmitted is LFM(chirp) signal, the time of arrival of the audio signal is computed by cross-...
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2answers
440 views

GPS CA Signal Acquisition

The coarse acquisition C/A GPS signal has a symbol rate or chip rate of 1.023 Mcps with code period of 1 ms. The code bandwidth is +/-1.023MHz (to 1st sinc nulls). I'd like to record this signal using ...
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1answer
60 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
487 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
118 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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1answer
663 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
571 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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2answers
1k views

Trouble with time-syncing two radio signals using cross-correlation

I posted a similar question a while ago here (I'm posting this follow-up since I'd like to focus more on cross-correlation now). I have a setup where I have two software-defined radios connected to ...
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0answers
122 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
50 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
940 views

Time Alignment of 2 Sensors Sampling the Same Signal with Different Hardware Delays

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
288 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
121 views

Group delay using cross correlation?

An input signal + (thermal) noise travels through a channel and can be measured at its output. Is it possible to use cross correlation between input and output signal to measure group delay? If not, ...
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1answer
300 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
380 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
698 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
30 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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1answer
4k views

Convolution and Cross Correlation on 2D Image

I have read that convolution and cross-correlation are the same thing, but convolution flips 180 degrees (images), or time reverses (sequences) the kernel, before performing the elementwise ...
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3answers
919 views

Downsampling from 100Hz to 60 Hz

I have two sensors measuring a single time varying signal . The first sensor (reference sensor) is sampling the data at 60 Hz and the second sensor (test sensor) is sampling the data at 60 Hz. I ...
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1answer
73 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
439 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
436 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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3answers
321 views

Interpreting this plot cross-correlation

I have an input signal $x(t)$ that is a white Gaussian random signal with mean 0 and variance 1. The signal $y(t)$ is the output of a linear filter with impulse response $$h(t) = |\operatorname{sinc}(...
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1answer
958 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
668 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
265 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
173 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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2answers
192 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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1answer
638 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
3k 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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2answers
90 views

audio signal time delay estimation(TDE) in indiviual and separate mics

common TDE problems algorithms(such as GCC) often require audio signals in different mics concurrently, however, is it possible to estimate audio signal time of arrivals(ToA) in different mics ...
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1answer
979 views

Cross Correlation in Java (Android) Using FFT (Frequency Domain Convolution / Correlation)

I want to implement cross-correlation with the start-symbol and the signal using FFT. I zero-pad both signals to length N = x.len + y.len -1 Using the convolution theorem: ...
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0answers
80 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
403 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
2k 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
611 views

Cramer Rao Lower Bound for Cross Correlation (Time Shift Estimation)

UPDATE 2 Okay, I think I understand now why the defined CRLB is not applying to my use case. In my use case, we have very high SNR, and the the first signal $x_1$ is always the same. So the classical ...
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1answer
222 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
946 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
385 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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