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Questions tagged [cross-correlation]

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2
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1answer
71 views

Deriving the Langrangian interpolation polynomials in Cook-Toom convolutions

I'm working through Blahut's 'Fast Algorithms for Signal Processing'. Trying to develop an intuition for the Cook-Toom algorithm for convolutions as used by Lavin and Gray in their Winograd paper for ...
2
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1answer
103 views

GCC-PHAT for Multiple Sound Sources

Can GCC-PHAT be used to detect multiple time-delays (that is, having multiple acoustic sources simultaneously)? The documentation for the gccphat(sig,refsig) ...
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0answers
28 views

Pearson correlation coefficient vs mutual information

I recently computed both the pearson coefficient and the mutual information of two time series as well as the corresponding error bars, and what I find out in the end is a significant level of ...
1
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1answer
148 views

Cross correlation to compute delay between two lines does not work

I have zero experience with signal processing, and I am stuck in what I believe to be a very simple problem. I am trying to use the xcorr in matlab to find delay between two signals. The signals are ...
2
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1answer
100 views

Reduce noise of sensor by combining two

I've had the basics of signal in university but little real-life practice. I've got an acceleration sensor with a digital output signal (signed 16 bit value). This signal is a little noisy. The ...
2
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1answer
159 views

Discrete Time Fourier Transform (DTFT) cross correlation property

I came across this property of the Discrete Time Fourier Transform (DTFT) and I am having a tough time proving it. In general, consider two real signals $x[n] \: \& \: y[n]$. If $$ x[n] \...
3
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2answers
334 views

Is maximizing hamming distance the same as minimizing correlation?

For the design of an error correcting code, I might wish to maximize the distance between the codewords $\sum a_i \oplus b_i$. For spreading sequences I'd like to minimize the cross-correlation at $t=...
0
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0answers
29 views

Decorrelation for Adaptive Feedback Cancellation: How does it work?

I am going through lecture slides on adaptive feedback cancellation right now, and several decorrelation measures are mentioned. As I understand, these are important in order to avoid a bias in filter ...
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0answers
44 views

Measure How Much Pattern Is Present In Signal

I have some pattern signal. This pattern signal will be played in noisy room. Then it will be recorded and processed. I need to show that my processing algorithm improves the signal. My idea is to ...
3
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1answer
200 views

Strong (0,0) pixel among an otherwise normal cross correlation peak

I am working on an imagery registration problem via cross-correlation and am seeing a weird phenomena sometimes. First, I am pre-processing each image by subtracting the mean image brightness from ...
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0answers
31 views

Phase lag changes cross spectrum

I have a same noise passing through two different ARMA filter. The autospectrum of first filter is given by S11=G1*G1*S_in where S_in is input spectrum created by set of random numbers. Similarly the ...
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2answers
1k views

How to compare and measure the similarity between two between two signals?

I'm working on different sensors data, the question is this: I have two signals (coming from two different sensors measuring two different phisical charactheristcs of the same "object"). I know for a ...
1
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1answer
107 views

Why the spectral coherence is unity for all frequencies between single-frequency time series and itself

In the example below, I am plotting the coherence between time series and itself. The time series do has one frequency.The coherence magnitude was one for all frequencies. I wonder why it is not zero ...
1
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2answers
124 views

Cross-correlation of filtered random processes

I have a wide-sense-stationary (WSS) process $\{x(t)\}$ and two linear filters with impulse functions $h_1$ and $h_2$. Let $\delta(\omega)$ be the power spectrum of $\{x(t)\}$ and $$H_1:\omega\...
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1answer
30 views

Detecting multi-path propagation when one acoustic signal is dominant

I am sending an acoustic signal from a source to a receiver where there are limited number of paths the signal can travel. I want to detect if there has been multipath propagation or not when one path ...
1
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1answer
206 views

Faster Algorithm to convolve/correlate two sparse 1-D signals in python (or any language)

I have two signals which I need to correlate or convolve. Each signal is sampled non-uniformly and the values of the signal I have with me are the timestamp and the magnitude of the signal at that ...
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0answers
18 views

match a pattern in a stream of bits

I feel my question is somewhat related to this, but I'm not sure how to do what I want. I get transmissions of ~1000 bits at a time, which may be corrupted by noise. To try and infer data from ...
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1answer
92 views

Correlation between frequency and initial phase estimates using FFT

Why is there a high negative correlation between frequency estimation errors and initial phase estimation errors when measured using FFT? I have a simple code showing this negative correlation. is ...
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0answers
60 views

Finding recorded sub-signal in the original audio signal

I have the original record of a song, and some fragment of the same song recorded by a microphone. I need to find the time where the fragment is appearing in the original. I have tried to use cross-...
0
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1answer
83 views

How to group similar patterns together that are shifted along the x axis?

I have a set of time series plots that are shifted along the x-axis. I am looking for an algorithm using which I can group them together. My end goal is to average them. While reviewing the ...
2
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1answer
147 views

Correlation of independent random processes

Suppose $X(t)$ and $Y(t)$ be two independent random processes. Is $E(X(t_1)Y(t_2))$ necessarily zero?
5
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1answer
306 views

Maximum cross-correlation coefficient value for time delay estimation

I am using cross-correlation for time delay estimation of two synchronized recordings ($x_1$ and $x_2$) of a fixed sound source from two different locations. I understand that the delay is associated ...
0
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0answers
255 views

Cross Correlation as Noise Reduction, is this possible?

If I have two sensor measuring the same signal but from two different locations from the source, and I get two different readings of the signal, each with slightly different noise. Is there a way to ...
2
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1answer
110 views

Cross Correlation dimensions

I have been trying to do the cross correlation of two signals, and I am expecting the output to have the same dimensions as the two signals have. However what I am seeing is that the cross correlation ...
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0answers
23 views

DOA estimation of moving, radiating source in the near-field with nonuniform Doppler shifting

I am trying to estimate the DOA of a radiating source using two passive sensors. In the case of a stationary source, I find the lag $k$ of the maximum in the sample cross-covariance sequence $E \...
0
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1answer
88 views

Signals Cross Correlation from Their Power Spectral Densities?

For two real valued signals $f$ and $g$ with their corresponding power spectral densities $|F(k)|^2$ and $|G(k)|^2$ Is there a way to get an intuition of how correlated $f$ and $g$ are just by looking ...
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1answer
52 views

What is the physical meaning of the cross-spectrum of two signals measured at two locations and different moment?

I am working with steady state pressure field measurement where sound pressure at multiple locations in the field needs to be measured. In my case, more than one microphone existing in the field at ...
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0answers
66 views

Threshold for CAF Surface

I am calculating a time partitioned Cross Ambiguity Function (CAF) by adding the surfaces of different time-sectioned CAFs together. Meaning, I calculate a CAF using 10 seconds of IQ data, calculate a ...
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0answers
87 views

Find a simple sine wave buried within noise, FFT or cross-correlation?

My recorded signal x = s + v, where s = A*sin(ωt) and v = noise. SNR < 1 or ~ 1. So the sine wave is buried under a lot of noise. I need to compare the relative amplitudes of s for each recording ...
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1answer
293 views

Time delay estimation between two complex signals(IQ)

I need to time align two complex signals. The two signals obtained were at different RF frequency before digitisation. So,I have two complex signals(IQ) and I need to do delay estimation and apply ...
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0answers
61 views

Time delay estimation of signals increasingly decorrelated

The problem may be summarized as follows: I have a stochastic signals and I want to measure an increasing delay, as depicted in the following picture. The picture represents the signal as it is being ...
2
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1answer
837 views

Normalized cross-correlation in frequency domain

I never worked with signal processing and never really used Fourier transforms before, still I am working on a project consisting on taking the output of an accelerometer to detect some movement ...
1
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1answer
106 views

Confusion in the derivation of convolution formula [closed]

$$x(t)=\int_{-\infty}^{\infty}x(\tau)\delta(\tau-t)d\tau=\int_{-\infty}^{\infty}x(\tau)\delta(t-\tau)d\tau$$ Due to linearity, $$y(t)=T\{x(t)\}=\int_{-\infty}^{\infty}x(\tau)T\{\delta(\tau-t)\}d\tau=\...
2
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1answer
2k views

Matched filter and cross correlation in digital processing

I am very new to signal processing, and a bit confused with the matched filter. Assume that I have a time series and a specific waveform I need to identify in it. By definition: a matched filter ...
2
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1answer
70 views

False negative probability of cross-correlation

Suppose $D$ is a string of length $L$ where its values are uniformly distributed in $[-a,a]$. Also, all values of $D$ are independent (i.i.d). $X$ is a noisy version of $D$ in this way: $X=D+N$ where ...
2
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1answer
907 views

GCC-PHAT (Generalized cross correlation) always peak at delay=0 on real audio signal

I have studied the GCC-PHAT algorithm to estimate TDOA on audio signals at 2 mics. Here is my MATLAB implementation: ...
0
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2answers
612 views

Why can Sum of Squared Differences (SSD) seen as cross-correlation?

In this slides, on page 4, the SSD can be seen as cross-correlation: http://www.lira.dist.unige.it/teaching/SINA/slides-current/pyramids.pdf http://www.cse.yorku.ca/~kosta/CompVis_Notes/ssd_cross-...
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0answers
221 views

Preamble detection using cross-correlation

I am generating a preamble with a sequence of [1 -1 1 -1 1 -1....] and spread with a barker-11 sequence. Now, the transmitted signal becomes [B(Barker), -B(Inverse of Barker), B, -B,....]. In channel, ...
0
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2answers
97 views

Correlation between 2 signals of uneven dimensions

As a part of my work, I am trying to correlate the audio signal in a video with the pixels of each frame. The steps I follow are: Audio sampling rate and frame rate of the video are known. So, ...
1
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2answers
242 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 ...
2
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0answers
601 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 ...
4
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1answer
2k 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 ...
0
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1answer
69 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
203 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 ...
0
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1answer
127 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 ...
0
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2answers
103 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
82 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 ...
2
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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 ...
0
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1answer
293 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. ...
1
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1answer
826 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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