Questions tagged [cross-correlation]

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104 views

How to find correlation between two signals regarding peaks?

In a super-resolution task, I try to predict the higher frequencies of a signal. X low-resolution (lr) is my input and Y high-resolution (hr) is the target. Where X contains only frequencies till 2 ...
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1answer
73 views

Why Cross-correlation work better than Generalized Cross-correlation GCC-PHAT in MATLAB?

Fs = 192000; t = 0:1/Fs:(0.01-(1/Fs)); F1 = 10000; x = 1*sin(2*pi*t*F1); nSamplesGausswin = length(t); w = (gausswin(nSamplesGausswin))'; s = w .* x; this is ...
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2answers
563 views

Convolution v.s. Cross Correlation in Digital Image Processing

I understand that from mathematical point of view, only difference between Convolution and Cross Correlation is that Convolution is commutative, while Cross Correlation is not. In many articles ...
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140 views

Why are the Fourier transforms of autocorrelation and cross-correlation different?

I'm almost definitely misunderstanding this, but as far as I can tell we can equate the Fourier transform of the auto-correlation function $R_{xx}(\tau)$ with power spectral density (PSD) like so: $\...
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1answer
33 views

Variance of circular vector correlation

Say I have two zero-mean vectors, with a size of N and the translation between them is k. Say the image signal std is $\sigma_s$ and the noise std is given by $\sigma_n$. What is the variance of the ...
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20 views

What happens to crosscorrelation of two noise generator if one of them were to be inverted

I have two noise generator u1 and u2 and their crosscorrelation is given, what will happen to this crosscorrelation if u2 or u1 were to be inverted?
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52 views

How to extract information about each constituent 'wave' of a signal?

I have a vector containing wind speeds sampled at 1Hz over ten minutes. I have applied a lowpass filter of 0.25Hz to get only the wind speeds I am interested in. I now want to use MATLAB to ...
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1answer
38 views

Synchronize device to audio stream - Approach

I am working on a device which's actions should be synchronized to the audio played. The audio stream is known in beforehand and can be altered to contain signals for the synchronization. But the ...
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1answer
135 views

Difference Fourier Shift Theorem and Cross Correlation Theorem

can someone explain me the difference between the Fourier Shift Theorem and the Cross Correlation Theorem? The shift theorem says that a delay in the time domain corresponds to a linear phase term ...
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2answers
63 views

Transforming digitized noisy signal before applying cross-correlation

I'm trying to grasp the concept of cross-correlation as it applies to CDMA in the GPS C/A signal where noise is involved and the SNR is low. My understanding is that before calculating the cross-...
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1answer
113 views

Autocorrelation Computation with MATLAB

I have done the computation of the autocorrelation of a sequence (vector), here called "frame", and I have plotted it. Here the code: The resulting graph is: I do not understand the position of the ...
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345 views

Matlab normxcorr for 1D signals

I am very surprised not to find a version of normxcorr2 for 1D signals in Matlab ! I implemented something like that by hand (with 2 for loops, and normalizing the template as well as the window under ...
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66 views

Simulink cross correlation issue

here is the Simulink model that i'm using : The matlab function script : function tau = fcn(sig,refsig) tau = gccphat(sig,refsig); The errors :
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1answer
46 views

Synchronising audio in realtime without knowledge of original signal

Was doubting whether this is the right SE forum to ask my (elaborate) question, so don’t hesitate to let me know if it’s not. Also, if anyone knows of a better way to title the question, feel free to ...
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3answers
325 views

How to reliably compute the group delay of a comb filter

I applied the following FIR comb filter in real-time: y[n]=x[n]-x[n-40] Since this is an FIR, the group delay is D=(N-1)/2=20 samples. After applying the filter ...
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1answer
83 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 ...
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1answer
170 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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32 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 ...
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1answer
213 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 ...
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1answer
141 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 ...
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1answer
223 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] \...
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2answers
413 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=...
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1answer
224 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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1answer
56 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
3k 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 ...
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1answer
132 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 ...
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2answers
199 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
34 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 ...
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1answer
320 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
20 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
111 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
71 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-...
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1answer
85 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 ...
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1answer
177 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?
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1answer
377 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 ...
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0answers
352 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 ...
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1answer
159 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
25 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 \...
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1answer
100 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
66 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
77 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
123 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
427 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
69 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 ...
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1answer
1k 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 ...
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1answer
117 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=\...
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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 ...
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1answer
71 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 ...
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1answer
1k 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: ...
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2answers
905 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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