Questions tagged [cross-correlation]

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526 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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238 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
140 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
593 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
9k 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
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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0answers
78 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
348 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
264 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
200 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
808 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
380 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
347 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
522 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
153 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
1k 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
261 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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132 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
438 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
110 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
187 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
48 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
756 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
462 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
727 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 ...
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1answer
5k views

How to normalize output of $\tt scipy.signal.correlate$

I have 2 different signals and I'm trying to cross-correlate then using Python 2.7 and scipy.signal.correlate. How do I normalize my results (such that the max ...
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1answer
3k views

Correlation of two signals at different sample rate

I have a signal $X$ and I want to find signal $Y$ in $X$, I can achieve this by cross-correlation. Signal $X$ is sampled at $8000\textrm{ Hz}$, and $Y$ signal is sampled at $44100\textrm{ Hz}$. My ...
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1answer
222 views

Relationship between time average and cross spectrum

I have two signals $x(t)$ and $y(t)$ which I can sample at arbitrary $\Delta t$ and $N$. I am interested to the signals product time average $\langle x(t)y(t)\rangle_t$. In particular I want to ...
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1answer
347 views

Help in interpreting the auto correlation graph

I want to check if a time series is (a) random (b) independent. For these I am using the autocorrelation (AC). Autocorrelation refers to the correlation of a time series with its own past and future ...
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1answer
3k views

How to find the period of a noisy signal using MATLAB's $\tt xcorr$?

Here is my code: function [ T ] = FindPeriodicity2(x,Fs) ac=xcorr(x,x); [~,locs]=findpeaks(ac); T=mean(diff(locs)/Fs); end and when I pass the signal ...
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1answer
79 views

How to calculate the variation of delay?

I have 1 transmitted signal transmits to the receiver. Every time transmit, I collect data from the receiver, I use the transmitted which I just transmitted and received data, correlate them, then I ...
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2answers
1k views

How to calculate Time Delay Estimation?

I have 2 data files, which links are attached below: Transmitted data Received data Those binary data are read by this MATLAB code: %% EDIT: clear all; close all; format long; ...
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449 views
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1answer
814 views

identification of sounds within audio signals

I am looking for methods to identify sounds within audio files. I was hoping to find some ready-made user-friendly software to do this but haven't found it yet. I am familiar with Matlab and some C++...
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2answers
415 views

Features of a non-periodic signal for comparison

I am looking for comparing a signal (256 / 512 point discrete | non-periodic ) (obtained after extracting some features from the captured image) with a database of around 5000 signals (256 /512 point ...
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1answer
772 views

Time delay estimation in low SNR

So I am interested in finding delay between two noisy narrowband signals,for example, two arterial pulse waveform. I can easily get a correct estimate of delay using cross-correlation method, but it ...
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1answer
461 views

Understanding time delay estimation for GPS?

I really need help to understand these questions which is highlight, for the GPS situation, I hope anyone who has been working in this situation before, please help me to have a clear understanding ...
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1answer
2k views

When to use cross spectral density versus cross correlation?

All my life, I've used cross-correlation to analyze the strength of the relationship between an input signal and the output signal. I use this to determine which ...
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2answers
574 views

Range and motion in received signals by radar

I've got two signals which are consecutive received signals by a radar system. The signals' values are complex (in form $x+\textrm iy$). I have generated a trasmitted signal using the info available. ...
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0answers
449 views

Finding lag times for multiple time series

I have $N$ time series which have unknown time offsets relative to each other. I want to estimate the $(N - 1)$ time offsets, $\tau_{i,i+1}$, which maximise the sum of the cross-correlations between ...
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2answers
13k views

How to compute the cross correlation of two fuctions

I am trying to implement Matlab's cross correlation function but I can't seem to replicate the results obtained when using Matlab's built in function "xcorr". Documentation for xcorr can be found ...
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1answer
772 views

A special case of 2 jointly Weak-Sense Stationary (WSS) stochastic processes

I know that 3 conditions must be met in order a pair of stochastic processes $X(t)$ and $Y(t)$ to be characterized as jointly WSS: 1. $X(t)\;\; WSS$ 2. $Y(t)\;\; WSS$ 3. $R_{xy}(t_1,t_2) = R_{xy}(...
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1answer
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xcorr in MATLAB for periodic function

I have a periodic signal and I want to find it's autocorrelation function. I can calculate it exactly: $$R_{uu}(h) = \frac 1M \sum_{k=0}^{M-1} u(k)\cdot u(k-h)$$ But will ...
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1answer
1k views

Angle of arrival (AOA) estimation using FMCW radar using MUSIC algorithm

I am working with FMCW phased array radar with only upchirps. The range doppler matrix is obtained using the two dimensional fast Fourier transform on multiple chirps. I want to obtain the angular ...
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818 views

Detecting delay and sample drift in audio files (wav, mp3, etc.)

In my application, I have an audio recording with background music. I know which song is playing in the background and have a copy of the original song (wav, mp3, etc.). The goal is to align the ...

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