# Questions tagged [cross-correlation]

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### Channel Impulse Response using USRP(N310) and Gnuradio

I'm attempting to find the Channel Impulse Response using USRP(N310) and Gnuradio. I'm using a single USRP for both transmission and reception. The antennas are positioned 3 meters apart in a hall, ...
92 views

### CFO limit for correct LTE Zadoff-Chu Synchronization

I am working with Zadoff-Chu sequences in a Python simulation of an LTE-like communication system and need to understand the effects of carrier frequency offset (CFO) on these sequences. Specifically, ...
32 views

### Cross-quantilogram method

What is this method in general? What is the main difference between the quantile cross-spectrum (QS) approach developed by Baruník and Kley (2019) and the cross-correlation function (QS) developed by ...
1 vote
132 views

### Proving that the autocorrelation of a signal is the convolution with its time-reversed complex conjugate

I need to prove the property $$f(x)⊕f(x)=f(x)⊗f^*(-x)$$ That is the autocorrelation of a function is the convolution with its time-reversed complex conjugate. I have constructed most of the proof but ...
114 views

### what degree of accuracy does quadratic interpolation add to fft cross-correlation?

I am not a dsp engineer, so I might be missing some obvious background, but I've been doing my best to educate myself. Let me know if there's more info needed. I am using an fft cross-correlation ...
55 views

### Reference signal minimizes the MSE across similar signals with delays

I am dealing with the following problem: I have $M$ signals ($x_1, x_2, \cdots, x_M$), each of length $N$, which are supposed to be similar, up to a certain delay between them and noise. I am ...
1 vote
60 views

### Separate two images using a statistical approach

So I have a fundamental question (for which I can't find a good answer anywhere). Say we have two images (A and B) and their mixed image (C) as follows: Now say that I've been given Image (A) and ...
76 views

### How to simplify several cross correlations used for feature extraction

I have a system where I cross correlate recorded audio signals with several smaller generated signals to extract feature vectors that later I use in a kNN matching. The system works the way I want it ...
37 views

I'm facing confusion about the definition of the convolution between two discrete periodic signals. Basically, the definition of convolution between s and ...
1 vote
40 views

### Detect same point spread functions between two microscopy images

So say I'm given two image datasets (Image 1 and 2 - attached). I want to be able to find the point spread functions that are the same between the two images (so parameterize the PSFs based on some ...
1 vote
68 views

### Finding delay between signals

This should be a simple problem, yet I can seem to figure out what am I doing wrong. I have a bunch of 1-D signals which I expect to look the same up to: shifting, maybe some scaling, and noise. I ...
448 views

### 2D FFT Cross-Correlation in Python

How to replicate scipy.signal.correlate2d(x, h) with arbitrarily sized x and h? ...
1 vote
395 views

### Is 2D circular cross-correlation with FFT done as described in this source?

Given input images x and h of same size, greyscale 2D and potentially complex, we seek circular ...
133 views

### Discrepancies in 2D cross correlation results using FFT

I'm trying to implement 2D cross-correlation to acquire the displacement of these two small images (interrogation windows). The issue is that the result from Cross-Correlation (CC) is different ...
514 views

### Efficient 2D convolution/cross-correlation along only one axis (1D output)

I wish to convolve/cross-correlate two images and but, only horizontally, yielding 1D output. So, first output point would be sum(x * h), second ...
132 views

### Emergence - what constitutes a minimally coherent source that "just begins" to produce stationary interference patterns?

A superposition of two signals with different frequencies will never produce visible (i.e. stationary) interference patterns. Such waveforms will produce spatiotemporal beat patterns, but they rapidly ...
1 vote
134 views

### Examples of audio files that are challenging to cross-fade

What can be recommended as challenging tests for cross-fading/mixing of music? I am looking for examples of music-titles that exhibit severe volume dips when cross-faded or mixed. Ideally answers ...
57 views

### Similarity between signals

Let's say we have two signals with fast ascending in the beginning, then one slowly decays while another remains at a constant level. An illustration plot is attached. How to compare the similarity ...
1 vote
85 views

### Feasibility of TDOA localization with a single moving receiver and stationary source

Every paper/article I've read on the subject of TDOA localization is concerned with some combination of 2+ stationary receivers (or, sometimes, 1 stationary + 1 moving). There are also some papers ...
1 vote
69 views

### Finding the variance of the normalized correlation coefficient

I saw in Correlation: A Magnitude or Power quantity? post the derivation for $\rho$ (the mean of the normalized correlation coefficient) and its relation to the SNR of the signal. I'm looking to see ...
455 views

### Find out time offset between two substantially same audio tracks

Say we have two audio tracks of the same movie but from different sources. The length of the animated logos at the beginning is different, so the actual movie audio starts slightly earlier on one ...
58 views

### FFT2D on a vector 1D

My question is related to this post I have a 1D vector, the target vector, represented as 2D (knowing the nr of cols and rows) to which i need to apply an FFT2D. Having only the FFT1D, in order to ...
26 views

### How can I correlate two noisy voices in order to enhance their result?

I have an array of two microphones, spaced out, which continuously transmits audio input to a central processing unit. There is a slight delay between them, which is sometimes variable because they ...
247 views

### 2D Cross-Correlation on different sized images

As per this post the cross-correlation between 2 images is obtained as it follows: ...
15 views

### How to implement cross-correlation for 2 Images in c++ [duplicate]

I need to implement cross-correlation of 2 images in C++. The process is unclear to me since i do not seem to find a definite formula for it. What i thought this means: FFT2 on both images multiply ...
100 views

### Cross corelation between two complex-valued Time Series Objects

I am exploring the cross correlation function in Julia between two complex-valued Time Series Objects Z1 and Z2 with this simple code: using DSP Compute the cross-...
1k views

### 2D Cross-Correlation using 1D FFT

I need to calculate cross correlation between 2 images which I read in 2 vectors, both of them uni-dimensional. As per my understanding I need to do the following operations: FFT(1D) on vector 1 and ...
64 views

### Estimation of time-varying velocity

Objective: Estimate the mechanical tension of a cable using the velocity of the waves travelling along it. Experimental setup: I have a cable in tension equipped with accelerometers. I measure a ...
1 vote
119 views

### Find $E[Z^2(t)]$ when $Z(t) = X(t) - Y(t)$ where $Y$ is the output of a LTI system with WSS process $X$ as its input

I received this as a practice problem (part b only). I was able to figure out that $E[Z^2(t)]$ = $R_X(0)+R_Y(0)-2R_\text{XY}(0)$ but did not see how to continue. Checking the answers, I saw this line ...
75 views

### Cross correlation of OFDM short preamble produces two peaks

I am trying to cross correlate the short preamble of an OFDM transmission. This is the preamble I am using: ...
302 views

### Efficient way to calculate $n$ first elements of cross-correlation using FFT

The cross-correlation between two signals can be calculated using $\texttt{IFFT}\left(\texttt{FFT}(a) \cdot \overline{\texttt{FFT}(b)}\right)$ for two binary signals $a$ and $b$. How could one speed ...
1 vote
119 views

### Limited cross-correlation for multiple signals

I have $N$ signals, each of length $\tau$, with $N\ll \tau$, eg. $\tau=10^8$ samples and $N=100$. I want the $r=10$ first components of all pairwise cross-correlation for the $N$ signals. The naive ...
525 views

### How to convert between 2d convolution and 2d cross-correlation?

I am using cross-correlation for the purposes of image stabilisation. The images which I'm processing can sometimes be rather large. The contents of the image are often repeating patterns. For these ...
115 views

### Link between maximum delay of cross-correlation and phase velocity

I try to express the relation between: the delay obtained by maximizing the cross-correlation between two signals $x$ and $y$ noted $\tau_{x,y}$ and the phase velocity noted $v_p(\omega)$ In the ...
777 views

### How to interpret cross correlation output?

The output of cross corelation shows the similarity between the two signals. But in what respect is there a similarity? I didn't quite understand how I should interpret the output. How should I ...
1 vote
57 views

### CIR calculation from SDR data: RTL-SDR, bladeRF

We’re developing a prototype using bladeRF and various Python scripts for processing IQ samples. The system works mainly around 2.4 GHz frequencies: Wi-Fi and Bluetooth. One of the needed functions is ...
798 views

### How to decide whether a recording contains a signal of interest?

I am currently implementing an acoustic communication system in Matlab. For synchronization purposes, every transmission contains an upchirp preamble. The receiver uses cross-correlation to find the ...
115 views

### Using cross-correlation of spatially shifted data to gain geometric information

Cross-correlation is usually used to estimate e.g. lags between signals that are detected by different sensors at different times. In my case, the situation is slightly different in that I measure ...
170 views

### Estimation of the attenuation of two waves on a linear sensor array

Context and objective I am trying to estimate the attenuation coefficients ($\alpha_u$ and $\alpha_v$) of two waves ($\overrightarrow{u}$ and $\overrightarrow{v}$). These waves propagate on a linear ...
1 vote
258 views

### Detecting a known alarm signal in an audio stream

I am going to detect alarm sounds (like from a fire detector) in a live stream. (I have asked similar questions here before, I'm now at the stage of actually doing it). I will not really want to ...
250 views

### Extract a signal from noise, so I can view noise spectrum only?

I have a perfect modulated signal. I have the same signal but with noise, this noise is from non linear amplification. Is it possible, to extract the clean signal so it's just leaving the noise? The ...
270 views

### Autocorrelation & Cross-Correlation -> Main uses in DSP??

Please help understanding the DSP usage of Autocorrelation & Cross-correlation It seems this is strongly linked to calculating phase offsets, frequency offset for carrier recovery, symbol timing ...
181 views

### Cross Ambiguity Function Peak Width

I am trying to plot the Cross Ambiguity Function of two OFDM signal (1024 subcarriers) reflected from two targets, which are separated by 30m. The problem I am facing that the CAF peak width at the ...
231 views

### Find offsets of two audio files with several sections in common

I have two audio files that have mostly identical* content, most of which is just people talking. A typical example would be two files, each approximately an hour long, in which ~55 minutes of the ...
388 views

### Cross-correlation seems defined backwards

Suppose $f$ and $g$ are real. Why $$C(\tau)=(f\star g)(\tau) = \int_{-\infty}^{\infty} f(t) g(t + \tau)dt \tag{1}$$ and not  C(\tau)=(f\star g)(\tau) = \int_{-\infty}^{\infty} f(t) g(t - \tau)dt\...
166 views

### Is maximum cross-correlation achieved at the origin?

Let $x[n]$ and $y[n]$ be two DT random signals with $x[n]\xrightarrow{\mathcal{H}}y[n]$ through some system $\mathcal{H}$ that is deterministic yet unknown.\ Define both the autocorrelation and cross-...
1k views

### Delay/Lag calculation using cross correlation in frequency domain

I need to compute cross correlation of two signals using frequency domain. Hence, I am using the below equation for calculation. max(IFFT(FFT(a)*conj(FFT(b)))) ...
1 vote
241 views

### Resolution of phase measurement using cross Correlation

The setup is the following: I am using a RedPitaya board to measure the phase shift of two input signals. These input signals will sweep logarithmically from 1kHz to 100 kHz in 10 seconds. Currently, ...
1 vote