Questions tagged [statistics]

Statistics is the study of the collection, organization, analysis, and interpretation of data.

Filter by
Sorted by
Tagged with
34
votes
5answers
34k views

Determining the mean and standard deviation in real time

What would be the ideal way to find the mean and standard deviation of a signal for a real time application. I'd like to be able to trigger a controller when a signal was more than 3 standard ...
14
votes
4answers
5k views

ICA - Statistical Independence & Eigenvalues of Covariance Matrix

I am currently creating different signals using Matlab, mixing them by multiplying them by a mixing matrix A, and then trying to get back the original signals using FastICA. So far, the recovered ...
12
votes
3answers
6k views

How to Average Complex Responses (and Justification)?

I am developing software that calculates the response of a system by comparing the FFT of input and output signals. The input and output signals are divided into windows and, for each window, the ...
12
votes
7answers
7k views

Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can ...
10
votes
3answers
2k views

What Does It Mean Exactly When Two Parts of a Signal Are Correlated?

I stumble quite often upon the notion that two or more parts of a signal are correlated to describe semi-formally that they belong together. For example in image processing, two pixels on an edge ...
10
votes
0answers
1k views

Ensemble learning, multiple classifier system

I am trying to use a MCS (Multi classifier system) to do some better work on limited data i.e become more accurate. I am using K-means clustering at the moment but may choose to go with FCM (Fuzzy c-...
9
votes
2answers
3k views

Why is Gaussian noise called so?

Can you please explain: why is a specific type of noise called "Gaussian noise"? Why is it relevant to call it Gaussian? Please, explain in layman's terms.
9
votes
1answer
2k views

What is the connection between analog signal to noise ratio and signal to noise ratio in the IQ plane in a quadrature demodulation system?

We would like to compute the quantitative relation between analog noise near the LO frequency and the statistics of points found in the IQ plane after IQ demodulation. In order to completely ...
7
votes
1answer
3k views

Magnitude-squared Coherence calculation inconsistence

I have to calculate the magnitude-squared coherence (MSC) between two signal. However, using a routine that uses only one taper (or no tapers at all) my result is always 1, despite the signals are ...
6
votes
3answers
204 views

Regression vector size for prediction, reconstruction and filtration with adaptive filters

I am working with adaptive filters and similar adaptive models (mainly with gradient adaptation) for a few years. I and my colleagues always struggle to find out the correct size of regression vector. ...
6
votes
1answer
325 views

How to discern the distribution function of mean-squared coherence values?

This probably walks a fine line between Cross Validated and this site, but I think the practical application of it lies more on the signal processing side. I have had the occasion to record some EEG ...
5
votes
2answers
153 views

Difference between $\mathbb{E}[\mathbf{x} \mathbf{x}^{\rm{H}}]$ and $\mathbb{E}[(\mathbf{x}-\boldsymbol{\mu}) (\mathbf{x}-\boldsymbol{\mu})^{\rm{H}}]$

Let us have a random vector $\mathbf{x} \sim \mathcal{CN} (\boldsymbol{\mu}, \boldsymbol{\Sigma})$ with $\boldsymbol{\mu} \neq \mathbf{0}$. What can we say about the relationship between the elements ...
5
votes
1answer
5k views

How can I calculate the Expectation for a particular known vector?

Let us say I have a row vector $X = [x_1, x_2, x_3, \ldots, x_n]$ and another row vector $Y = [y_1, y_2, y_3, \ldots, y_n]$. I want to check whether the two vectors are statistically independent or ...
5
votes
0answers
170 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
4
votes
2answers
1k views

Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions... Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ is ...
4
votes
1answer
2k views

Cross-correlation or cross-covariance of non-zero mean signals

Cross-correlation for uniformly sampled signals is defined as [1] $$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$ Cross-covariance for wide-sense stationary (...
4
votes
1answer
768 views

How is cross-correlation related with orthogonality?

In linear prediction we can say that in case of optimum linear predictor the error with be orthogonal to data. And when we derive minimum mean square error for $\underline{y} = \mathbf{a}\underline{x} ...
4
votes
2answers
2k views

FFT, How to decide if there is a signal among noise?

I have sets of data of different deep sky objects. My job is to check for any periodicity. I use IDL to run an FFT and wavelet methods to check for a signal. To test my code I ran the IDL built in ...
4
votes
2answers
229 views

Scatter plot: calculate box where 80 % of the points are

I've a scatter plot with x- and y-axis. Now I want to calculate a rectangle which displays where 80% of the points in this plot are. I'm not very familiar with statistics, so I don't know the method ...
4
votes
1answer
158 views

Getting error in fit

I was wondering if anyone had run into the problem of trying to estimate errors in their signal processing on spectroscopic data. I know that many people use spectroscopic techniques to estimate ...
4
votes
1answer
2k views

What is a good distance measure for matching SIFT descriptors depending on the distribution of their noise?

I have read some papers about distance measures like Euclidean, Manhattan or Chi-Square for matching gradient based image descriptors like those computed from the SIFT Algorithm (128-D vectors). Most ...
4
votes
0answers
118 views

Relative beat detection for two audio recordings

I'm trying to synchronize (overlap) two audio recordings of the same song: a complete HQ version, and an incomplete, noisy version (phone recording for example). The noisy recording may have had its ...
3
votes
3answers
4k views

Capacity of cascade binary symmetric channels

Let's imagine that we have interconnected in cascade $L$ binary symmetric channels each with the same transition probability $p(y|x) \in \{p, q=1-p\}$, where the output of each BSC is connected to the ...
3
votes
2answers
735 views

Filtering random Signal

My question is easy one actually. First, I generate a random signal using randn() function of MATLAB like this: Then, I design a FIR filter of order 200 of pass-...
3
votes
3answers
649 views

How to estimate the mean of a clipped signal?

An accelerometer is used on a high vibration environment (a bicycle) to measure gravity. The signal clips, so data higher than a clipping value is clamped to that value. So, simply filtering the ...
3
votes
3answers
292 views

How to determine, calculate and plot a probability distribution for a given set of numbers?

A device is rotating with a particular wind speed and producing such pulse frequencies in a minute: ...
3
votes
1answer
135 views

Characterizing real-time sampled signal

I have a signal which is sampled in real-time. At every time interval I receive a value. I need to characterize this signal as active or inactive (to take priority in the control actions). By active ...
3
votes
2answers
62 views

Lightweight test for bimodal distributions?

Here, and in the stats stackexchange, seem to be answers that reference tests for bimodal distributions that involve iterative binning or iterative curve fitting methods. However "eyeballing" a plot ...
3
votes
1answer
4k views

What is a covariance matrix?

Suppose you have k samples from each of the N elements of a uniform linear array (ULA) of sensors: What is the physical meaning of a covariance matrix? How do you form a covariance matrix with the ...
3
votes
1answer
241 views

Example of non-equivalence of the two PSD definitions

According to the book Introduction to Spectral Analysis by P. Stoica and R. Moses, the power spectral density (PSD) $P(\omega)$ can either be defined as the discrete-time Fourier transform (DTFT) of ...
3
votes
1answer
146 views

Independence of Noise at Each DFT Output

My math may be a little rusty, so I would like confirmation or correction or my calculations here. Given white noise samples, $x_i$, which are IID and zero-mean, and variance $\sigma^2_x$. I want to ...
3
votes
3answers
191 views

Extracting common signal without knowledge about noise [closed]

Given two noisy time series thought to contain a common signal, $$ x_1(t) = s(t) + n_1(t), \quad x_2(t) = s(t) + n_2(t), $$ what is the best way to determine $s(t)$ without assuming any distribution ...
3
votes
0answers
2k views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
2
votes
1answer
140 views

adjust mean of signal using exponential

I have discrete signals whose values are between 0 and 1. I wish to post-process such a signal such that the mean of its values equals 0.5, yet keeping maximum and minimum values 0/1 intact. ...
2
votes
2answers
196 views

Histogram Counts of a 2d Matrix

I am currently working on a project in which I have a 10 x 2 matrix: A. I want to find the top 3 number of occurrences of each row using MATLAB. ...
2
votes
1answer
1k views

what does it mean to have a decorrelated colour space?

I'm working on the problem of colour transfer between images. In the literature there's a common practice that consists in performing the transformations on images in what is called a decorrelated ...
2
votes
1answer
1k views

Fixed SNR with unitary noise variance

I've just one question : How can I write a model like y = x + w,( with w a white gaussian noise) with a fixed SNR and a noise variance equal to 1. What coefficient may I have before x ? Thanks !
2
votes
1answer
482 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary process in time (in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary ...
2
votes
2answers
320 views

Isolate High Variance vs Low Variance Sections of Signals

I have the following one-dimensional signals: The goal is to identify the sections with smaller variances compared to the rest (For Python, that is to get their index value in the array). In the ...
2
votes
1answer
67 views

Concept About Estimated Standard Deviation

I am looking for the concept about estimate standard deviation. Actually I'm not sure how can I get a concept the estimate standard deviation ? If you know the concept, then would you let me know this ...
2
votes
2answers
139 views

Measure of intermittency/continuousness of a signal

I have three signals (below) each having the same standard deviation, however, are clearly very different temporally. Is there some such metric that could be calculated for each of these signals to ...
2
votes
1answer
464 views

Why does circular symmetry of complex envelopes mean that $\mathbb{E} \Big[\mathbf{x}[i] \mathbf{x}^T[i] \Big] = \mathbf{0}$?

I am making my way through this paper here, and I understand everything up to equation 16, and I am stuck here. Long story short, the vector $\mathbf{x}[i]$ here is an $N$ by 1 vector, consisting of ...
2
votes
1answer
376 views

How to transform data to uniform distribution (uniform percentiles)?

Given the list of data points (normalized in [0,1] range), I plot the histogram of values and compute percentiles (shown as x ticks). How to find a transformation of data values so the histogram is ...
2
votes
2answers
123 views

How to solve equations for the MMSE receiver?

Given the following equations for the achievable rate of the Minimum Mean-Squared Error Receiver [1]: $$\mu = \frac{1}{K-1} \sum_{i=1, i \neq k}^{K}{\frac{1}{Mpd_{i}\left(1 - \frac{K-1}{M}+ \frac{K-1}...
2
votes
1answer
156 views

Standard deviation is varying with change in amplitude of DC signal

I am trying to make sense of the below code. I am taking a large sample so that I get good estimates for standard deviation. ...
2
votes
2answers
466 views

What does the frequency axis of a Power Spectral Density mean?

I have never really understood what the frequency axis meant when we plot the Power Spectral Density(PSD). Does it correspond to frequency as we get after we take the Fourier Transform of a time ...
2
votes
1answer
352 views

Detection of sine signals with random amplitudes

Problem statement: I am designing a NP detector for the following detection problem: $\mathcal H_{0}: x[n] = A_0\cos(2\pi f_0n) + w[n]$ $\mathcal H_{1}: x[n] = A_1\cos(2\pi f_0n) + w[n]$ where: $...
2
votes
1answer
524 views

Subsample Time Delay Estimation

Often we need to estimate the time difference of arrival between two signals to find the location of a target. Many algorithms gives the time delay corresponding to a sample number or time delay is a ...
2
votes
1answer
638 views

Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
2
votes
1answer
501 views

Signal Processing in Amateur Radio Astronomy

I am an amateur astronomer and I took recent interest in Radio astronomy and I am also new to Digital Signal Processing. My team is trying to build a radio telescope. I am interested in the data ...