# Questions tagged [statistics]

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

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### How to apply statistical algorithms of signal processing to 'regulate' variation of a curve?

Below I am posting 2 graphs. I want to regulate the curvature of first graph using some statistical methods such as use of standard deviations, and modulate my graph to look like second one. I am not ...
961 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 ...
708 views

### What do we espect Likelihood function used for?

In my understanding, I let make a example. For example, you can see in the following picture. Consequently, We want to find ^sigma. and We have already known the observation data(which is random ...
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### Combining different Likelihoods - Particle Filter

I am new to particle filters and have a problem when it comes to the weightening (using SIR to be precise). The problem is that my different state-variables are subject to different noise-...
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-...
394 views

### How to detect overall error between two signals and also track changes occurred

I need to develop an algorithm that will compare two signals (1 Reference Signal and other is measured signal values from sensor) and generate some metric(s) to describe changes between them. I am not ...
876 views

### Can we calculate moments (mean, var, skewness, kurtosis) of a signal in frequency domain?

The computation of the mean, variance, skewness and kurtosis of a time series in the time domain is straightforward from their ...
7k views

### What does standard deviation of noise 1 mean?

In theory of noise,Typically, the standard deviation of noise has 1 and mean has 0. I think that the reason of noise mean has 0 that we can assume that all noise signal go to zero when we sum it all. ...
1k 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 ...
121 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. ...
32 views

### Kalman Filter - Gaussian representation

I'm trying to understand well the kalman filter, as a result i'm having this question : Why do we represent noise with a Gaussian ? what does this really mean intuitively ?
68 views

### Equivalence between noise covariance of real and complex models of received signal

I have a question on the equivalence of two models (complex vs. real) of a received signal in ISI channel. Yet its simplicity, I am a bit confused. Model #1: Complex Assume we transmit a complex ...
375 views

### Wiener filter yielding negative MSE (and MMSE)

I implement a Wiener filter using the following code ...
389 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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### Determining the covariance of point clouds in real-time

So basically I have a set of multidimensional data that I need to determine the covariance of between dimensions in real-time. Each point that comes in is a vector. I have gotten the mean and variance ...
401 views

### Variance of correlated noise

I think this is an easy question but I am confused about the answer. Assume we have correlated noise distributed as $$n \sim \mathcal{N}(0,\sigma^2 \:A),$$ where $A$ is a given square matrix. If we ...
1k views

### How to test if error has zero mean?

I know how to calculate the mean of a data set. In DSP, I think zero-mean should means that the error fluctuates around zero, and the mean of errors at any interval is zero. So what about the error in ...
38 views

### Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?

e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is? Also, ...
39 views

### variance of filtered polynomial

Consider the following system: What is the variance of $y$, $\mathbb{E}(y^2)$ ? (EDIT: I know input signal has infinite power but will be made bandlimited by $H$. Both $H$ and $G$ are simple ...
83 views

### Obtaining n values from n-1 sensors

As the questions states, lets consider we have 3 gas sensors giving me data for: A B C Note that only sensors for A and B give absolute values, yet we need the absolute values for all four species:...
2k views

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

Cross-correlation for uniformly sampled signals is defined as  $$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$ Cross-covariance for wide-sense stationary (...
144 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 ...
90 views

### Received signal envelope PDF to power PDF [Wireless Communications]

I am deriving the probability density function (pdf) of the received wireless signal envelope in multi-path fading channels. I wish to transform this envelop PDF to the power PDF of that signal. I ...
59 views

### Discrete entropies

I've been given a problem where I need to find the entropy of two random variables. I can find part of the answer, but not all of it. I am given the following: $X$ is a uniformly distributed random ...
520 views

### Maximum likelihood estimator for multiplicative Gaussian noise

So I'm trying to derive an analytical solution for a MLE that should estimate a static value polluted by multiplicative Gaussian noise. The vector of measurements $\tilde{\boldsymbol{d}}$ is given as ...
42 views

### Optimize online weighted kurtosis algorithm

I am currently working on a Simulink block designed to perform an online computation of the weighted kurtosis typical of a certain signal. This block is part of a larger control algorithm, which will ...
584 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-...
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### Why are the observation features of an HMM-based recognition/synthesis system modeled by a Gaussian distribution?

Why are the observation features (namely MFCCs) of an HMM-based recognition/synthesis system modeled by a Gaussian distribution? Even the state duration is modeled by a Gaussian in this paper: K. ...
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 ...
400 views

### How do I interpret these autocorrelograms?

Hello signal processing wizards. I am young and feeble, and would like some help interpreting my spike-train autocorrelograms of six isolated neurons. These histograms were created using the code ...
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 ...
137 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. ...
1k views

### Expected value of signals

If I have two signals $x$ and $y$ and this expression $E\{x[n]y[n-k]\}$, what is the expected value of the product? I have a basic understanding of EV based on probability, such as E[X]=\sum_{i=1}^{...
423 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 ...
542 views

### How to compute the statistics of the DFT of correlated noise?

I would like to know how to compute the statistics of the discrete Fourier transform of a noise signal. To illustrate what I mean, I will first explain in detail a computation I have managed to do ...
70 views

### What does it mean when one model fit the data better than does a comptitor model?

I'm trying to review MLE (maximum likelihood estimation). What does it mean when one model fit the data better than does a comptitor model?