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

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4
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3answers
221 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 ...
2
votes
2answers
154 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 ...
1
vote
0answers
19 views

The autocorrelation of a WSS process as a linear operator

If I'm given a autocorrelation matrix of a WSS process what interpretation should I put on the resulting vector. More concretely the matrix takes the form $\begin{bmatrix} x_1 & x_2 & ...
1
vote
0answers
35 views

Solving an array signal processing estimation problem based on the Rayleigh quotient

The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by $$ R(\mathbf{C},\mathbf{a}) := ...
1
vote
0answers
23 views

Statistics of the output of a high bitrate signal filtered through a narrow band low pass filter

I was wondering what would be the statistics of the output of the filtering of an extremely wideband signal (e.g. 10 Gbps random data stream) through a narrowband low-pass filter (e.g. 10 MHz LP). I ...
0
votes
0answers
23 views

use multiple Fisher test for periodic components

I know that there is a Fisher test for periodic component detection, one example is there: http://www.mathworks.com/help/signal/ug/significance-testing-for-periodic-component.html But let us suppose ...
0
votes
0answers
39 views

calculate variance of periodogram

I would like to know how to calculate the variance of periodogram? As I know variance is a big problem of periodogram. Namely increasing length of time series increases also variance of periodogram, ...
0
votes
1answer
47 views

What is the mean power of a complex random variable?

Say $\alpha$ is a complex random variable, then which one of the following expressions is correct? $\mathbb{E}[\alpha^2]$ or $\mathbb{E}[\alpha \alpha^*]$?
1
vote
3answers
57 views

comparison between frequency offset estimators

I have been working frequency offset estimation in OFDM. The objective was to compare different frequency offset estimation techniques. By using MATLAB, I have simulated three different estimation ...
2
votes
2answers
46 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
71 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 ...
1
vote
0answers
40 views

DSP, Related Math, Statistics, and Jitter Primers [closed]

I'm a CS who took an internship at an EE shop, and I'm trying to do some work developing in house and client applications for a chip designer, and I'm having some fundamental communication problems. ...
1
vote
0answers
101 views

Yet Another Peak Detection Request

I looked over the other entries regarding peak detection and none seem to answer my question. I'm working with Fourier spectra of digitized audio that can't be measured again. There are no ...
0
votes
0answers
75 views

Constant amplitude, uniform phase - what's the distribution of the complex signal then?

The well-known relationships for zero-mean circularly-symmetric complex Gaussian $z = a + jb = |z| \exp(j\varphi)$ signals are the amplitudes $|z| = \sqrt{a^2 + b^2}$ are Rayleigh-distributed the ...
0
votes
1answer
120 views

wiener filter (non-causal) calculating covariance matrices

I'm learning about the Wiener filter, and I'm working on my own implementation. I'm starting out with the non-causal filter, and I need to calculate some covariance matrices. If the signal is assumed ...
3
votes
3answers
98 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: ...
1
vote
2answers
73 views

On computing the number of independent values from a signal's bandwidth?

Can anyone help me understand where the value of $2$ comes from in the following statement? ...
2
votes
1answer
92 views

How to detect quadrilaterals in a point cloud?

How can I detect a quadrilateral in a point cloud that looks almost like a rectangle? How do I set the criteria (i.e orientation, size etc) to get the shape for example in the image below?
1
vote
1answer
120 views

How to compute the statistics of the DFT of 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 ...
2
votes
0answers
128 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 ...
0
votes
0answers
27 views

Mutual information between speakers utterance

I want to compute the Mutual Information (MI) between each sub-band of the speakers. However, I am confused about it. Let's explain it in other way. Suppose that we have N speakers who pronounce M ...
0
votes
2answers
108 views

Normalized cross-correlation in detail

I'm trying to implement a normalized cross-correlation algorithm but I don't get what in fact is this measure. What confuses is the wikipedia definition: $\frac{1}{n} \sum \frac{(f(x,y)- ...
1
vote
0answers
70 views

Random signal modeling with Matlab

I want to build a detector of sorts. Say I have a bunch of signals and they all share some patterns, like some peaks in frequency or something more complicated that I can't bother to calculate by ...
5
votes
0answers
99 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. ...
0
votes
1answer
121 views

Error Propagation through an IFFT

I'm not sure how to approach this problem. I will describe what I am trying to do, and what some of my matlab outputs look like. I'm not trained in signal processing or anything, so please be ...
2
votes
1answer
139 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 ...
1
vote
3answers
850 views

How can a signal have no DC component

I am reading a nice book on DSP The Scientist and Engineer's Guide to Digital Signal Processing It mentions In electronics, the mean is commonly called the DC (direct current) value. How ...
2
votes
1answer
521 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 ...
4
votes
0answers
42 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 ...
1
vote
1answer
145 views

Fisher ratio or F_ratio

I am confused while writing code to implement Fisher’s F-ratio. Suppose I have 4 speakers, each speaker pronounces 2 words and each word has 3 frames and each frame has 30 sub-bands. $u$ is mean of ...
0
votes
1answer
286 views

what is probability density function (PDF) of periodic signal

anybody knows what is the best pdf for periodic signal ? I have signal with 480 samples (16000*0.03=480) but I could not find the exact pdf for that. sometimes it appear like 2 mixed Gaussian.
4
votes
2answers
129 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 ...
1
vote
1answer
149 views

Amplitude calculation

I've got an array of different values representing the y-values in a plot: ...
0
votes
2answers
107 views

Expected value of a Delta function times a function

I have a output signal $Y(t)= \sum_{n=-\infty}^{\infty} Z_n \delta (t-n\tau) h(t)$ and $Z_n$ is a random variable with equal probability to be $+-1$ and h(t) is $sinc(\frac t {\tau})$ and the ...
4
votes
0answers
562 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 ...
1
vote
1answer
91 views

Establishing the function of a decaying signal

I have a set of samples from a signal. The signal is erratic in behaviour at the beginning but then it settles down and oscillates around the value of 100 (the frequency of oscillation is not ...
4
votes
0answers
59 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 ...
2
votes
1answer
240 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 ...
3
votes
2answers
309 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 $x(T)$ ...
4
votes
2answers
309 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 ...
6
votes
5answers
993 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 ...
3
votes
1answer
82 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 ...
1
vote
0answers
39 views

Statistical Signal Analysis - what to read [duplicate]

Possible Duplicate: Introduction to Statistical Signal Processing Currently I am doing an (undergrad) class on statistical signal analysis, but I find the reader at hand (no book, buh) very ...
2
votes
0answers
60 views

Predicting Positional Displacement with a Bivariate Gaussian Distribution

In my computer-vision problem, a blob can move either forward or backwards (with a slight chance of moving sideways) along its directional axis. I am seeking a bivariate model because I need to ...
3
votes
3answers
208 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 ...
8
votes
3answers
1k 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 ...
7
votes
0answers
408 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 ...
4
votes
1answer
2k views

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

Let's say I have a row vector $X = [x1, x2, x3, ..., xn]$ and another row vector $Y = [y1, y2, y3, ..., yn]$. I want to check whether the two vectors are statistically independent or not. Now two ...
12
votes
4answers
2k 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 ...
14
votes
5answers
5k 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 ...