Questions tagged [statistics]
Statistics is the study of the collection, organization, analysis, and interpretation of data.
160
questions
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0answers
63 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}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
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0answers
35 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 ...
1
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0answers
66 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
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0answers
216 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 ...
1
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0answers
196 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 hand....
1
vote
1answer
871 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 ...
1
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0answers
64 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 hard ...
0
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1answer
474 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 ...
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2answers
494 views
Interpretation of Histogram in Statistical Image Processing
I am learning statistical image processing by myself. In papers and books, it always show the histogram of original images and gradients as the following image shows. The histograms of images vary ...
0
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2answers
757 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)- \overline{f})...
0
votes
2answers
173 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 ...
0
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1answer
33 views
Complex gaussian random variable [closed]
In my work i need to generate circularly symmetric complex gaussian random variables with non zero mean and certain variance in matlab.
I know the command for generating in case of zero mean , but ...
0
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1answer
2k 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 $\left(16000*0.03=480\right)$ but I could not find the exact pdf for that. sometimes it appear like 2 mixed ...
0
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1answer
17 views
Statistics to characterize time-domain envelope of acoustic signal
I am interested in comparing 0.5-second 44100/s signals when different ADSR envelopes are applied to them. However, I don't want the comparison to be as fine-grained as simply calculating a 5000-...
0
votes
1answer
10k 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.
...
0
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1answer
12 views
Questions in a Character Degradation Model Paper
I have questions in the ‘Noise region definition’ and ‘Noise generation process’ of the paper “A character degradation model for grayscale ancient document images”.
In Noise region definition, ...
0
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1answer
60 views
Derivation of Circular Mean Square Error
I would like to understand how Eq. (36) in [2] was derived:
The rationale behind the definition of circular sample mean in Eq. (37) is clear, but there is no motiviation for the CMSE definition in Eq....
0
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1answer
34 views
Radio Signal Stationarity
A radio signal recording of a wireless communication system (e.g: Wi-Fi traffic) is beaconized, channelized and subject to noise.
When working with such an RF signal, numerically transformed to a ...
0
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1answer
49 views
Differences in moving window rms due to sampling rate
I have a 10 second recorded signal band pass filtered from 100-500 Hz. The original sampling rate is 10 kS. Now I run a moving window RMS with a window length: 10 ms on the signal (10/1000 * sampling ...
0
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1answer
37 views
Demonstrate the mean of the sample variance
Let's suposse I have a vector of elements $x(n) = \{x(0), x(2), \cdots ,x(N-1)\}$ from a random process X of mean $\mu_x$ and variance $\sigma_x^2$. I want to see if I can estimate the mean and ...
0
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1answer
48 views
Channel direction
I am reading a book called Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency, and it implies that $$\frac{\mathbf{h}}{\sqrt{\text{E}\left\{\|\mathbf{h}\|^2\right\}}}$$ is the channel ...
0
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1answer
281 views
Problem understanding the Expectation Operator
I know that the Expectation Operator $E\{x\}$ four discrete values is
$$ \sum_k \alpha Pr(x = \alpha_k)$$
and its very intuitive when speaking out a formula which contains the Expectation Operator. ...
0
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1answer
134 views
Why doesn't law of large numbers apply to this stationary time-series?
There's a paragraph in Wikipedia that states the following:
Let Y be any scalar random variable, and define a time-series $\{X_t\}$, by
$$X_{t}=Y\qquad {\text{ for all }}t$$
Then $\{X_t\}$ is a ...
0
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2answers
595 views
pdf of the sum of gaussian distributions using fft Ask [closed]
I am trying to derive the pdf of the sum of independent random variables. At first i would like to do this for a simple case: sum of gaussian random variables. I was surprised to see that i don't get ...
0
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1answer
117 views
Received Signal Error vs. BER
It is my understanding that the least squares algorithm (e.g., in equalization) minimizes the received signal error. However, minimizing the received signal error does not necessarily equate to ...
0
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1answer
84 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 ...
0
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2answers
105 views
Help in proper notations and mathematical formulation
For a given series, $S = \{-1,0,-2,1,etc\}$. The number of elements in $S$ is $N = 100$. Each $s_i$ belongs to a alphabet from a finite alphabet set $\mathcal{A} = (a_1=0, a_2=1, a_3=2, a_4=3, a_5=-1,...
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2answers
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 ...
0
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1answer
523 views
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 ...
0
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1answer
122 views
This is an expression for the computation of kurtosis.
However, I don't understand what the subscript '4x' or the parameter (0,0) stand for. Could anyone explain ?
0
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1answer
74 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?
0
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1answer
954 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 ...
0
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1answer
701 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 ...
0
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0answers
13 views
Permutation test on two simultaneously recorded EEG signals
I have two EEG signals that are simultaneously recorded (and has been further synced) using two EEG devices, namely device 1 (ground truth) and device 2 (investigational device).
Imagine one device ...
0
votes
0answers
5 views
Consistency check of Kalman Filter
I am interested doing the consistency check of the Kalman filter. There are several measures like Posterior Cramer Rao Lower Bound (PCRLB), NIS (Normalised Innovation Squared), NEES(Normalized ...
0
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0answers
30 views
Texture Analysis and Statistic Models
Let's assume we have a random binary texture image $X(i,j)$ that comes from a Markov-Gibbs model with zero boundary conditions.
The probability distribution Gibbs function is: $$Pr(X)=\frac{1}{Z}\exp(-...
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0answers
16 views
Standard Deviation of Character Gradients in a Document Image
I have the paper titled "CG-DIQA: No-reference Document Image Quality Assessment Based on Character Gradient". It is all about assessing the quality of the document image based on its blurriness. To ...
0
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1answer
32 views
Cepstrum of white gaussian noise
What are the statistics of the cepstrum of gaussian white noise?
\begin{align}\newcommand{\Nfft}{ {N_{\mathrm{FFT}} }}\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT}
x_i &\sim \...
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0answers
29 views
What does Allan variance really means? [duplicate]
Let a sensor (e.g. accelerometer) with a combination of white gaussian noise and random walk noise.
The loglog plot that is usually shown as function of a time parameter, affine decreasing for a ...
0
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0answers
15 views
About convergence of KL divergence: if the two probability distributions are type, does the law of large number work?
If I pick $N$ samples from $P_X$ and $P_Y$, they are two independent discrete distributions.
$X_1,X_2,\ldots,X_N$ are drawn i.i.d from $P_X$, and $Y_1,\ldots,Y_N$ are drawn i.i.d from $P_Y$.
I got $...
0
votes
1answer
39 views
Generalized Likelihood Ratio test for correlated data
Consider a sequence of random variables $\overline{z} = \{z(k-M+1), ..., z(k)\}$, with probability density depending upon a scalar parameter $\theta$. It is intended to decide between two hypotheses
...
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0answers
27 views
CWT coefficients as features for ML algorithms
I use CWT coefficients as features in ML algorithms and then I did the feature selection using the chi-square test but recently I figured out that the chi-square test can only be applied for ...
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0answers
28 views
Test of statistical significance of power-spectrum against red-noise
I have a process which is most probably red-noise and my goal is to know if the peaks or pits are "real" or just due to random fluctuations.
I would like to know if there is exists a test of ...
0
votes
1answer
102 views
Block by block CCDF and PAPR analysis in MATLAB
There are few signals (OFDM-like modulation scheme with uniformly distributed data source) generated by my script. I need to compare scheme performance in sense of CCDF (Complementary Cumulative ...
0
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2answers
27 views
How to sketch output PDF given the transformation?
Question:
Let Random variable $X$ with $PDF$ = $f_{X}(x)$ be the input to device with input output characteristics as shown below then sketch the $PDF$ of $Y$ i.e, $f_{Y}(y)$
My attempt:
for X>0
,$...
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0answers
44 views
What is the error rate in compressed sensing?
Let $x \in \mathbb{R}^n$ be a $k$-sparse vector. Given $A \in \mathbb{R}^{m \times n}$, we have a measurement vector $y$ given by
$$y=Ax$$
Let $\hat{x}$ be defined as follows
$$\hat{x}:=\arg\min_{z\...
0
votes
1answer
60 views
How would I fit a distribution to this image noise?
I have collected some noise data from a dimly lit CMOS image sensor. The distribution of pixel values is tallied below:-
I'd like to be able to simulate this sensor noise. How would I fit a ...
0
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0answers
162 views
What is the difference between Statistical Signal Processing and Estimation and Detection?
Looking at the syllabus of Statistical Signal Processing in different university I see a lot of correlation with that of Estimation and Detection? In some universities, these are seen the same. For ...
0
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0answers
33 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 ?
0
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0answers
449 views
Wiener filter yielding negative MSE (and MMSE)
I implement a Wiener filter using the following code
...
