In signal processing, estimation is a technique for approximating an unobserved signal from an observed signal containing noise.

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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?
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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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Why do we find the Maximum Likelihood Estimate on denoising?

Question1. To understand Maximum Likelihood concept in the denoising, I'm looking for matlab example. I can't quit a catch the concept. Especially about denoising. So would you please let me know ...
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Sparse Channel Estimation in OFDM System

Compressive sensing methods are used in channel estimation when the channel is thread as sparse where there are zero points in the signal representation. I am in the beginning of the sparse signal ...
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2answers
55 views

How do can we cancel out noises while listening voice on headphones?

It's a common problem that while talking with the another person on Smartphones with the help of regular headphones,we get very annoying sounds at background . The opposite person's voice gets mixed ...
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1answer
48 views

How to estimate the noise of an image?

I want to know how to estimate the noise of an image? Also is this represent the camera's noise? Does anyone know how to estimate the noise of an image or camera? Update: Especially, I want to ...
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13 views

Frequency and amplitude estimation with missing samples

My input signal is given by $$ x[n] = A\sin(2\pi f n/F_s + \varphi)$$ The signal is uniformly sampled at a sampling rate of $F_s $[Hz]. However some of the samples are missing. Assume that there are ...
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2answers
125 views

Signal decompositon

I am not a good in writing algorithm but please follow below steps 1.There are 4 1D sinusoidal periodic signals.3 of them are given by \begin{cases} x(t)=4\sin(10\pi t) \\ y(t)=8\cos(20\pi t) \\ ...
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24 views

How does the OFDM system receiver decide the OFDM symbol length? [duplicate]

I am trying to understand how the receiver decides the length of OFDM symbol in time domain before it goes into DFT process at the receiver. The complete OFDM symbol (with Cyclic Prefix added) is ...
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34 views

Is there a principled way to distinguish between these signals?

Consider these two signals: They both describe a biological process going on in the same subject. The blue one is obtained at rest and the red one after the subject is perturbed. Is there a ...
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26 views

Estimation of Hit Time Using Kalman

I have the following model for Kalman Filter. The Dynamic Equation: $$ \begin{bmatrix} {r}_{k} \\ {v}_{k} \end{bmatrix} = \begin{bmatrix} 1 & -T \\ 0 & 1 \end{bmatrix} \begin{bmatrix} ...
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3answers
130 views

How to estimate the period of a pulse train?

I am trying to find the period of a pulse train like signal. I have reviewed the following questions but I did not find a clear-cut answer to the problem, 12892, 16502, 6260. I do not know the ...
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156 views

How to estimate for an exponential in WGN

Question: Formulating a Maximum likelihood estimator: So, the likelihood will be $p(y;\mathbf{h}) = \frac{1}{{(2 \pi \sigma_\eta^2)}^{T/2}} \exp{(-(y - y_0(t))^2)/ 2\sigma_\eta^2}$. Then, I ...
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1answer
45 views

Help in formulating the log-likelihood expression for AR model

An IIR system is excited by a signal $x_n$ described as follows: $x_n$ is the binary input to the system. This is how I proceeded : The original data $y_t$ is a noisy version of a time series ...
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1answer
40 views

What is an AMDF?

The wikipedia page for Average Magnitude Difference Function/Formula (AMDF) appears to be empty. What is an AMDF? What are AMDF's properties? What are AMDF's strengths and weaknesses, as compared ...
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26 views

can measurements go out of the uncertainty bounds?

In the below picture, the measurements are inside the $\pm 3 \sigma$ bounds. In my experiment, the measurements sometimes go out of the uncertainty bounds. This is a snapshot of my plot where the ...
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3answers
130 views

FFT bin interpolation for low frequency with DC offset

I have a noisy signal in I/Q format with a peak frequency that constantly changes between 0.5Hz and 4Hz. The sample rate is 64Hz. I want an output showing the current peak frequency with a maximum lag ...
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1answer
38 views

Does the OFDM MMSE Channel Estimator Require Prior Channel Knowledge?

The OFDM MMSE channel estimator seems to require a-priori knowledge of the channel to calculate the MMSE estimate. See equation 8 here: http://cache.freescale.com/files/dsp/doc/app_note/AN3059.pdf. ...
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158 views

Duration of unknown rectangular pulse with additive white Gaussian noise

Problem. There is a discrete signal $f[i]$ (example below). It is known, that $f[i]$ have a form of rectangular pulse with additive white Gaussian noise. $f[i] = s[i] + n[i]$, $s[i] = ...
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51 views

Distribution of a signal covariance matrix

A common estimation problem in signal processing assumes the following signal model \begin{equation} \mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n} \end{equation} where ...
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40 views

Estimate Image power spectrum of the noise

I want to implement Wiener filter. I have original image and image blured with linear motion. The one thing I am lack of(to implement it) is Noise power spectrum. I know that it is hard task. I've ...
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53 views

Phase Estimation in speech enhancement

I am reading a recent paper titled "Phase Estimation of Speech Enhancement - unimportant, important, or impossible?" by Grekmann et al. published in the 2012 the IEEE convention. The paper proposes an ...
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1answer
98 views

What is the Intuitive description of circular symmetric complex zero mean white Gaussian noise?

Suppose we have an added discrete noise signal defined as: $$y[n]=x[n]+w[n], $$ where $w$ is zero mean white Gaussian noise. Question: When we say white noise, is it sufficient to say that it is ...
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1answer
104 views

dominant eigenvectors of an unknown matrix

Do you have any idea about how we can find the principle eigenvectors of an unknown matrix ${H}$? The elements of $H$ are unknown in general. If you are familiar with channel estimation procedure in ...
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9 views

GAPES- like estimation methods

I'm searching for a-parametric methods for gap estimation. These methods don't have to relay on spectral analisis. I need these algorithms for comparison between GAPES with other algorithms. thanks.
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27 views

Conceptual queston on Z transforms and time series model (Part2)

I am learning the fundamentals of signal processing and time series models and I am having a hard time to follow due to lack of basics related to $z$ transforms and autoregressive model. I am facing ...
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Coefficient Estimation

In the classic paper "Channel Estimation in Narrowband Wireless Communications Systems" by Arslan and Bottomley, section 3.1 talks about estimating the channel coefficients. The text reads "One of the ...
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15 views

Estimating plant parameters from noisy frequecy response data

I have to estimate the parameters of a 1st order transfer function, namely, the coefficients, through experiment. I ran a few experiments and I have a bunch of input-output data vectors. The ...
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1answer
55 views

Effect of Sampling frequency on RMS estimation

I have a simple, but interesting question for you. I have to compute the RMS (root mean square or standard deviation) value of a time signal which represents in my case a velocity mesasurement over ...
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1answer
123 views

Discrete algorithm for low pass filter

I am working on a position controller for a marine vessel. I have an measurement signal containing the y-position of the vessel that consists of both low frequency (<.1 rad/s) and high frequency ...
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1answer
56 views

How to periodically estimate states of a LTI if the output is measured irregularly?

How can I periodically estimate the states of a discrete linear time-invariant system in the form $$\dot{\vec{x}}=\textbf{A}\vec{x}+\textbf{B}\vec{u}$$ $$\vec{y}=\textbf{C}\vec{x}+\textbf{D}\vec{u} ...
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1answer
95 views

How to learn MUSIC algorithm?

I was actually preparing for my semester project and decided to take up Frequecncy estimation.I ll directly come to the point that I want to know how should I learn MUSIC algorithm. How do I start it? ...
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85 views

why adding noise enhances the accuracy sometimes?

I am applying simple FFT to estimate the frequencies of the oscillations. The real values of frequencies are known to me as I made a synthesis signal for simulation.Thus, I can calculate the error ...
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28 views

Prediction error in least squares with a linear model

In the classical linear model with $$Y=X\beta +\epsilon,$$ where $Y \in \mathbb{R}^n$ is the observation, $X\in \mathbb{R}^{n\times p}$ is the known covariates, $\beta \in \mathbb{R}^p$ is the ...
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64 views

Estimate the Discrete Fourier Series of a Signal with Missing Samples

Assuming we have a discrete signal $ { \left\{ x \left[ n \right] \right\}}_{n = 1}^{N} $. Which has a Discrete Fourier Series. Now, assume I'd like to estimate its Discrete Fourier Series ...
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61 views

Hardware Transfer Function Estimation

Suppose you have the ability to inject any arbitrary waveform into a piece of analog rf hardware and collect and digitize the output for analysis. If you wanted to characterize/estimate the transfer ...
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42 views

When does l1 regularisation give a sparse solution?

I was maximising a likelihood function, which is convex. I know that the system has a K-sparse solution. I wanted to know the conditions (or some sufficient conditions) on the likelihood function ...
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83 views

The Standard Deviation of The Derivative of a Signal

Given a signal with zero mean and a standard deviation of 0.1 sampled at 5000 Hz. What would be the Standard Deviation of its 1st, 2nd and 'n' derivative? For instance, let's say we measure the ...
2
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1answer
122 views

Maximum Likelihood through a noisy channel

I have random variables $X_1, X_2, \cdots, X_m $, which can take $n$ values and is distributed iid according to $\Theta=(\theta_1, \theta_2, \cdots, \theta_n)$. That is $X_k$ can take values ...
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35 views

Separating fast decaying signal from a slowly decaying signal

I have a discrete signal $x[n]$ which is exponentially decaying but the decay constant is not known. This signal is observed over a certain time period, say $T$. The only known detail about $x[n]$ is ...
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1answer
31 views

Fusing motion and color in particle filter

I am trying to implement particle filter to track a car bounded by a box. First i used color histogram as my likelihood function and implemented PF, where i was using the bhattacharya distance to get ...
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1answer
129 views

Maximum likelihood estimation in presence of colored noise

I am trying to test system identification in presence of measurement noise (1) A white Gaussian noise (2) Colored noise - pink, violet. When we are estimating parameters we do so in presence of iid, ...
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40 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}) := ...
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1answer
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Variance of an Implicit Function of Kalman State Vector

Given a state vector given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following: $$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$ ...
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1answer
102 views

What is uncorrelated noise

In many applications such as estimation theory, when we need to estimate a parameter then we usually consider in presence of white gaussian noise of zero mean and some standard deviation. During ...
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64 views

minimizing the mean squared error?

I'm reading this book "Applied Optimal Estimation" by A. Gelb. In the example 1.0-1, there are two measurements $z_{1}$ and $z_{2}$ with some noise for measuring $x$ as following $$ z_{1} = x + v_{1} ...
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Spectral estimation from noisy time-series data

This is the first time I'm posting a question on here so I hope I'm doing it right. I've tried searching on here for an answer but haven't found anything particularly relevant. I have some data ...
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2answers
431 views

Hermitian symmetry in OFDM systems

I am trying to understand the usage of Hermitian symmetry in OFDM systems and have a couple of questions regarding this. What is the reason of using the Hermitian symmetry in OFDM? How can we ...
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1answer
182 views

DOA estimation 2 sources time delay estimation uniform array

I am new to signal processing, so sorry if the question is superbanal. I have been spending more days than I would admit on this and can't find the error. I have two triangle waves that are emitted ...
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3answers
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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 ...