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

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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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33 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
118 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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151 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
43 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
35 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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24 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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112 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
36 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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145 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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27 views

Help in blind deconvolution by MLE of 1 D signal

[Paper - A computationally fast approach to maximum-likelihood deconvolution by Chong-Yung Chi, Jerry M. Mendel and Dan Hampson link presents an ...
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50 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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34 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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1answer
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
88 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
96 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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25 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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10 views

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
47 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
117 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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52 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
89 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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84 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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58 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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3answers
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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41 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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2answers
76 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
117 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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34 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 ...
4
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1answer
121 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}) := ...
2
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1answer
46 views

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
92 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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1answer
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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66 views

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
392 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 ...
2
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1answer
170 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
91 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
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2answers
129 views

How to understand the type of noise

Suppose that I am receiving RF signals contaminated with noise through antenna. This signal is digitally sampled. How can I understand the type of noise(Gaussian,Uniform etc). Any algorithm is there ...
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1answer
235 views

Using a Wiener Filter to Estimate a Transfer Function

As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, How would you put a minimum MSE criteria on how well the estimated filter weights ...
3
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2answers
342 views

Estimate the transfer function of an unknown system?

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
2
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1answer
76 views

Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $ M \in {R}^{NxN} $ Positive Definite Matrix. Let $ \hat{x} $ the MMSE of $ x $ given $ z $. How come the following are equivalent of minimizing $ E[{(\hat{x} - x)}^{T}(\hat{x} - x)] $: $ ...
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1answer
179 views

Carrier frequency offset (CFO) estimation based on Symbols

In (1), it's said that: If two identical training symbols are transmitted consecutively, the corresponding signals with CFO of $\epsilon$ are related with each other as follows: ...
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2answers
128 views

minimum SNR requirements for maximum likelihood frequency estimation

In certain applications, you have enough SNR available to, for example, perform an FFT and identify peak location and hence the signal frequency. If my understanding is correct, parameter estimation ...
2
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2answers
852 views

Carrier frequency offset (CFO) estimation using cyclic prefix

I understand the cyclic prefix, but in (1) it's said that: "If we consider that the channel effect is minimal and can be neglected. then the phase difference of the CP and the OFDM symbol which the ...