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

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14 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
62 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
32 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
71 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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0answers
75 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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0answers
25 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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0answers
36 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
50 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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0answers
40 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
59 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
96 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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0answers
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
24 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 ...
3
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1answer
78 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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0answers
37 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
votes
1answer
44 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
61 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 ...
0
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1answer
58 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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0answers
50 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
96 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
111 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
68 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
109 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
190 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 ...
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2answers
218 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
73 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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0answers
29 views

Minimizing the sum of squares of autocorrelation function of residuals instead of sum of squares of residuals

I am trying to fit my model to some experimental data and I am using a simulated annealing algorithm. My objective function has so far been the sum of squares of the residuals: $\sum_{i=1}^n (y_i - ...
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1answer
134 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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0answers
23 views

Estimating Model Weights for Point-Process Input/Output Systems using Probability Theory

Problem: I have a point-process input & output, x & y and I am attempting to estimate a 2nd order nonlinear Volterra-like model for them in the form: $$ Eq. 1: y[t] = k_0 + ...
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2answers
107 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
487 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 ...
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0answers
57 views

What are variance and bias in spectral estimation (specifically periodogram spectral estimation)?

So far, I have read that all the non-parametric estimation techniques decrease the frequency resolution in order to decrease the variance in the spectral estimate What is the general "overview" ...
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0answers
81 views

Prony method for undamped signal

i have one question related to sinusoidal model,as i know Prony's method for parameter estimation is used for damped signal,when amplitude of signal decreases as time varies,but is it relevant to ...
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3answers
103 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: ...
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2answers
79 views

Estimating the amplitude of a particular frequency

I am relatively new to DSP and have been reading a lot on the internet. I have a couple of questions. I have a signal in the form of a function $$ f(x) = A_0 + A_1 \cos(\omega_1 x) + A_2 ...
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0answers
31 views

Kalman Filter Properties with Biased (By Constant) Measurements

Assuming I have a filter with the following form: $$ \begin{bmatrix} {r}_{k} \\ {\dot{r}}_{k} \end{bmatrix} = {F}_{k} \begin{bmatrix} {r}_{k - 1} \\ {\dot{r}}_{k - 1} \end{bmatrix} + {v}_{k} $$ $$ ...
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0answers
26 views

If test statistic is $T(\textbf{Y})=\frac{1}{N}\sum\limits_{n=1}^N |Y[n]|^2$ then what is $T(\textbf{Y}|H_1)$?

There are two hypothesis: $H_0:Y[n]=W[n]$. $H_1:Y[n]=X[n]+W[n]$. $X[n]$ and $W[n]$ are independent of each other. $W[n]$ is zero mean Gaussian with variance = $\sigma^2$; however we only know the ...
2
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0answers
181 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 ...
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0answers
45 views

Incorporating delayed data in Kalman filter

my guide has told me to get familiarized with state estimates and kalman filter ....the problem is that: 1) I am totally new to this topic and finding it really difficult to understand due to lack of ...
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2answers
68 views

DFT detemine frequencies

I am just begining learning about DFT and I am bit unsure on what is happening mathematically during DFT. I've sampled a signal , a sine wave sin(1000*2*pi*t). And performed DFT to calculate the ...
0
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1answer
42 views

How to identify stable deltas in a noisy signal

This is a problem I have had to deal with in several different contexts now. Given a real time signal which you expect to act as a noisy step function (periods of stability separated by quick changes ...
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1answer
109 views

Frequency and damping estimation with Prony method?

I have a sinusoidal time domain signal with few damped exponential components. i.e. ...
2
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1answer
45 views

What is the set of most predictable or in other words most self-correlated signals?

Which signals or set of signals is the most predictable or in other words most self-correlated (autocorrelation)? I think one of them is $x(t)=c$, for all $t$, where $c$ is a scalar constant. The ...
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0answers
58 views

Sampling Clock Offset estimation

I want to estimate sampling clock offset. I am currently referring this paper " CRAMER-RAO BOUNDS FOR DATA-AIDED SAMPLING CLOCK OFFSET AND CHANNEL ESTIMATION ". Is there any other method to estimate? ...
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0answers
32 views

MMSE Estimation of Noise Corrupted Signal

I just learnt the MMSE (minimum mean square estimate) in my stochastic processes course and I am experimenting it on matlab. So I have a noise corrupted signal Z. ...
7
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7answers
919 views

Obtain a signal's peak value if it's frequency lies between two bin centers

Please suppose the following: The frequency of a signal's fundamental has been estimated using FFT and some frequency estimation methods and is lying between two bin centers The sampling frequency ...
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94 views

Symbol timing recovery algorithms

I am trying to implement the symbol timing recovery loop and for that I have chosen two algorithm to compare my results one is feedforward and Gardner TED. One thing that is confusing me is smoothing ...
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0answers
58 views

Estimating Position Based on Range Measurement

I want to present Kalman Filter problem. For simplicity I'd assume the simplest dynamic model - Piece Wise Constant Velocity. The state vector and dynamic model are given by: $$ \begin{bmatrix} ...
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2answers
106 views

Relation between Kalman filter and Sequential linear MMSE estimation

Are the results of applying Kalman filter and recursive linear MMSE estimation process the same ?
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2answers
118 views

Why is PSD estimated, and not simply computed?

I apologize if this comes as a basic question, but I am struggling to understand why the PSD can only be estimated and not directly computed. For example, this thread discusses several such PSD ...