Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [estimation]

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

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How does this FLL work?

I'm trying to get my head around how band-edge frequency locked loops work. In particular, a diagram from this paper: Specifically, what does the Tanh() function and the conjugate product of the two filters accomplish? Explanations and references…
Phil Frost
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How to distinguish signal and noise eigenvalues of autocorrelation matrix for MUSIC algorithm?

MUSIC (multiple signal classification) algorithm is introduced in Schmidt, Ralph. "Multiple emitter location and signal parameter estimation." IEEE transactions on antennas and propagation 34.3 (1986): 276-280. An important part of this algorithm is…
Jeon
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MSE of an estimator

In the book Fundamentals of Statistical Processing, Volume I: Estimation Theory by Steven M. Kay on page 19, it say that the mean square error of an estimator, $\hat{\theta}$, given the true value, $\theta$, is defined…
Zero
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Correlation between a signal segment and its stretched replica

In my application the measurements are affected by temperature and the signal is stretched over time, though preserving relatively similar structure. I want to find incremental stretching between pairs of consecutive signals. Having a pair of…
Alex Z
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Estimation Theory - Basic Question

I'm just starting estimation theory for my DSP course and I'm a bit confused about the classic example given everywhere which aims to show that two unbiased estimators can have different variances. I'm just wondering how they did that step that I…
AlfroJang80
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Steps for proving Tweedie's Formula

Assuming that $f_{X|D}(x|d)=e^{\alpha d x - \psi(d)}f_0(x)$ for some constant $\alpha$ such that it is a valid pdf for every value of $d$, i want to establish that: $$\mathbb{E}[D|X=x]=\frac{1}{\alpha}\frac{\partial}{\partial x}\lambda(x)\quad…
Oriol B
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error variance of frequency and phase estimation using DFT

What is the error variance of estimating the (frequency) and (initial phase) of a sinusoid using DFT. please provide references if possible.
Amro
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Can you explain likelihood function in the equation?

In the paper here, just before equation 12, authors introduce likelihood function $\pi(r|\theta)$. What does $\theta$ represent here ?. What is the intuitive explanation behind equation 12?
Sajil C K
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Can the numerical variance be lower than Cramer-Rao Lower Bound?

For a sample mean unbiased estimator, which achieves the CRLB, I plotted the variance and compared it to the theoretical CRLB. The plot below shows what I got. I have small number of samples to calculate this variance. The black line is the…
Zero
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Variance of expectation estimator

Given a set of $N$ iid samples, $x_k$, of random variable $X$ and the expectation estimator, $$E[X] \approx \frac{1}{N} \sum_{k=1}^N x_k,$$ how do I find the variance of this estimator (not the variance of $X$) as a function of $N$? I would only…
user827822
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Time length difference estimation between a waveform and its stretched and a bit distorted copy

I'm trying to solve the following problem and will appreciate your help. In the example I have two signals. The 1st is the original signal and the 2nd is a some slightly stretched version of it. The 1st signal I segment into N overlapping windows…
Alex Z
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Any estimation algorithms that allow a user to indicate that certain Solutions are impossible?

Variations of the Kalman filter and other algorithms are used for navigation and target tracking. Often times certain solutions might as well be deemed impossible based on known topography in the area. Without accounting for the topography, the…
Ted Ersek
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Summing over constants

I'm following some notes and I came across an example which said that for this x_n with a proposed estimator of the mean, that it is an unbiased estimator for the DC level. I'm trying to do it out myself But as you can see, I'm ending up with an…
AlfroJang80
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Frequency estimation of N FFTs of one sine signal in AWGN

Assume N receivers, detecting the same sine signal in AWGN with FFT, then we have N peaks for the same frequency corrupted by noise. How to use the N FFT observations of the same signal to get a more accurate estimate of the frequency. My first…
Amro
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