# 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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### Is it possible to estimate variance of noise for a step answer signal?

I know there is not possible to find the true noise of a measured signal. The only way to "find" the noise is to estimate the noise. Noise has the mean 0, but the variance varies. So assume that we ...
4answers
227 views

### Estimate Filter Coefficients from the Result of Linear Convolution with a Known Signal

If I have samples of input say x(1:500) and it passes through FIR filter with 9 taps and some unknown coefficients. The output y(1:508) is also known. The aim is to estimate the filter response in ...
1answer
621 views

### Cramer Rao Lower Bound for Cross Correlation (Time Shift Estimation)

UPDATE 2 Okay, I think I understand now why the defined CRLB is not applying to my use case. In my use case, we have very high SNR, and the the first signal $x_1$ is always the same. So the classical ...
0answers
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1answer
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### confidence interval estimate for coherence

Is there any solution for estimating Confidence interval of coherence derived by Welch method with overlapping segments? Moreover, the window length is not same for all the observations, only the ...
1answer
342 views

### 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 ...
1answer
1k views

### Maximum Likelihood Estimator (MLE), MMSE and LS - Are All of Them Regressor, Estimator and Predictor?

Can all three criteria ML, MMSE, and LS be called regressor, estimator, and predictor ? If not, an intuitive explanation of why they can't be, would be good.
0answers
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1answer
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### What would be the variance for complex number?

When $x$ is a zero mean random variable then $$\sum_{n=1}^N x_n x_n^T = N \sigma^2_x\,\text,$$ where the variance is $\sigma^2_x$. I'm considering Complex Normal Distributions where the real and ...
1answer
183 views

### Time series forecasting on dsp embedded systems

I have a time series analysis algorithm that uses arima modeling and fits a model to the time series and gets the residual values. It is more of a statistical signal processing algorithm than a ...
1answer
454 views

### Maximum likelihood estimator of active time delay and passive time delay

A typical time delay estimation problem has the model: \begin{align} x_1(t) &= s(t)+ n_1(t) \\ x_2(t) &= a s(t-D) + n_2(t) \end{align} Where $n_1$ and $n_2$ are considered to be ...
1answer
245 views

### What method to use for interpolation and extrapolation?

Below are discrete samples { t1, f(t1) }, { t2, f(t2) }, ... ,{ tn, f(tn) } using Mathematica syntax. {{7.0,0.354887404925574},{7.3,0.4003399403324751}, {7.6,0.5849632195845474},{7.9,0....
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### How to Implement and Minimize Maximum Likelihood Expression in MATLAB

I need to check if the estimation algorithm has converged or not. I am using the Maximum Likelihood estimation method. For convergence check, we see if the log-likelihood has reached its maximum value ...