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0
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0answers
26 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 ...
0
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0answers
22 views

detecting frequency bursts in GSM using ALE, mystery peaks

http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=1404796 I've implemented the algorithm in the mentioned paper. From the error function, I can clearly see the filter converging to the FCH (Frequency ...
1
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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
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0answers
83 views

Least Angle without matrix inversion?

Sorry if this is too damned long. I did what I could to abbreviate it. I'm new to numerical work with matrices. I believe I have a way to compute Least Angle without explicit matrix inversion. I'm ...
1
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2answers
140 views

Difference between Equiripple & Least Squares design for FIR digital filters

For an efficient and optimized digital FIR filter design, there are two methods available broadly, Equiripple filter design & Least Squares filter design. A general method for designing a filter ...
3
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2answers
227 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 ...
1
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3answers
130 views

Force Linear Phase for a FIR filter synthesized using Berchin's FDLS?

As a follow-on to this post, how would you force linear phase for a FIR filter you synthesized using Berchin's FDLS?
1
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4answers
197 views

Best signal processing method for this application?

I have a signal I'm getting from a sensor (shown below in the photo of an excel plot) and I need to process it to get it to look something like the red line I've overdrawn on it. Sort of a moving ...
0
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1answer
65 views

Estimation of input signal to obtain the desired output signal for an unknown filter

Suppose $h(n)$ is a finite impulse response which is unknown. We can feed any input signal $x(n)$ into the system and observe the corresponding output signal $y(n)$. From this, is it possible to ...
1
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0answers
53 views

How to fit a function (find a lower bound) to (for) the plots?

I am dealing with a complicated optimization problem with two parameters $N, K$. Setting $K =$ constant and finding the minimum for different $N$'s lead to a set of function values. I can do this for ...
0
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2answers
180 views

Conceptual question on least square estimation method

What is meant by Least square plus Gaussian method of estimating the parameters of an unknown system? I am aware of least squares in general but some works refer it as least square+gaussian method. ...
3
votes
2answers
193 views

How do you combine 2 least squares estimates?

Say you want to compute the least squares estimate of $w$ from a data-set: $$ \begin{bmatrix}d_1 \\d_2 \\\vdots\\d_N \end{bmatrix} =\begin{bmatrix} x_1 \\x_2 \\ \vdots \\x_N\end{bmatrix}w + ...
4
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3answers
1k views

How to remove the periodic oscillations from a signal

The task that I have is to remove the annual and semiannual oscillation from a set of temperature measurements, taken over several years, by means of least squares method. I found the method ...
2
votes
1answer
119 views

Doubt on Weighted Least Square Estimation

This is a page from the book linear algebra,geodesy and gps by Gilbert Strang.... the page explains about the justification of the inverse of the of the co variance matrix of measurement vector $b$ ...
2
votes
2answers
122 views

Least Square Error Estimation doubt when can we write $(A^TA)^{ -1} = A^{-1}(A^T)^{-1}$?

I am new to linear algebra and have this simple question... in least sqaure estimation...the best estimation of the equation $Ax = b$ is $x_{Estimated} = A (A^t A )^{-1} A^t b$...the projection of $b$ ...
13
votes
1answer
371 views

How to tell if an error surface is convex? (Is it determined by the Covarinace matrix or the Hessian)?

I am currently learning about least-squares (and other) estimations for regression, and from what I am also reading in some adaptive algorithm literatures, often times the phrase "... and since the ...
13
votes
1answer
418 views

How do I improve LMS / NLMS filter performance?

Are there ways to increase computational performance of a normalized least squares (NLMS) filter? Multidelay block frequency-domain (MDF) filters have been proposed to do this, but they also take away ...