# Questions tagged [least-squares]

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### Doubt regarding scaling of Welch Overlap Segment Averaging with Lomb Scargle

I am doing something similar to this question Comparison of results own implementation and python signal.welch. In my case there is no Welch method associated with the scipy lomb scargle spectrum so I ...
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### Constrained Least Squares Filter Design

I would like to design a complex FIR filter, $h$, for a known signal that produces a desired output: $d$ = $s*h$ (where $s$ is my signal and $d$ is the desired filter output). Let $S$ be the ...
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### What procedure to find the parameters of a given filter prototype to fit a desired frequency response?

To model the frequency response of a system, I am looking for a method to fit the response of cascaded bi-quad filters to the response of that system using an optimization algorithm. The $S$-domain ...
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### High Dynamic Range FIR Filters

Related to this question on using the Windowing method for FIR filter design versus the optimized algorithms such as least squares (firls in MATLAB, Octave and ...
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### How to find point of inflexion of a digital signal?

Let's say I would like to find a point of inflexion of a digital signal which has been gathered via sampling of a continuous time domain signal with sampling period $100\,\mu s$. The digital signal ...
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### Noise Variance and Sampling in the Linear Regression Context

I am new to signal processing, so please bear with me. My question applies to any general problem of estimation from noisy measurements but I will like to understand this through a problem given here. ...
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### Questions on the Generalized Tikhonov Regularization

My first question is about the quadratic functional that is used in generalized Tikhonov regularization: $$\Psi(f)=\frac{1}{2}\|f\|^2_\Gamma=f^T\Gamma f.$$ In the above equation what does $\Gamma$ ...
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### Variational Regularization Method in Image Processing

I would like to understand better variational regularisation methods in image processing. In particular, the formulas in this image: Why formula (3.13)? In the notes that I read I cannot find ...
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### Difference equation system identification

Suppose I have a difference equation modeling a vehicle like this: $$d[k+1]=d[k]+a\cdot u[k]+b,\tag1\label{eq}$$ where $d[k]$ is total distance traveled at time $k$, $u[k]$ is engine input at time $k$ ...
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### Unable to estimate for AR model using OLS, Yule Walker and MLE

I am learning estimation methods following the book of Steven Kay, "Fundamentals of Statistical Processing, Volume I: Estimation Theory " Theory says that if the measurement noise is ...
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1 vote
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### How to find the value of regularization parameter/s when having one or multiple priors

I am working on a image reconstruction framework, specifically interferometry. In simple words we have data that is pertubated by noise, say $$V^o_i = V_i + \sigma_i$$ Where $V^o$ is a complex ...
1 vote
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### Building a FIR filter from an arbitrary frequency-magnitude response curve (eg. Least Squares fitting) [duplicate]

I'm trying to create a FIR filter from a magnitude equation, where my starting equation provides the magnitude (amplitude) between 0 and 1 for any given frequency in Hz. I posted the magnitude ...
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### Simultaneously minimize and maximize two cost functions

I want to solve the following optimization problem, in which I have two cost functions $J_1 = \mathbf{w}^T R_1 \mathbf{w}$ and $J_2 = \mathbf{w}^T R_2 \mathbf{w}$, where $R_1$ and $R_2$ are covariance ...
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### Quadratic Programming with Linear Equality Constraints

I need to solve an equality constrained minimization problem as give below $$\min_{\textbf{w}} \mathbf{w}^TR\mathbf{w}$$ such that $$X\mathbf{w} = \mathbf{1}$$ where $R\in \mathbb{R}^{n\times n}$ is ...
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### Complex Least Squares Approximation

In the case of frequency domain FIR filter design, the error function given by : $$E(\omega)=H(e^{j\omega})-D(e^{j\omega}) \tag{1}$$ is a linear function with respect to the unknown filter ...
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### Why Isn't the ML Estimator (MLE) in MIMO Spatial Multiplexing Obtained by the Least Squares Solution?

In the simplest scenario of MIMO spatial multiplexing: $$\mathbf{y} = H\mathbf{s} + \mathbf{n}$$ where: $\mathbf{s}=[s_0,s_1,...s_{M-1}] \\\mathbf{y}=[y_0,y_1,...y_{N-1}]$ \$\mathbf{n}=[n_0,n_1,......
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