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Questions tagged [least-squares]

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“Under-determined” case of observation filter (Remote Microphone Virtual Sensing)

Introduction - Formulation I am trying to tackle a problem of virtual sensing, where the sound field pressure is estimated at a location remote from measuring sensors. The block diagram of the system ...
• 1,314
1 vote
51 views

lsqcurvefit using dynamic input data

I have input vector $\boldsymbol{u}$ and output vector $\boldsymbol{y}$ of length $N$, and I use $u_k,y_k$ to denote the $k$-th elements of $\boldsymbol{u}$ & $\boldsymbol{y}$ and $u_{k-1}$ as the ...
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1 vote
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Tune Least Squares Support Vector Machine (LS-SVM) With Grid Search Optimization

I am looking for LSSVM with Gride Search optimization in Python, but could not find it. Scikit learn has SVM with Grid Search but not for LSSVM.
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What are some good questions for a graduate level signal processing course?

I am currently taking an graduate-level Advanced Signal Processing class and I have a midterm soon. However, the midterm is not only open-book but it is also open-internet and untimed. Now I have no ...
93 views

Fit Data Samples with a Robust Fit

I have a data from a sensor which the connection model of $x$ and $y$ is known: For instance, in the case above, the model is linear. The issue is how to handle outliers. Specifically when there are ...
• 20.1k
1 vote
51 views

IIR filter design for "data-aided" least-squares filtering

Consider a discrete-time signal consisting of a desired signal component and noise, as follows. $$y_k=d_k + n_k, \qquad k\in\{0,1,\dots,K-1\}$$ This signal is applied to a linear time-invariant (LTI) ...
• 489
36 views

How can I implement simple robust regression?

I have many datasets like this: to which I am trying to fit lines: $$y = a + bx$$ However as you can see there are some outliers in each dataset. The number varies from data set to dataset. I am ...
• 1,783
479 views

FIR filter design with nonlinear phase from measured amplitude and phase responses

I am having trouble when design FIR filter fitting to the complex data (i.e., amplitude and phase responses from measurements). I did try to use Matt. L's lslevin method here since this method is to ...
1 vote
111 views

Equalization with FSK

What are the downsides of using an LMS (or least squares) equalizer with FSK signals? What are the tradeoffs on doing equalization pre-demoduation vs post-demodulation? Most literature I can find ...
1 vote
113 views

Numerical issues in scipy's Savitzky Golay filter coefficients for large polynomial order

Consider the design of a Savitzky-Golay filter of window length 101 and (high) polynomial order 20. Using scipy version 1.10.1, the filter coefficients can be obtained in python as: ...
• 489
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Least squares filter with non-linear phase and independent weights for phase and magnitude

Intro My question is related to a previous one linked here. I am interested in non-linear phase FIR filters with a specific desired phase response. After I tried the options in the linked question I ...
• 319
139 views

Fitting high order rational function to frequency response measurement data

I need to model measurement data of a frequency response with physically meaningful band-pass filters. All Measurements happening in die range of 20Hz to 20000Hz I have to work with python. The ...
144 views

Solving inverse problem using black box implementation of the kernel

My question is related to Solving regularized least squares problem using black-box computation of $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T\mathbf{x}$. In case, the problem is formulated as: \begin{...
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Jointly determining the weighting matrix and target vector in weighted least square

I have the same weighted least square form weighted least square composed of diagonal weighting matrix $W$, IDFT matrix $F({\omega})$, desired response vector $D({\omega})$ and FIR Filter ...
128 views

Solving regularized least squares problem using black-box computation of $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T\mathbf{x}$

Let $\mathbf{A} \in \mathbb{R}^{n \times n}$. I'm working in a problem where I have a black-box algorithmic solution to compute the products $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T \mathbf{x}$ given ...
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1 vote
66 views

How do I apply Least Squares to determine the coefficients of a linear time-invariant filter having the desired output?

I'm trying to solve the following problem: Consider a linear time-invariant filter with linear phase: $$H(e^{j\omega}) = a_0 + \sum_{i = 1}^{N} 2a_k\cos(k\omega)$$ Determine the coefficients of this ...
723 views

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Solving Sparse Model with given Dictionary Using LASSO

I was trying to solve a problem where the basis matrix contains the components of $\sin(nx)$, $\cos(nx)$, $\sinh(nx)$ and $\cosh(nx)$. Say the $n$ varies from 1 to 100. While solving the lasso linear ...
1 vote
35 views

How to find the solution of nonlinear least square (NLS) equation for freqeuncy estimation

I am struggling to understand the theory of parametric methods for power spectral estimations of line spectra. And I want to find the solution of nonlinear least square (NLS) method for estimating ...
• 11
1 vote
1k views

Solve Undetermined Linear System Using NumPy's lstsq() Function

I would like to understand what I am doing wrong here. I am trying to perform polynomial regression by minimizing the least squares, $||Au-y||^2$, where $y$ is the given data and $A$ is the matrix ...
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