# Questions tagged [least-squares]

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### 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
69 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 ...
71 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: ...
34 views

### 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 ...
102 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 ...
117 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{...
47 views

### 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 ...
117 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 ...
153 views

1 vote
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### 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 ...
567 views

26 views

### 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
33 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 ...
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 ...
344 views

### Use Recursive Least Square as an "Actual" Filter?

I am currently studying recursive least square (RLS) and as far as I understand, the setup is (for example) that we are given a process with uncertain parameters/noise and we want to adapt parameters ...
1 vote
82 views

### Why is the concept of a "state covariance matrix" necessary in estimation?

I'm currently taking a course in optimal estimation (and it's still very early in the course). Much of our work is based around the idea of a measurement model $y=Hx + v$ This model assumes our ...
356 views

### Jacobian Computation in Least Squares IIR Filter Design

Long time lurker and first time poster - but unfortunately I haven't had any joy untangling this on my own. I've been studying Mathias Lang's thesis, Algorithms for the Constrained Design of Digital ...
334 views

### System Identification with a Limited Bandwidth Input Signal and Region of Interest

Given a FIR filter $h[n]$. Its action can described as: $$\mathbf{y} = \mathbf{H} \mathbf{x} \\ \mathbf{y} = \mathbf{X} \mathbf{h}$$ where $\mathbf{H}$ and $\mathbf{X}$ is a Toeplitz matrix. If $h$...
1 vote
138 views

### Difference Between a 1st Order SG Filter And a Least Squares Moving Average

I have been studying SG filters and i recently found another filter which seem to be commonly used in financial data smoothing which is the least-squares moving average, this filter is also called ...
841 views

### Learning the Coefficients of Auto Regressive (AR) Model Using Least Mean Squares (LMS) Filter for Signal Prediction

I want to do two things. Estimating Coefficients of AR model using LMS Using Coefficients found in step 1 and predict future samples of a signal using AR equation. I don't have a desired signal so I ...
1 vote