Questions tagged [least-squares]

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21
votes
3answers
4k views

FIR Filter Design: Window vs Parks McClellan and Least Squares

Are there any advantages to use a window approach over Parks-McClellan (further abbreviated here as PMcC) or Least Squares algorithms for FIR filter design of a low pass filter? Assume with today's ...
3
votes
1answer
2k views

Use MATLAB to Restore a Signal from a Given Degraded Signal Using Tikhonov Regularization

Anyone could share how to develop an application in MATLAB to restore the signal from a given degraded signal using Tikhonov regularization i.e restoring the signal $f$ via solving $$ \min || g - f ...
1
vote
2answers
320 views

Least Squares Fitting to Inverse Exponential Function

I have a time series of measurements that resembles the shape of an exponential function. The samples are a bit noisy and sometimes there is a weak sine like ripple signal ontop of it. Simplified the ...
4
votes
1answer
254 views

Direct Correlation (DC) Time Delay Estimation: Variance Keeps Decreasing for Increasing SNR?

I'm trying to reproduce the results from this paper "Discrete time techniques for Time Delay Estimation" doi:10.1109/78.193195, for both the correlation and Least Squares. I've generated a random (...
1
vote
3answers
147 views

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 ...
3
votes
3answers
386 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?
3
votes
2answers
10k 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 ...
2
votes
4answers
302 views

Sequential Form of the Least Squares Estimator for Linear Least Squares Model

I'm currently working on a project in which I need to find the tilt of a surface. Let's assume I'm only concerned with a single dimension tilt (i.e. slope) to begin. I currently have the ability to ...
5
votes
1answer
4k views

What's the Difference Between LMS and Gradient Descent Adaptation?

I found algorithms that seems the same to me, but they are described with different names (in field of adaptive filtering). For example: LMS - least-mean-squares seems to be GD - stochastic gradient ...
4
votes
2answers
3k 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 ...
4
votes
3answers
6k 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 ...
4
votes
1answer
1k views

Constant Modulus Algorithm and the Gradient Operation

CMA is a blind channel equalization algorithm with the details presented above. I am facing 3 difficulties and shall appreciate help Q1: Does $H$ and the bar over $\bar{y_k}$ represent the Transpose ...
1
vote
2answers
62 views

What Is the Definition of Linear Predictive Coefficients When the Optimal Value Aren't Unique?

Linear predictive coefficients of signal y are defined as the best $k$ coefficients $a_i, i = 1, \ldots, k$, that will approximate $y_n$ by $-\sum_{i=1}^k{a_iy_{n-i}}$. (Best approximation is that ...
0
votes
1answer
121 views

Least Squares FIR for Type II

Following this paper (see the Matlab example at the end), I am trying to make a least-squares algorithm in Octave, but for type II (I know about firls). For type I ...
0
votes
1answer
129 views

How to Apply Least Squares Estimation for Sparse Coefficient Estimation?

The model is expressed as, $$y(n) = \sum_{i=0}^{p-1} r(i) x(n-i) + v(n) \tag{1}$$ where $\mathbf{r} = [r_1,r_2,\ldots,r_p]^T$ is the sparse channel coefficients of length $p$, $\mathbf{x} = [x_1,x_2,....