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1answer
63 views

Equalizers with low data rate systems

In case of using equalizers with ZigBee systems, what type of fading does the channel show, flat or frequency selective, fast or slow? Is the inter-symbol interference (ISI) problem encountered in ...
0
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1answer
52 views

Recursive Least Square Adaptive Linear Equalizer

For the adaptive filter to work properly, a desired signal d(n) needs to be provided. The output from the equalizer y(n) is subtracted from d(n) to produce an error signal, which is used to adjust the ...
0
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1answer
82 views

Design of FIR filters with arbitrary magnitude and phase responses

I found many information in this thesis "Algorithms for the Constrained Design of Digital Filters with Arbitrary Magnitude and Phase Responses",i want to understand it. This question is a ...
1
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1answer
68 views

Sequential non-linear least squares problem

I have the the following non-linear function, $$s(x;A_k,\mu_k,\sigma_k)=\sum_{k=1}^2 A_k \exp\left(\frac{-(x-\mu_k)^2}{\sigma_k^2}\right)$$ with unknown (but deterministic) parameters $A_k,\mu_k,\...
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3answers
102 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 ...
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1answer
37 views

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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0answers
24 views

How do i estimate the momentary white noise out of three signals sampled at different frequency and phase?

I have three signals sampled at different three frequencies $Fs_1, Fs_2, Fs_3$. They all suffer from the same white noise source. I allow my self, if needed, to sample at a higher frequency than ...
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2answers
53 views

What is the definition of Linear Predictive Coefficients when the optimal value is not 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 ...
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2answers
155 views

Why Is Non Linear Least Squares Method from MATLAB and Alglib Gives Different Results on the Same Data?

i'm trying to rewrite my Matalab prototype for some DSP to C++ and encountering a displeasing problem. I'm trying to fit data to a function $y = a * (\pi / 2 + arctg(b * x))$. In Matlab it works well ...
2
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2answers
62 views

Finding the Best Gaussian Smoothing Kernel to Minimize the Discrepancy Between Two Images

Suppose we have two grayscale images, $A$ and $B$. $A$ and $B$ very strongly resemble each other, such that the mean of the absolute difference $\lvert A - B\rvert$ is fairly small. Suppose further ...
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2answers
59 views

Solving LASSO ($ {L}_{1} $ Regularized Least Squares) with Gradient Descent

To the best of my knowledge, state of the art methods for optimizing the LASSO objective function include the LARS algorithm and proximal gradient methods. I was wondering however, if the LASSO ...
2
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1answer
514 views

Python: Least Squares Support Vector Machine (LS-SVM)

I'm looking for a Python package for a LS-SVM or a way to tune a normal SVM from scikit-learn to a Least-Squares Support Vector Machine for a classification problem. The goal of a SVM is to maximize ...
1
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1answer
41 views

Obtaining Correct (Least Squares Sense) Affine Transform Parameters Between Two Images

I have two images that I want to compute the affine motion model parameters. The model that I use is $$x' = a_1x+a_2y+a_3$$ $$y' = a_4x+a_5y+a_6$$ To calculate those 6 parameters, I picked 6 points (...
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2answers
125 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 ...
0
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1answer
88 views

Received signal error vs. BER

It is my understanding that the least squares algorithm (e.g., in equalization) minimizes the received signal error. However, minimizing the received signal error does not necessarily equate to ...
1
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1answer
128 views

Least Squares Linear Phase FIR Filter Design

In explication ''the geometric interpretation of least squares'' Typically, the number of frequency constraints is much greater than the number of design variables (filter coefficients). In these ...
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0answers
34 views

Solving amplitude and phase for know frequencies using Least Square

I supposed that I have $X(t)$ that is composed of waves that I don't know anything about it (how many waves, their frequencies, amplitude, phase). I will inject this data $X(t)$ with generated data ...
1
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1answer
65 views

RLS Algorithm (Memoryless)

I have been studying the adaptive filters lately and now when I am at RLS (Recursive Least Squar) Algorithm I came across the term used in the weighting function of the RLS called forgetting factor ($\...
0
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1answer
82 views

Properties of Optimization Techniques in Filter Design

I have this design , Can you tell me about the type of filter and the algorithm just viewing this design, or should there be other information?
3
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0answers
100 views

Least Squares Approximation for FIR Filter Design

Following this paper , I am trying to make a least-squares algorithm in MATLAB, but for type I (I know about firls()). ...
2
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1answer
205 views

How to Use the DFT (FFT) to Solve a Least Squares Regularization Problem (Inverse Problem)?

Let $X$ and $K$ be an image and a Point Spread Function (PSF), respectively. The blur image $B$ is obtained as follows $$B = X * K$$ I want to solve the following general regularization problem $$...
5
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1answer
168 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 (...
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0answers
33 views

Solve for transfer function coefficients embedded in a non-linear system

Given a complex input signal $x$ and real input signal $v$, a 4th order (for simplicity) transfer function $H(z)$ is first applied to $v$ to obtain $w$, which in the time domain is represented by the ...
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1answer
173 views

Estimate a transfer function from ARX models - Is ARIMAX better?

There is diffrent models which can be used to create a dynamical model by using least squares. Those models are following: ARX ARMAX ARIMAX OE BJ But if my goal with creating a dynamical model is to ...
0
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1answer
160 views

Difference between Leaking factor and Forgetting factor

I am using a Recursive least square adaptive filter to process electromyography signals and it is working decently so far. I decided to implement an LMS adaptive filter as a noise cancellation, so ...
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0answers
34 views

Digital Filter Design Accuracy [duplicate]

Having only dealt with digital filter scarcely, the question dawned to me when I used the firls function in matlab to design an equalizer with a certain gain response. In general, can we prescribe ...
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6answers
261 views

The Least Norm Solution of Under Determined Linear System

Suppose I have a matrix $$A= \begin{pmatrix} 1 & 0 & 1 & 0\\ 0 & 1 & 1& 0\\ \end{pmatrix} $$ where the variables are channel information like assume $X_1$, $X_2$, $X_3$ ...
0
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1answer
323 views

Maximum Likelihood Estimator (MLE), MMSE and LS - Are All of Them Regressor, Estimator and Predictor?

Can all three criteria ML, MMSE, and LS be called regressor, estimator, and predictor ? If not, an intuitive explanation of why they can't be would be good.
0
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1answer
54 views

1/f^2 weighting for least-squares FIR

I am currently modifying the firls.m from Octave to allow all types of FIRs, differentiators, and Hilbert transformers, while taking a peak at Matlab's. I see there ...
0
votes
1answer
92 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
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2answers
197 views

How to add group delay?

I was confused about the value of group delay, I am not sure whether my opinion is correct. For example, if I want to add a group delay of $0.25$ time units to a zero-phase signal, does it mean that I ...
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2answers
83 views

Matlab : Stuck in implementing Least Squares estimator for this model

The formula to estimate $\mathbf{h}$ is then $$\hat{\mathbf{h}} = (X^T X)^{-1} X^T \vec{y}\tag{2}$$ I think this can be implemented in Matlab using ...
0
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1answer
105 views

Part 1- 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,....
1
vote
1answer
267 views

What Is the Difference between RLS, LMS and Wiener Filter? When Is One Preferred Over Another?

I'm dealing with a channel equalization problem where the channel is modeled as a WSS process. I understand LMS utilises a Wiener-like approach, ie it converges to the optimal (wiener) solution. I ...
19
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3answers
2k 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 ...
6
votes
2answers
496 views

Zero Phase Filter: Determining Initial Conditions for Forward Backward Filtering

Is anybody familiar with Gustafson's algorithm for minimizing transients in forward backward filtering [1]? I'm trying to implement it and my first guess was to check Matlab's filtfilt.m, since they ...
0
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1answer
57 views

Estimating Q/Damping Factor from noisy measurements

I have a damped, tuned circuit and want to measure its Q factor. The hardware sends an impulse 'ping' and samples the output as it rings down. Is there an efficient way to fit an equation of the form ...
1
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0answers
51 views

MIL given for RLS equations vs the Woodbury derivation [closed]

Can any one help me in deriving the matrix inversion lemma rule for RLS algorithm? I don't know how to start with. Many books have just stated but they haven't derived it.
0
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1answer
147 views

Least Squares with Non Zero Mean Noise

What happens if the noise has no zero mean? I mean, if the exercise is something like: $$y(k) = A x + \eta(k)$$ When I have zero mean, I start from: $$y = A x$$ $$\Rightarrow \hat{y} = A \hat{x}$$ ...
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0answers
105 views

Instability problem in NLMS adaptive algorithm

I have been used NLMS algorithm to equalize 4x4 MIMO signals, but the bit-error-rate (BER) after equalization is unstable with iterations. I don't know if it is the normal behavior of the adaptive ...
3
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3answers
206 views

LMS filter weight update

I have a general question regarding Least mean squares adaptive filters. Using the example of noise cancellation, I understand that if you have a set of reference signals (S) and corrupted signals (S+...
5
votes
1answer
2k 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 ...
8
votes
2answers
993 views

Is the Kalman Filter a Best Linear Unbiased Estimator (BLUE) for Heteroscedastic Noise?

According to the Gauss-Markov Theorem, a ordinary least squares estimator is BLUE if the noise entering a system is uncorrelated with zero mean and is homoscedastic (has a constant finite variance). I ...
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0answers
16 views

Why would prefiltering measurement data affect the least squares estimate?

In estimating parameters in a discrete time model I've often seen the use of filters applied to the input data, before its applied to least squares processing. I've been told that the filters are ...
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 ...
2
votes
1answer
89 views

What is the technique to find variance of estimation error

Given an $n$-vector $y$ (responses) and a design matrix $X$, I wish to fit them with a simple linear regression model $$y=X\beta+e,$$ or, $y_t = x_t'\beta_0 + e_t$ where $e\sim\mathcal{N}(0, \sigma^...
3
votes
1answer
688 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 ...
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0answers
263 views

Motion artifact cancellation from ECG signal using 3-axis accelerometer data

I have a ECG signal measured as a test subject is performing 3 different activities - sitting, walking(2mph) and jogging(5mph) and also the corresponding 3-axis accelerometer(X,Y and Z) signals. I can ...
0
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1answer
37 views

Regularized Least Squares by Laplacian Operator - Optimal Value of the Regularization Factor (Lagrangian Multiplier)

Consider the cost function $$f(X,\lambda) = \|AX-b\|_2^2 + \alpha \|LX\|_2^2$$ $A:$Measurement matrix($R_{m\times n}$,$m \ll n$), $b:$observation vector($R_m$), $L:$Laplacian operator($R_{n \times n}...
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2answers
501 views

Least squares and auto and cross correlation

I am trying to understand why auto and cross correlation helps find the best fit line in least squares. I have an equation as stated here: $Ax=b$ -- I have not exact solution, so I use the least ...