5
votes
Adaptive filtering: Optimum filter length and delay
In order to be able to choose an optimal value for the delay $\Delta$ it's important to understand how the system works. The purpose of the delay is to decorrelate the desired signal $s(n)$ and the ...
- 91.2k
4
votes
Accepted
Filtered-X LMS algorithm and built-in MATLAB implementation
I think you are mixing the estimated, real and modelled responses. You can kinda safely assume that the real transfer functions $h_{N_{p}}$ and $h_{N_{s}}$ are never known. This, of course, is in the ...
- 1,353
4
votes
Accepted
Gradient descent algorithm not converging
Your step size is too large. The upper limit $2/\lambda_{max}$ for the step size $\mu$ is valid if the update is defined as
$$\mathbf{w}_{k+1}=\mathbf{w}_{k}-\frac{\mu}{2}\nabla J(\mathbf{w}_k)$$
The ...
- 91.2k
3
votes
Algorithm for "adaptive phase rotation" in iZotope RX 8
This is an interesting topic. I assume that the goal can be expressed as designing a time-variant allpass filter (phase distortion) that minimize amplitude peaks while retaining the frequency ...
- 3,555
3
votes
Is a neural network an adaptive filter?
An adaptive filter is a special case of a neural network (NN). They have in common that they multiply an input x[n] with weights w[n], the result y[n]=x[n]w[n] is compared to the target t[n] (e.g. the ...
- 31
2
votes
Regarding the choice of cost function in adaptive control - squared error vs absolute error
This is an interesting question since both squared error and absolute error are convex functions, so they are both going to give the optimal solution when minimized. My intuition is that the $\ell_2$-...
- 637
2
votes
Accepted
Control theory: how do you initialize input for a model predictive controller?
This algorithm in general tries to solve an optimization problem each step, defined as,
$$
\begin{aligned}
& \underset{\textbf{u}}{\text{minimize}}
& & \sum_{i\ =\ 0}^{N-1}\left[x^T\!(k+1+...
- 994
2
votes
Accepted
What is usual independence assumptions on adaptive filters
I think there is an error in your referenced independence assumption.
$w(k)$ should be the update part $\Delta w(k)$ i.e the
$w(k+1)=w(k)+\mu \Delta w(k) =w(k)+\mu \frac{x(k)*e(k)}{c+x(k)^Hx(k)}$
...
- 284
2
votes
Accepted
Stochastic approximation algorithm
The issue is possibly that the input signal you have chosen is not persistently exciting. This means that the signal doesn't "excite" enough modes of the filter in order to be able to accurately ...
- 25.9k
2
votes
Applying Photoshop's "Shadow / Highlight" Correction Using Standard Image Processing Algorithms
This Mathematica code substitutes a "gamma" operation for whatever Photoshop's "Amount" parameter controls, but it achieves roughly the same result.
...
- 121
2
votes
Accepted
RLS Algorithm (Memoryless)
In its bare classical form the RLS algorithm, recursively (for every new iteration), solves the classical problem of least squares; by computing the optimal FIR transversal filter coefficients $w[n]$ ...
- 28.4k
2
votes
Is a neural network an adaptive filter?
or is it called a neural network because it is "fancy"?
Machine neural networks are called such because they deliberately emulate the functioning of biological neural networks, in an ...
- 12.9k
2
votes
Accepted
Convergence of the RLS Algorithm for a Forgetting Factor $ \lambda < 1 $
The convergence itself depends on the eigen values of the empirical correlation matrix (See remark below).
By setting $ \lambda \leq 1 $ we allow the filter to adapt in the non stationary cases.
We ...
- 20.2k
1
vote
DSP microchip in Phonak products
Most companies will consider this type of information confidential, so it will be hard to come up with a parts number. Hearing aides processors are extremity constrained in terms of size, power ...
- 47k
1
vote
Algorithm for "adaptive phase rotation" in iZotope RX 8
(I'm just now getting back to this because I haven't logged in for a while BUT) I did find out how I think it works so quickly. It's actually random. You take a given window and randomize the phases ...
- 31
1
vote
LMS Adaptive Filter for system identification
In general for a standard LMS you can only ensure convergence if the stepsize $µ < 1 / (2p\sigma^2)$ . With p being the filter order and $\sigma^2$ the variance of the input signal x. Therefore if ...
- 165
1
vote
Approximate a Known System with Adaptive Filter and an Unknown System in a Series
The problem with your diagram is that the calculation of the error isn't done on the output of the adaptive filter.
The adaptive filter minimizes the error based on the idea the error is a function ...
- 20.2k
1
vote
How to differentiate two different signals from their combined signal
If the recording is anechoic than this is simple enough: assuming that the distance between the microphones is $d$ than you can estimate the front source as
$$x_f(t) = m_f(t-d/c_0) - g \cdot m_r(t)$$
...
- 47k
1
vote
Accepted
How to choose a fixed adaptation step for decision feedback equalizer
I'm leaving the answer here, if somebody ever stumbles upon the same question.
About LMS: Both DFE and ARC employ Least Mean Squares (LMS) adaptive algorithms: DFE is an adaptive filter and ARC can be ...
- 396
1
vote
Accepted
Unknown symbol/expression in text about adaptive filters (cst)
The standard normalized step-size LMS algorithm computes the current step-size according to
$$ \mu = \frac{c}{s_k^T \cdot s_k} $$
where $c$ is a suitable scale factor and $s_k^T \cdot s_k$ is the ...
- 28.4k
1
vote
Is CMA equalization applicable for OFDM
No.
OFDM isn't constant modulus (i.e. constant envelope) in time domain, if you look at it as one system. It's quite the opposite; it's known for its high PAPR (which you probably know!). This is the ...
- 32k
1
vote
Block LMS with overlapping blocks
There is no hard rule regarding convergence speed of the block-LMS vs sample-by-sample LMS. It really depends on the scenario.
On top of my head is the following two (stationary) scenarios:
A very ...
- 21
1
vote
Is document image binarization a closed research field
First, in science, a field is rarely closed, sometimes asleep only. Resistance to low-contrast, real-time, badly scanned, composite documents/writers or from aging medium seem to remain challenges, ...
- 32.1k
1
vote
Stochastic approximation algorithm
To do system identification using a driving function, it is necessary that the driving function $x[n]$ be broadbanded, meaning that the driving function has a Fourier Transform of non-zero value over ...
- 21.1k
1
vote
Accepted
Regression vector size for prediction, reconstruction and filtration with adaptive filters
Suppose that you are adapting $w$ to minimize $\text{E}(y[n]-w[n]*u[n])^2$ where
$$y[n]=h[n]*u[n]+\nu[n]$$
$y[n]$ and $u[n]$ are known and $\nu[n]$ is an additive noise component.
With a long enough ...
- 321
1
vote
Upsampled input to an Adaptive filter?
Prior to upsampling, you have a white signal meaning every single frequency in the Nyquist bandwidth from $-\pi$ to $\pi$ is represented. This is a requirement to obtain an impulse (because the ...
- 1,422
1
vote
How the Gain Term $ K \left( n \right) $ Is Derived? Why Is It Called Gain?
In all adaptive signal processing schemes, be it a Least Mean Squares (LMS), Recursive Least Squares (RLS) or a Kalman Filter, The fundamental concept is the update of some parameter: such as the ...
- 28.4k
1
vote
What's the Difference Between LMS and Gradient Descent Adaptation?
I can add that LMS algorithm has a sample-based update.
1
vote
Modeling ADC in Active Noise Cancellation
You are correct that the system will attempt to invert the ADC filter. In acoustics this is not usually a problem because there is not much energy at those frequencies.
If your application is not a ...
- 626
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