Questions tagged [numerical-algorithms]
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34 questions
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Where is this code for BCH decoder comes from?
recently I found a matlab code for BCH decode, the code seems to be:
I've found several iBM algorithm such as riBM, RiBM, SiBM..., but none of them looks like this code, for example, for RiBM ...
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How to solve KES equation of BCH in SiBM algorithm?
I have a BCH decoder which solve KES equation using RiBM algorithm, the RiBM Code in matlab is follows:
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Why does Kalman Filter have numerical problems when there is no measurement noise?
The book I read (Optimal Control and Estimation by Stengel R.F.) has this passage
The trouble with this system is that the equivalent noise covariance matrix $R_k$ is singular because the observation ...
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How to determine the effective radius of a top-hat filter applied twice?
I'm working with top-hat filters in real and Fourier space and trying to determine the effective radius when applying a top-hat filter of radius $R_1$ to an image that has already been filtered with ...
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Computationally Efficient Implementation of Kalman Filter
I know there are many formulations of the Kalman Filter. A few I can name are:
Classical Covariance Form
Informational Filter Form
Square-Root Form or Factor Form
But somehow it's hard for me to ...
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Statistical technique for distinguishing between artefacts and no artefacts [closed]
I would like to know how to create an algorithm from the table below in order to distinguish between data that has artefacts and data that does not.
I'm trying to leverage video attributes like ...
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Derivation of 9 point Laplacian filter
I'm reading a paper on how construct isotropic laplacian filter, and perhaps because it's an old paper, the notation in it really bothers me a lot. So can someone please explain it to me? For example, ...
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Numerical Stability for Channel Estimation
In this post:
Compensating Loudspeaker frequency response in an audio signal
I derive the Wiener-Hopf equations for least squares equalization (and channel estimation if we swap Tx and Rx) from the ...
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Extended CORDIC for general Lie groups and algebras via representations
CORDIC is a well-known method for quickly computing exponentials and logs, including trig functions and their inverses by decomposing the angle into conveniently computable increments and then ...
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Efficient Log2 and dB from Floating Point and Fixed Point Representation
Floating point representation encodes a binary number using a mantissa $a$ and exponent $b$ according to $(1+a)\cdot 2^b$, where $a$ is an unsigned fractional fixed point number such that $1\le 1+a &...
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Getting displacement from the accelerometer data for vertical motion
I have an accelerometer sensor with gyro and need to figure out the vertical displacement from the acceleration data. The device that contains the accelerometer will move up and down in fairly ...
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How to Solve a Composition of Convolutions from Regularized Least Squares Model in Frequency Domain
Assume we need to solve the model:
$$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| \boldsymbol{h} \ast \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \frac{\lambda}{2} {\left\| \boldsymbol{g} \...
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Solving linear equation of discrete convolution kernels using black box model for the convolution
In Solving inverse problem using black box implementation of the kernel the solution depends on solving the equations of the form:
$${\left( {H}^{T} H + \lambda {G}^{T} G \right)} x = y$$
Where $H$ ...
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Is there any method to incorporate boundary periodic conditions into the kernel summation over unstructured data points?
Supposing that there are $N$ particles distributed inside a periodic cubic box of volume $V=L^3$, I want to divide the cube into a regular mesh and calculate the following summation at each grid point ...
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Matrix-vector multiplication representation of Total Variation function
I'm reading a paper - Total Variation Superiorized Conjugate Gradient Method for Image Reconstruction on total variation regularization and conjugate gradients. In page $3$, the authors define the ...
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Convergence of the RLS Algorithm for a Forgetting Factor $ \lambda < 1 $
I have a question regarding Recursive Least Squares (RLS) adaptive filter.
According to Wikipedia (Recursive Least Squares in Wikipedia), to prevent infinite memory one introduces a forgetting factor $...
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How is the transfer function of a state space representation computed in practice?
I know that if you have a linear time invariant system defined by
$$ \dot{X} = AX+BU $$ $$Y = CX$$ by "Laplacing" the previous equations, you get the following transfer function in the ...
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Other Methods for Numerical Integration
I know four common methods for numerical integration of signals such as Midpoint, Trapezoid, Simpson's rule, and FFT integration property. Are there other methods?
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Generate the Matrix Form of 1D Convolution Kernel
As a follow up to Generate the Matrix Form of 2D Convolution Kernel, could someone explain how to generate the matrix form of a 1D convolution kernel?
How different convolutions shapes are handled?
...
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CORDIC-Taylor-DDS algorithms
DDS algorithm is really nice algorithm for creating sinus signal. It is really useful for signal resolution and use of LUT.
CORDIC uses LUT and numerical methods. But I don't get high resolution ...
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Digital integrator
I have been implementing a control software where I need to calculate a magnetic flux based on the measurement of the phase voltages of a three phase grid (basically three sinewaves) according to the ...
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Numerically finding impulse response from a wave equation
I'm developing a song synthesizer (like Yamaha's Vocaloid). I decided to mimic the acoustics of human speech. I modeled the space between articulators as a solid of revolution, and came up with the ...
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Arbitrary precision FFT and IFFT
For evaluating the performance of algorithms that use double-precision floating point numbers, or to pre-calculate double-precision floating point data to the best precision, it would sometimes be ...
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How to figure out number of multiplications in rational sampling
I am trying to understand the following:
Consider a system implementing a rational sampling rate change by $\frac{5}{7}$: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency $\...
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Trajectory Planning and Optimal Control
When finding control inputs for ODE systems, gradient based solutions are often used. With the increase computational power will these solutions still be important over things like Monte-Carlo ...
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Best Approach to Rank Complex Magnitude Comparision Problem
This is in reference to the responses for an efficient algorithm for the comparison of bounded fixed point complex numbers at this post.
Efficient Magnitude Comparison for Complex Numbers
See the ...
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Efficient Magnitude Comparison for Complex Numbers
Is there a more efficient algorithm (or what is the most efficient known algorithm) to select the larger of two complex numbers given as $I + jQ$ without having to compute the squared magnitude as
$$...
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solution on the time domain becomes “periodic” after the inverse fourier transform
I was trying to solve european option pricing problem using Conv method (introduced by Lord in 2008 https://pdfs.semanticscholar.org/0632/460bd50b2151f74ac40028df4cc60e73a884.pdf).
The final step of ...
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Understanding Fourier Transforms in abstract math terms
I am having a hard time implementing a method that computes Fourier transform coefficients for the complex form using the trapezoid rule.
I have floated questions in the math and stackoverflow ...
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Numerical higher order derivatives and time axis
I have a rather elementary question. Suppose we wish to study even-derivatives of an instrumental signal say second fourth and sixth derivatives and plot it as a function of time. With each successive ...
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How can I specify the distance between values in such row
I have a question, about verifying the value which are near to each other in such row, Is there any algorithm which can determine that ?
Suppose I have a vector $z_i =$ {$z_1 , z_2, z_3, . . . ., ...
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Solving LASSO ($ {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 ...
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What Approximation Techniques Exist for Computing the Square Root?
I have very limited resources as I'm working with a microcontroller. Is there a taylor-series expansion, common lookup table, or recursive approach?
I'd prefer to do something without using math.h's ...
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