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0
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1answer
34 views

Determinant of Hessian approximation (SURF)

I have a question regarding formula in SURF article by Bay et al. Theory Given a point $p=(x,y)$ in an image $I$, the Hessian matrix $\mathcal{H}$ in $x$ at scale $\sigma$ is defined as follows $$ ...
0
votes
1answer
21 views

Wavelet transform: How to compute the initial coefficients when only samples are available?

In standard MRA we have that the space of functions at scale J can be expressed as $$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$ where $V_0$ is spanned by the orthonormal system of the ...
1
vote
1answer
49 views

Very-short Hilbert transform FIR (or “recursive”) approximations

Hilbert transform is a quite sensitive topic here, since Gabor's paper, Theory of Communication, J. Inst. Electr. Engineering, London, 1946. Perhaps even more important than the Fourier transform. ...
-1
votes
2answers
48 views

How to choose basis functions that contribute most efficiently per term to an approximation of an image f(x,y)?

GOAL: I would like to approximate some positive, scalar function, $f(x,y) > 0$, on a 2D field of finite size i.e. $x=[a,b],y=[c,d]$ OBSTACLE: I am familiar with the set of basis functions used ...
0
votes
0answers
18 views

Piecewise approximation of 3D surface

I've used general piecewise polynominal approximation schemes in the past for general function approximation with a single variable. I now have a problem where I need to approximate a 3D surface ...
5
votes
1answer
52 views

Looking for a better algorithm for finding the slope of an input signal

I've got an input signal that while sloping up, approximately bounces off an imaginary line. I'm looking for the equation to that imaginary line. I have a method, but is very brute force and it ...
0
votes
1answer
65 views

Wavelet decomposition

For the following code, X=[2 2 3 100 4 0 98 100 90 2 3 67 98 0 6 6 89 9 21 78] [C,L]=wavedec(X,N,'db1'); where N is the ...
0
votes
0answers
29 views

Unexpected peak after up & down sampling

I am working on signals to check how approximation can change the results. I am testing on example that can change frequency from 22kHz to 20 KHz. I prepare this script in MatLab ...
0
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0answers
169 views

frequency response of Gaussian filter

In Matlab, the function freqz can produce frequency response in terms of transfer function and the function freqz2 can produce frequency response for FIR filter. It seems that I can's use the input ...
0
votes
0answers
72 views

Second-order sections from complex coefficients

I have an impulse response ir that I need to approximate with an iir because of realtime requirements. For stability I want to break down the 10th order IIR generated with Steiglitz-Mcbride to biquads ...
0
votes
1answer
45 views

How to determine best fit from two?

I'm studying some variances ($\sigma^2$), that in my case, they must depend by velocity squared $v^2$. So, in my experimental proofs, I have plotted a graph of $\sigma^2/v^2$, and I was hoping to ...
1
vote
0answers
125 views

MATLAB implementation Spline Fitting

Let $s(t)$ be a signal that can be approximated by a uniform spline function of order $K$ (say $K=2$): $$s(t)\approx\sum_{n\in \mathbb{Z}}c_n\beta_+^{(K)}(t-n) $$ Suppose that we know the ...
0
votes
0answers
33 views

which one is the most appropriate approximation way between legendre polynomial and taylor polynomial?

I trying to implement such as $$f(x)=\log\left(\frac{\tanh(1+x)}{\tanh(\delta+x)}\right),\quad x\in (0,1),\quad\delta\in (0,1)$$ equation to Hardware logic. So i think i need some way to ...
0
votes
1answer
44 views

Calculating Signal Approximation Error (Theoretical signal - Real hardware signal)?

I've got a FIR filter, which I developed in IC. Now, when I got my results, I ended up with two signals: Theoretical signal calculated through MATLAB as a response to my input. Real response given ...
1
vote
1answer
92 views

Standard deviation of Gaussian corresponding to perfect low pass filter [1,1]

For a time discrete signal, the rect-filter (for 1D signal [1,1]) is a perfect low pass filter. I was wondering, what is the best gaussian approximation of this filter? For a current problem, I ...
0
votes
1answer
483 views

How to use Expectation maximization to estimate poisson noise matlab [closed]

I delved into the state of the art of algorithms for Poisson noise estimation in order to estimate the variance, I found that the Expectation Maximization algorithm is very used and it is very ...
0
votes
2answers
231 views

Mathematical proof of relationship between derivative and convolution

What I'm looking for is the mathematical proof of why we can calculate derivatives as a simple convolution of a mask, and how do we get that mask? I know it has something to do with how the derivative ...
1
vote
0answers
58 views

How to fit a function (find a lower bound) to (for) the plots?

I am dealing with a complicated optimization problem with two parameters $N, K$. Setting $K =$ constant and finding the minimum for different $N$'s lead to a set of function values. I can do this for ...
-3
votes
1answer
89 views

How to combine similar signals to generate another one?

Assume there are 11 signals. These signals are very similar to each other in both time and frequency domains. (And the similarity between them is not random; they are similar because they have somehow ...
1
vote
1answer
558 views

Signal approximation using linear combination of functions

How I can approximate the signal $x(t)=0.001\,t^3 \exp(-0.1t)$ in the interval $[0,100]$ using a linear combination of the following functions: $f_1(t)=A_1$ $f_2(t)=A_2\cos(0.05t)$ ...
6
votes
2answers
4k views

Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ...
1
vote
1answer
97 views

Establishing the function of a decaying signal

I have a set of samples from a signal. The signal is erratic in behaviour at the beginning but then it settles down and oscillates around the value of 100 (the frequency of oscillation is not ...
2
votes
1answer
402 views

Approximating pixel location in scale space

I'm implementing a scale-space with o octaves and s scale levels in each octave. Each octave is half the size the previous. I have keypoints found in each octave, I need to approximate the real ...
8
votes
2answers
1k views

Estimate Taylor series coefficients from samples of a function

Say I have measurements of a function $y = y(x)$, sampled at $x_i$ with some noise, that could be approximated by a Taylor series expansion. Is there an accepted way of estimating the coefficients for ...
13
votes
3answers
6k views

What is the best first-order IIR approximation to a moving average filter?

Assume the first order IIR Filter: $ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $ How can I choose the parameter $ \alpha $ s.t. the IIR approximates as good as possible the FIR which is the ...