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0
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0answers
23 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
40 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
62 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
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0answers
30 views

How to acquire the `mainlobe` width to be less than the separation between two components that we wish to distinguish?

How does the mainlobe width of your window affect your ability to resolve the two components? Suppose a safe choice is to ...
0
votes
1answer
274 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
141 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
52 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
85 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
304 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: $f_1(t)=A_1$ $f_2(t)=A_2\cos(0.05t)$ ...
4
votes
2answers
2k 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
91 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
336 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
596 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 ...
12
votes
3answers
2k 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 ...