Questions tagged [approximation]

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What approximations are involved in STFT of a convolution?

I have two equations in time domain: $$x_k(t)=\sum_{i=1}^N s_i(t)\star h_{ki}(t)+n^a_k(t)$$ and $$x_k(t)=\sum_{i=1}^N s_i(t)\star h_{ki}(t)\star n^c_k(t)$$ which explain the additive and convolutive ...
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203 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 ...
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How to Approximate / Fit a Function and a Lower Bound on It?

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 $...
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158 views

Techniques to reject noisy neural network input

Suppose an artificial neural network is used to approximate a sine wave (shown in red in the graph below), given the linear input variable $x$ (scaled such that the ANN input is $x_{\rm nn}\in[-1;1]$)....
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109 views

“Improved” MZT/IIM type One pole LPF

Some time ago, while playing with all kind of approximation of common math functions, I came up to this idea to calculate a1 coefficient for a 1st order LPF filter: \begin{array}{l}a1=-(1+x+\frac12x^...
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39 views

Some difficult-to-approximate signals to test an signal extracting algorithm

I am searching for some strange signals in order to test an algorithm that I am developing. I've found an article by Donoho and Johnstone where they propose to test the algorithms using Blocks, Bumps, ...
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1answer
1k views

Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT

I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
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66 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 ...
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131 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 ...
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115 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 ...