Questions tagged [polynomial]

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Polynomial Response

I was referring to the below paper from @robert bristow-johnson https://www.researchgate.net/publication/266675823_Performance_of_Low-...
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36 views

Estimating the complexity by the calculation of the number of real multiplications in a general polynomial function

For the following memory polynomial equation, $y(n)=\displaystyle\sum_{m=0}^{M-1}\displaystyle\sum_{p =1\\p\,\textrm{odd}}^{P}a_{m_p} \, x(n-m) \, |x(n-m)|^{(p-1)}$ The total number of coefficients ...
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87 views

numpy.linalg.lstsq underdetermined case

I would like to understand what I am doing wrong here. I am trying to perform polynomial regression by minimizing the least squares, ||Au-y||^2, where y is the given data and A is the matrix where the ...
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1answer
67 views

Deriving the Langrangian interpolation polynomials in Cook-Toom convolutions

I'm working through Blahut's 'Fast Algorithms for Signal Processing'. Trying to develop an intuition for the Cook-Toom algorithm for convolutions as used by Lavin and Gray in their Winograd paper for ...
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39 views

Difference Between a 1st Order SG Filter And a Least Squares Moving Average

I have been studying SG filters and i recently found another filter which seem to be commonly used in financial data smoothing which is the least-squares moving average, this filter is also called ...
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1answer
88 views

Is it correct to call a Savitsky-Golay filter of degree 0 a simple moving average?

I had this question after seeing that polynomial regressions fit polynomial functions of different degrees to a time-series, since the mean of a time series is a constant and that a constant is also a ...
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0answers
43 views

How to select the sign of the square root of each element of a DFT in obtaining the square root of a polynomial?

I want to find the square root of a polynomial by the following process: Compute the N-element DFT of its coefficients, maybe padded with zeros. Compute the complex square root of each of the N ...
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2answers
243 views

Recursive filter with truncated polynomial impulse response

How can we recursively implement a causal discrete-time truncated infinite impulse response (TIIR) filter with an arbitrary truncated polynomial impulse response: $$h[n] = \begin{cases}\displaystyle\...