Questions tagged [polynomial]

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2
votes
3answers
77 views

IIR to FIR, is a best fit polynomial usually necessary?

I'm messing around with IIR/FIR filters and want to convert the former to the latter. I set up a classic impulse response calculation. X[4] = 1.0 Y[0] = 0.0 Y[1] = 0.0 ...
0
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2answers
34 views

Fitting a polynomial to a ridge in an array

I have an array of numerical data. Say, ...
1
vote
0answers
13 views

What are the applications of Non Unique Factorization Domain (Non-UFD) in signal processing? [closed]

Let $m$ be a composite, and $\mathbb{Z}_m$ is the residual ring of modular $m$. The $\mathbb{Z}_m$ is clearly a Non-UFD. What are the applications of the polynomial with coefficients defined on $\...
0
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0answers
29 views

Polynomial Response

I was referring to the below paper from @robert bristow-johnson https://www.researchgate.net/publication/266675823_Performance_of_Low-...
0
votes
1answer
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 ...
0
votes
1answer
140 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 ...
2
votes
1answer
71 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 ...
1
vote
0answers
46 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 ...
1
vote
1answer
129 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 ...
1
vote
0answers
49 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 ...
2
votes
2answers
252 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\...