Questions tagged [polynomial]
The polynomial tag has no usage guidance.
11
questions
2
votes
1answer
250 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 ...
2
votes
1answer
83 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 ...
2
votes
1answer
38 views
Relation between Gaussian derivatives and Gausian-windowed Cosine function
I am doing some research on UWB radars which transmit a pulse given by:
$$
g(t) = p(t) cos(2\pi f_{c}t) = A e^{(-\frac{t^{2}}{2\tau ^{2}})} cos(2\pi f_{c}t)
$$
In some other papers, the transmitted ...
2
votes
3answers
131 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
...
2
votes
2answers
289 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\...
1
vote
0answers
19 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 $\...
1
vote
0answers
54 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
0answers
56 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 ...
0
votes
2answers
36 views
0
votes
1answer
37 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
264 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 ...
