Difference between revisions of "Frequency roots"
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Let $\mathbb{T}=\{t_0,t_1,\ldots,t_n\}$ be a finite [[time scale]]. The roots of the following polynomial are called the frequency roots of $\mathbb{T}$: | Let $\mathbb{T}=\{t_0,t_1,\ldots,t_n\}$ be a finite [[time scale]]. The roots of the following polynomial are called the frequency roots of $\mathbb{T}$: | ||
| − | $$\mu(t_0) + \displaystyle\sum_{k=1}^{ | + | $$\mu(t_0) + \displaystyle\sum_{k=1}^{n-1} \mu(t_k) \displaystyle\prod_{m=0}^{k-1} (1+z\mu(t_m)).$$ |
=Properties= | =Properties= | ||
| + | |||
| + | =See also= | ||
| + | [[Time scale discrete Fourier transform]]<br /> | ||
=References= | =References= | ||
| + | |||
| + | [[Category:Definition]] | ||
Latest revision as of 15:28, 21 January 2023
Let $\mathbb{T}=\{t_0,t_1,\ldots,t_n\}$ be a finite time scale. The roots of the following polynomial are called the frequency roots of $\mathbb{T}$: $$\mu(t_0) + \displaystyle\sum_{k=1}^{n-1} \mu(t_k) \displaystyle\prod_{m=0}^{k-1} (1+z\mu(t_m)).$$
Properties
See also
Time scale discrete Fourier transform
