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 $\mathbb{T}$:
$$\mu(t_0) + \displaystyle\sum_{k=1}^{N-1} \mu(t_k) \displaystyle\prod_{m=0}^{k-1} (1+z\mu(t_m)).$$
+
$$\mu(t_0) + \displaystyle\sum_{k=1}^{n-1} \mu(t_k) \displaystyle\prod_{m=0}^{k-1} (1+z\mu(t_m)).$$
  
 
=Properties=
 
=Properties=
[[Frequency roots in integers]]<br />
 
[[Frequency roots in harmonic numbers]]<br />
 
[[Frequency roots in quantum time scale, q>1]]<br />
 
[[Frequency roots in quantum time scale, q<1]]<br />
 
  
 
=See also=
 
=See also=

Latest revision as of 00:41, 14 March 2018

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

References