# Difference between revisions of "Frequency roots"

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(Created page with "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) + \display...") |
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=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= | ||

+ | [[Time scale discrete Fourier transform]]<br /> | ||

=References= | =References= |

## Revision as of 03:45, 26 February 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

Frequency roots in integers

Frequency roots in harmonic numbers

[[Frequency roots in quantum time scale, q>1]]

[[Frequency roots in quantum time scale, q<1]]

# See also

Time scale discrete Fourier transform