Frequency roots

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