Difference between revisions of "Time scale discrete Fourier transform"
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Revision as of 03:53, 26 February 2018
Let $\mathbb{T}=\{t_0,t_1,\ldots,t_n\}$ be a finite time scale and let $z_n$ be a frequency root of $\mathbb{T}$. The time scale discrete Fourier transform at $z_k$ is defined by $$\mathrm{DFT}\{f\}(z_k)=\displaystyle\sum_{k=0}^{N1} x(t_k) \overline{e_{z_n}(t_k)} \mu(t_k),$$ where $e_{z_n}$ denotes the delta exponential.