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Diffstat (limited to 'chapter04/content_ch04.tex')
| -rw-r--r-- | chapter04/content_ch04.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/chapter04/content_ch04.tex b/chapter04/content_ch04.tex index c4e04f6..a5fc3bd 100644 --- a/chapter04/content_ch04.tex +++ b/chapter04/content_ch04.tex @@ -895,7 +895,7 @@ The \ac{DTFT} is derived from the \ac{CTFT}. Therefore, all properties apply lik Analogous to the Fourier and Laplace transform, the \acf{DTFT} is a special case of the z-transform. -\begin{definition}{Discrete-time Fourier transform} +\begin{definition}{z-transform} The \index{z-transform} \textbf{z-transform} of a time-discrete signal $\underline{x}[n]$ with the sampling period $T_S$ is: \begin{equation} \underline{X}\left(\underline{z}\right) = \mathcal{Z}\left\{\underline{x}[n]\right\} = \sum\limits_{n = -\infty}^{\infty} \underline{x}[n] \cdot \underline{z}^{-n} @@ -1065,7 +1065,7 @@ The $N \times N$ transformation matrix $\underline{\mat{F}}$ is the \index{DFT m \begin{equation} \underline{F}_{pq} = \underline{w}^{p \cdot q} \end{equation} -where $\underline{w}$ is the $N$-th \index{primitive root of unity} \textbf{primitive root of unity}\footnote{The primitive root of unity divide the unit circle $e^{j \phi}$ into equally sized segments.}. +where $\underline{w}$ is the $N$-th \index{primitive root of unity} \textbf{primitive root of unity}\footnote{The primitive root of unity divide the unit circle $e^{j \phi}$ into equally sized segments.}.\nomenclature[Sw]{$\underline{w}_N$}{$N$-th primitive root of unity} \begin{equation} \underline{w} = e^{j \frac{2 \pi}{N}} \end{equation} |