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Four Forms of Fourier Transform

Depending on whether a signal $x(t)$ is periodic and discrete, its Fourier transform will take one of the four forms:

Four forms of Fourier transform (Table 5.3):


\begin{displaymath}\begin{tabular}{c\vert\vert c\vert c} \hline
& {\bf Signal $x...
...& ($T/t_0=N$) & ($F/f_0=T/t_0=N$)  \hline
\par
\end{tabular} \end{displaymath}

The Convolution theorem


\begin{displaymath}\begin{tabular}{c\vert\vert c\vert c} \hline
& Time domain &...
...\sum_{k=0}^{N-1} X_F[k]Y_F[n-k]$  \hline
\par
\end{tabular} \end{displaymath}

Parseval's formula


\begin{displaymath}\begin{tabular}{c\vert\vert c} \hline
I & $\int_{-\infty}^\in...
...sum_{n=0}^{N-1} \vert X_F[n] \vert^2$  \hline
\end{tabular} \end{displaymath}


next up previous
Next: Numerical Implementation of DFT Up: Fourier_Analysis Previous: Discrete Fourier Transform
Ruye Wang 2003-11-17