Fourier Transform Notation

The following notation will be used to state that $ X(\omega_k)$ is the Fourier Transform of $ x(t_n)$

$\displaystyle x \;\longleftrightarrow\;X \qquad [X=\hbox{\sc DFT}(x)]$ (A.1)

where $ \;\longleftrightarrow\;$ is read as ``corresponds to''. The notation $ XY$ or $ X\cdot Y$ denotes the vector containing $ (XY)_k=X(k)Y(k)$ , $ k=0,\ldots,N-1$ . This is denoted by `X .* Y' in Matlab, where X and Y are either column or row vectors.


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