Fourier Transform Notation

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

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