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\[
F(u) = \frac{1}{N} \Sigma_{x=0}^{N-1} f(x) e^{-j\frac{2\pi}{N}ux} 
\]
\[
f(x) = \Sigma_{u=0}^{N-1} F(u) e^{j\frac{2\pi}{N}ux}
\]
1D Fourier Transform Pair
\[
\frac{1}{\sqrt{a}} \ \ \varphi(\frac{x-b}{a}) \ \ \ a > 0; b \in R 
\]
Grossman-Morlet

\\
\[
2^{j/2} \ \varphi(2^{j}x-k) \ \ \ j,k \in Z
\]
Daubechies
\\

\[
\omega (t-l) \cos(\pi (k+1/2)(x-l)) \ \ \ k \in N, l \in Z
\]
Gabor-Malvar
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