The Meyer wavelet is an orthogonal wavelet proposed by Yves Meyer. As a type of a continuous wavelet, it has been applied in a number of cases, such as in adaptive filters, fractal random fields, and multi-fault classification. The Meyer wavelet is infinitely differentiable with infinite support and defined in frequency domain in terms of function ν {\displaystyle \nu } as
Ψ ( ω ) := { 1 2 π sin ( π 2 ν ( 3 | ω | 2 π − 1 ) ) e j ω / 2 if 2 π / 3 < | ω | < 4 π / 3 , 1 2 π cos ( π 2 ν ( 3 | ω | 4 π − 1 ) ) e j ω / 2 if 4 π / 3 < | ω | < 8 π / 3 , 0 otherwise , {\displaystyle \Psi (\omega ):={\begin{cases}{\frac {1}{\sqrt {2\pi }}}\sin \left({\frac {\pi }{2}}\nu \left({\frac {3|\omega |}{2\pi }}-1\right)\right)e^{j\omega /2}&{\text{if }}2\pi /3<|\omega |<4\pi /3,\\{\frac {1}{\sqrt {2\pi }}}\cos \left({\frac {\pi }{2}}\nu \left({\frac {3|\omega |}{4\pi }}-1\right)\right)e^{j\omega /2}&{\text{if }}4\pi /3<|\omega |<8\pi /3,\\0&{\text{otherwise}},\end{cases}}}
where
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