# Wavelet filter coefficients from the Morlet wavelet

How can I obtain the wavelet filter coefficients ( i.e. lowpass decomposition filter, highpass decomposition filter, lowpass reconstruction filter, highpass reconstruction filter) for the Morlet wavelet?

For convenience: the wavelet curve follows the equation $$\pi^{1/4} \exp(jwx) \exp(-0.5x^2)\,.$$

• Duplicate, see here. Short answer: It's not possible. – André Bergner Apr 11 '13 at 13:27

## 1 Answer

The critically-sampled lowpass/highpass and subsampled filter bank implementation of the Discrete Wavelet Transform (DWT) is only valid for a certain class of wavelets. And the Morlet wavelet family does not belong to this class.

Explained differently, discrete wavelets seldom have closed-form expressions, because of the constrains laid on the dyadic scales and filters. Since the Morlet wavelet is complex, you may want to invest in one of its discrete avatars, the dual-tree wavelet transforms, that are somewhat redundant however. I happen some personal references on the topic: