**6. Conclusion**

In this study, max-pooling frequency response is analyzed, and instead of a sliding or changing filter, the results shown a dynamic harmonic amplifier behavior. This phenomenon helps max-pooling to prevent the CNN from overfitting. This keeps the CNN learning rather than memorizing the dataset values, and thus achieving higher accuracy results.

Most of the wavelet models achieve high results, which point out that MRA can improve CNN pooling performance, especially when using hybrid models. However, by analyzing the results of the wavelet model that uses all the coefficients permanently, it is evident that having a nonlinear selecting mode, like a random model, to extract features in every iteration is essential.

In summary, contrarily to max-pooling, not been dependable on the signal shape gives more consistent results. In addition, the mix pooling methods exhibit that processing small regions produced better results than the opposite. All these factors are important to improve CNN performance. The model proposed takes the best part of both issues and moreover, it also takes advantages of having wavelet functions with different vanishing moments.

Finally, implementing two additional wavelet functions based on the lifting scheme shows its feasibility and enrich the model for future applications. Future works include the use of this model in harder imaging like infrared, ultraviolet or satellite imaging.
