4. Conclusion

The discrete wavelet transform was introduced based on the basic concepts of filter theory. It was shown how high-pass and low-pass filters can be constructed to produce wavelets and scaling functions. The properties of scale functions and wavelets are intimately linked to the slope and flexibility of these filters. In addition, an efficient method for implementing the discrete wavelet transform has been described. However, for the discrete case, the introduction of wavelets and scaling functions is not necessary at all, because all calculations can be performed using the various high-pass and low-pass filters.