Wavelet transform and filter banks theory relationship. A revision

• Trina Adrián de Pérez Universidad Simón Bolívar-Venezuela
• Margarita Juanatey Universidad Simón Bolívar-Venezuela
• Luis Urbano Universidad Simón Bolívar-Venezuela
• Rafael Banehs Universidad Simón Bolívar-Venezuela

Resumo

The search for methods to analyze signals, aimed at obtaining the attributes related to the physical properties that generate these signals, has always been a topic of interest to engineers and mathematicians. One of the most widely used techniques has been representing the signals in the time domain; frequency domain analysis or Fourier analysis complements this information. However for non-stationary signals another tool is needed. This produced the idea of a new signal representation using other basis functions to obtain a better time-frequency resolution compromise. This was defined as the wavelet transform. Also, in recent years, the theory of perfect reconstruction filter banks has been impulsed by the search of methods that optimize the storing and transmision of information. This paper introduces the waveet transform and perfect reconstruction filter bandks basics concepts and presents their relationships. This connection makes it possible to present a wavelet transform method based in a filter design that produces the best signal bands analysis.