Finite Impulse Response (FIR) filters have been the major players in the Wavelets and Multiresolution Analysis field; mainly due to their ease of design and understandable nature, as well as their well behaved characteristics such as stability and linear phase response. However it has been demonsirated that in a number ofcases Infinite Impulse Response (LW) filters are more appropriate. This paper describes a new solution for the wavelet conditions to derive stable UR filters that are matched in a least squares sense to specified frequency responses. The derived solution treats independently the numerator and denominator in the rational transfer fimction. This solution can be applied to any IIR wavelet filter bank satisfying the orthogonality and perfect reconsiniction conditions. Based on the proposed solutions, a new IIR wavelet filter bank with the low pass filter matched to a desired frequency response is developed.

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