An outline is presented for construction of wavelet filters with compact support. Our approach does not require any extensive simulations for obtaining the values of design variables like other methods. A unified framework is proposed for designing halfband polynomials with varying vanishing moments. Optimum filter pairs can then be generated by factorization of the halfband polynomial. Although these optimum wavelets have characteristics close to that of CDF 9/7 (Cohen-Daubechies-Feauveau), a compact support may not be guaranteed. Subsequently, we show that by proper choice of design parameters finite wordlength wavelet construction can be achieved. These hardware friendly wavelets are analyzed for their possible applications in image compression and feature extraction. Simulation results show that the designed wavelets give better performances as compared to standard wavelets. Moreover, the designed wavelets can be implemented with significantly reduced hardware as compared to the existing wavelets.