||Digital filters are fundamental and integral parts of many digital signal processing systems, such as communication systems, multimedia systems, speech systems, and radar systems. The designs of finite impulse response (FIR) digital filters and quadrature mirror filter (QMF) banks are considered in this thesis. Several algorithms for the frequency domain design of FIR digital filters and QMF banks are presented. The presented algorithms have shown to be very flexible in term of design specifications. Simultaneous time and frequency constraints can be easily and efficiently incorporated in the designs without compromising the performance of the presented algorithms. Design examples are presented to demonstrate the versatility of the presented algorithms. Other algorithms described in the literature cannot achieve all these goals. The algorithms also exploit the design of the FIR filters and QMF banks without explicit specification of the transition bands. We demonstrated that the presented algorithms allow an efficient tradeoff between different design parameters. In the case of FIR digital filter designs, the presented algorithms allow a tradeoff between ripple sizes and the transition bands bandwidth. In the case of QMF banks design, the presented algorithm allows a tradeoff between the transition bands bandwidth and the reconstruction error and/or the ripple sizes of the lowpass analysis filter. The iterative algorithm for QMF banks design is proved to converge analytically; while the convergence of other iterative algorithms for FIR digital filter designs are shown empirically through a large number of design examples. The design examples have shown that the presented algorithms converge efficiently. Therefore, we conjectured that the iterative algorithms for FIR digital filter design and QMF banks design are able to solve practical design problems in real world applications.