In this dissertation, the efficient design of low-complexity linear-phase Finite Impulse Response (FIR) filters for digital communication applications is investigated. The research developed here relies upon the main two categories of solution, namely, decomposing the overall filter in simple subfilters (subfilter-based solutions) and simplifying the filtering coefficients by eliminating multipliers (multiplierless solutions). For both cases, new proposals have been developed. The research contributions based on subfilters are focused on both, narrowband and wide-band cases. The Recursive Running Sum (RRS) filter, a useful filter characterized by its low complexity, is employed especially for low-pass narrowband cases. Four proposals that improve the magnitude response of RRS filters are introduced. The proposed schemes provide a more efficient balance between magnitude response improvement and the added complexity to the RRS filter in comparison with previous schemes developed in literature. The efficient design of Hilbert transformers, a special case of wide-band filter, is also investigated. A generalized method to properly combine identical-subfilter-based and periodical-subfilter-based schemes is introduced and it is shown that this method provides low-complexity filters. Cyclotomic Polynomial Filters (CPFs), a special class of subfilters, constitute low-complexity filtering solutions widely used in the efficient design of FIR digital filters and, because of that, they are studied in this dissertation. An important contribution to design CPF-based filters is presented, namely, the extension of the search space of CPFs beyond of the limits used in literature. From the results of this extension we have developed the theorem of preservation of unitary coefficients, the main contribution on this topic. This theorem enlarges the capabilities of CPFs by showing that any CPF can have a transfer function with unitary coefficients and with the lowest computational complexity. Finally, our contributions on multiplierless approaches are introduced with the basis on the implementation of constant multiplications as a network of additions and shifts. We develop an extension to the theoretical lower bounds for the adder cost and adder depth in the Single Constant Multiplication (SCM) problem. With this extension, the hidden theoretical lower bound for the number of adders required to preserve the minimum adder depth is revealed.