A digital down converter (DDC) that improves efficiency by taking advantage of the periodicity of the coarse mixing process and the memory inherent in the convolution operation performed by decimation filters. In embodiments, the DDC filters and decimates a received signal to generate subfilter outputs and coarse mixes the subfilter outputs for each frequency band of interest. Accordingly, the DDC eliminates the need for separate decimation filters for each of the in-phase (I-phase) and quadrature (Q-phase) signals of each frequency band. In some embodiments, for each frequency band, the DDC combines the subfilter outputs into partial sums for each of the I- and Q-phases. In some of those embodiments, the coarse mixing operation is performed by multiplying the partial sums by real multiplicands and performing a simple post-rotation operation. In those embodiments, the DDC significantly reduces the number of multiplication operations required to perform the coarse mixing process.