A novel structure for tunable complex-arithmetic heterodyne filters

The standard approach to designing a tunable complex heterodyne filter is to take a high-pass (or low-pass) digital filter and rotate it by multiplying by a complex exponential. This is a three heterodyne process that rotates the filter first to the left, then two to the right, and finally back to the left. An alternative is to use a complex digital filter to eliminate the frequencies in the bottom half of the unit circle such that a two heterodyne process can be used. The advantage of the two heterodyne process is not only the elimination of one heterodyne operation, but also a reduction in hardware due to the need to only calculate the real output of the last heterodyne stage.