## Note 66. Generating I and Q Channels Digitally: Generalization of Rader’s Approach

**Rader’s digital I and Q approach presented in Note 65 requires that the real bandpass IF signal be sampled at a rate equal to four times the signal’s bandwidth. This note shows how Rader’s scheme can be generalized to support sampling rates that are not four times the signal bandwidth.**

Rader’s efficient IIR design for the complex filter depends upon downsampling by a factor of four, which in turn drives the requirement that the sampled I/F bandpass signal be centered at a frequency equal to one-fourth the sampling rate. This constraint is required so that downsampling by a factor of four shifts the surviving sideband to a center frequency of zero. If an FIR filter, ...