Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

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, ...