This column continues our quest of building a complete software radio receiver. We'd like to place as many of its components as possible in either an inexpensive integer-based DSP or in an FPGA. This installment examines digital techniques for translating a complex signal from one center frequency to a different one.

More generally, complex frequency shifting is a powerful tool that moves a signal from any arbitrary frequency to any other. Either the source or destination frequency can be 0 Hz. You can also optionally invert the spectrum of the signal, if desired.

When demodulating a complex signal, you usually want to center the signal at 0 Hz. Doing so allows you to lower the sampling rate while still preserving the signal's integrity. This technique can also account for the inevitable tuning inaccuracies that occur in receiving systems such as due to oscillator variations.