Synthesizing I and Q signal data for DSP is typically accomplished in an SDR by implementing a Quadrature Multiplier immediately following the initial A/D conversion.  I and Q signal data is a necessary condition for DSP mathematics.

A GNU Radio flow graph simulation can be used demonstrate this important DSP process.  The flow graph is simpler than you might imagine and for this demonstration is depicted in a familiar classic configuration.  All that is required are two mixers, an input sinusoid, and two signal sources 90 degrees out of phase from one another.  Once executed, the flow graph outputs I and Q data to a Scope Sink.  The identical in frequency and the 90 degree phase shift of the I and Q signals can be viewed in the scope display.  In a non-simulation application, such as an ordinary SDR application, the output would be input to a DSP.

Quadrature Multiplier flow graph with a signal source and two multipliers

The signal source produces an unmodulated sampled sine wave.  If the source signal were modulated the output would be termed a ‘sinusoid’.  The signal sources for the two multipliers provide sampled signals that are 90 degrees out of phase: one source outputs a sine wave and the other source outputs a cosine wave.  It is these 90 degree phase shift inputs to the multipliers that are the key to the I and Q outputs of the Quadrature Multiplier.

Quadrature Multiplier Operating GUI:  Channel 2 depicted as the actual sampled digital data. Channel 1 depicted as a smoothed sine wave

Note the identical frequency and the 90 degree phase shift of the two sampled sine waves outputs.  These are the I and Q outputs of the Quadrature Multiplier.  For demonstration purposes, the Channel 2 output is displayed as the actual sampled signal by the series of dots.  Channel 1 is displayed as a smoothed sign wave.  The choice of display type for each channel is controlled by the Marker menu in the Operating GUI for the Scope Sink.  You can adjust the display type once the flow graph is executed.  Just remember, the actual Quadrature Multiplier output is a series of sampled data points, a series of dots on the scope display, not a smoothed sine wave.

The .grc file for this demonstration is available here: Quadrature Multiplier demo

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