Different from a frequency response graph, an impedance graph indicates load on the amplifier vs frequency. Software produces a sine sweep (or pink noise). This signal is taken from the PC output and amplified. Current (voltage across a known resistance) and voltage of the output is measured, and fed back into the PC. Software then calculates Impedance and compares it to the source signal.
Here is a comparison of a speaker before (gray) and after repairing a fault in the crossover (black). Note the significant difference in impedance at 4kHz.
LIMP by Artalabs is the software used in this project.
It has great calibration tools, and a thorough tutorial.
My example; Speakon connects to woofer / speaker box to be tested, 3.5mm TRS are used for simple interfacing with PC.
Constructed from several other PCB projects (TDA7294 50W amplifier, and Differential Scope Probe circuits), with point to point wired linear supply for simplicity. These were just things I had on hand at the time of construction.
Output of the amplifier passes through a 1R 10W sense resistor.
Sense outputs are voltage dividers, and PC mic level inputs are buffered.