How to use the FFT and Matlab's pwelch function for signal and noise simulations and measurements

This report describes how information on signal and noise levels can be extracted from an FFT when windowing is used. We explain in detail what the function pwelch from Matlab's Signal Processing Toolbox is doing, and how to read signal magnitudes out of pwelch-generated periodograms. The target group of readers are engineers who want to simulate (or measure) signal-to-noise ratios using FFTs or periodograms on a captured signal, e.g., a sigma-delta bitstream.