Why is the average power spectral density from the output of a Band-Limited White Noise block not equal to the Noise Power parameter when using an Averaging Power Spectral Density Block?

A simple Simulink model with a Band-Limited White Noise block source feeding into an Averaging Power Spectral Density Block will display an average PSD which is approximately three times smaller than the value I supplied in the Noise Power parameter of the Band-Limited White Noise block. I would like to know the reason as to why this could be taking place.

Answer 1

[MathWorks Support Team]

This change has been incorporated into the documentation in Release 2010a (R2010a). For previous releases, read below for any additional information:

The unit used for the average PSD in the Averaging Power Spectral Density block is the square of the magnitude per unit radial frequency: Mag^2/(rad/sec) and is displayed as a one-sided spectrum.

The Band-Limited White Noise block, however, is assuming a specification of a two-sided spectrum, using Hz as the unit for frequencies. This means that the factor between these two representations is exactly 1/2 * 2 * pi = pi, where the 1/2 is the compensation for one-sided vs. two-sided and the 2 * pi accounts for the conversion between rad/sec and Hz.