Underestimation of Power?

[Ulrich Fickel]

If I generate a time-domain signal of 1 Hz and 1V, the theoretical signal power should be 0.5 V^2rms.

I found the LV frequency tools return this value only if the signal length is an integer of the cycle length (1s, in this case).

If the signal has, e.g., the length of n cycles + Pi, the power decreases to about 0.2 V^2rms. This is much less than one should expect theoretically.

This decrement is similar for all signal lengthes, amplitudes, frequencies, and sampling frequencies I tested.
I did no zero-padding, my signal already had a length of a valid power of two.

How does this come? I tested with VERY long signals, but only the completeness of the last cycle caused this decrement.

[Stu 708]

If you do not have integer number of cycles in the waveform (which is the case most of the time) there are edge effects of the algorithm. That is why a window is typically applied to the data before processing. A Window (Hanning for example) will force the ends of the waveform to 0 to reduce these edge effects. Even after this windowing, the result will not be perfect. That is why multiple frame averaging is used to produce a more consistent measurement.
Stu

[Stu 708]

Sorry, I gave an incomplete answer before. When dealing with non integer number of cycles, the power is spread accross a couple of lines of the spectra. A band sum +-1 line around the target will yield the correct magnatude even without windowing. Be careful to perform the band sum correctly.
Stu