# Signal de-amplified before doing Power Spectral Density. Any effect?

I have a time-series signal (voltage, specifically) that was divided by 1000 before doing an FFT-based Power Spectral Density (PSD) (using LabView), giving the output in dB.

Question: What is the effect of this de-amplification on the validity of the PSD? And how can I amplify it back?

For integer data, scaling down a digitized sampled signal by 1000 increases quantization noise by 10 bits. That may or may not be a significant enough change (in S/N) to affect the accuracy of your subsequent analysis. It is also an information lossy process that cannot be reversed (unless you also have access to the data before it was scaled down).

The above does not apply to data in floating point format before scaling it down, as long as it does not underflow during scaling or analysis.

• So there's no way I can undo the result? (let's forget the quantization noise for now--the scaling was done after sampling, anyway) – student1 Jun 25 '14 at 2:09

Scaling a signal is not problematic and a FFT-based PSD is valid. You can easily scale back in the log scale by adding the appropriate factor. If you have single-sided power spectrum non-DC components have heights of $\frac{A_{k}^2}{2}$ Where $A_{k}$ is peak amplitude at frequency $k$. In your case $\frac{A_{k}^2}{2*1000^2}$ this would mean adding 60 dB to value converted to dBx.

Generally you must also consider gain of the window function used in FFT calculation if you are calculating power this way. But LabView probably takes care of this things automatically.

• How did you come with the value 60 dB, not 6 dB? – student1 Jun 24 '14 at 23:16
• (P.S. whoever downvoted, may you share your ideas with us?) – student1 Jun 24 '14 at 23:31
• Yes sorry, I was assuming that you convert to log scale using $10*log(P/P_{ref})$ this way you get 6dB*10. – Urban Kuhar Jun 30 '14 at 19:26