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Topic: phase randomisation, Zero Padding of IFFT, and Parseval
Replies: 2   Last Post: Jul 3, 2013 5:13 PM

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 Jim Schwendeman Posts: 7 Registered: 6/21/13
Re: phase randomisation, Zero Padding of IFFT, and Parseval
Posted: Jul 3, 2013 5:13 PM

So... It appears that part of my Parseval's equation was incorrect. I was using sum squared of the time-series, rather than variance. I'm now using TideMan's response from an alternate discussion:

>>This is Parseval's Law:
>>sum(PSD)*df must equal var(y)
>>The area under the spectrum must be the variance of the time signal.
>>In your case, I think df is 1.

Multiplying the time-series by sqrt(Fs) gives me a times-series variance that matches up with sum(PSD)*df.

Dividing the resulting FFT of the time-series by sqrt(Fs) provides me with the original PSD

Date Subject Author
7/3/13 Jim Schwendeman
7/3/13 Jim Schwendeman
7/3/13 Jim Schwendeman