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![]()
>>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