Averaging FFT of mutiple time series to get averaged fft results

[ishashukre]

Hi

I have multiple time series for the same set of measurement done at different times. Though all of them are not of same length but sampling frequency is same for all of them. When I do FFT of individual time series I will get magnitude & phase.

Is it correct to do linear averaging of the magnitude & Phase of FFT     OR         its necessary to convert magnitude & phase in to real & imaginary terms & then to averaging of real & imaginary parts for particular frequency & transform them back in to magnitude & phase.

To me later appear correct. Just want to confirm if there is any more simpler way to achieve this.

Thanks in advance

Isha

[johnsold]

If the data sets are of different lengths, then the FFTs will have different frequency resolutions and cannot be averaged by any simple technique.  I suggest that you determine the longest possible data set and then zero pad all data sets to that length before doing the FFTs. Or take subsets of the data where all the subsets are of the same length. After all the data sets are adjusted to the same lengths I think you can average the magnitudes and phases separately.

Lynn

[rpursley8]

If you are going to average in the frequency domain, then due to possible discontinuities in the phase, you should probably average real and imaginary and then convert to magnitude and phase.