1/f impact on GPDC


Would someone be able to explain to me (or link me and article) if there is an impact of the 1/f distribution of GPDC values? e.g., in my simulations and from looking at the plots in chap 28 of ANTS there isn’t much tf GPDC activity below 20hz (relatively) and it increases as a product of increasing frequency between 1 and 30hz. Is this as the book explains about the model order not being able to capture full cycles at lower frequencies?

And what is the solution then for studying GPDC in narrow band filtered data e.g 1-20hz? would we need a large model order? but to capture 1 full cycle @2hz this would be an order of 256 at an fs of 512hz.

Many thanks for any help,

What’s GPDC?

I don’t believe the 1/f will trivially impact Granger causality results. The Granger dependent variable is a ratio of variances, and so any overall differences in power will affect the numerator and denominator equally.

You’re right that lower frequencies are more difficult to estimate for a spectral Granger analysis. There unfortunately isn’t much that can be done about that. As you note, at “very” low frequencies, the model order needs to increase to get even one full cycle. So it’s possible that the result you describe is due to decreased SNR at lower frequencies.

On the other hand, you don’t need a sampling rate of 512 Hz to estimate 2 Hz activity. So one idea is to downsample to, e.g., 128 Hz for the lower frequency Granger analyses.

Mostly just PDC (https://doi.org/10.1109/ICDSP.2007.4288544).

Ok thanks I will try downsampling.

Right. PDC is the same as GC given Gaussian data.