Do I have a fuel pump problem

I'm not saying for sure that the filter is plugging up, but this is exactly how the engine does when the filter is.
Next it would start doing it at lower and lower speeds until the engine barely runs any longer or not at all, as the filter plugs up more and more.
Number one would be to check or put a new filter on it and then to the fuel pump if needed.
I will change fuel filter and check fuel pressure.