Don't I need to move a shrunk filesystem before resizing the partition?

I have a partition of some size X GB filled by an ext4 filesystem. Now, I want to shrink this partition (and the filesystem) to only take up the latter X/2 GB. I'm command-line tools and no parted. So, I've read (here and here for example) that I need to resize2fs and then use fdisk to shrink the partition. However, what about moving the filesystem by X/2 GB forward in the partition? Isn't that a necessary step?

Also, assuming this is necessary - should I use dd for moving the data, or is something else necessary/better?