God is gone up with a shout - That is, he has ascended to heaven, his home and throne, after having secured the victory. He is represented as having come down to aid his people in the war by the overthrow of their enemies, and (having accomplished this) as returning to heaven, accompanied by his hosts, and amidst the shouts of triumph. All this is, of course, poetical, and is not to be regarded as literal in any sense. Compare the notes at Psalms 7:7.
The Lord with the sound of a trumpet - Yahweh, accompanied with the notes of victory. All this is designed to denote triumph, and to show that the victory was to be traced solely to God.