Fluctuating Water Pressure Issues! Help

The water pressure to my house (all faucets and outside bibs are the same) is fluctuating. When I turn on a faucet, the water starts off fine, drops to a trickle then slowly builds back up to full pressure. The cycle takes 6-10 seconds and is consistent. I have lived here 4 years and it just started happening a few weeks ago. A plumber blames the city and the city says I have an issue within my house and it is not there problem. All I want to do is get my water pressure back. Any ideas... most people I know are stumped.