There are some patents out there that are very basic and most trivial. Can I patent and/or manufacture a product that builds on a patented product (I don't own the "basic" patent)

For example, there are a lot of patented power supply strips that turn off devices based on a "master" device's power draw (your computer peripherals switch off if the "master" computer goes into standby).

I want to build "smart remote" power supply strips that not only does the above **but also** can be configured over WiFi and household remote control (so that you can turn your power-hungry fax machine on/off remotely or while watching TV)

If I build my version of "smart remote" power supply strips am I infringing on the existing patented power supply strips?