Belden Inc. late Friday revealed a $380 million offer to buy Digi International Inc., a Minnetonka-based maker of telecommunications equipment, and said it went public after being turned down by Digi earlier this week.

Belden, a St. Louis-based firm that also makes telecom equipment, said the product portfolios of the firms meshed with each other and noted that the companies have collaborated together in the past.

"Digi's capabilities in wireless and embedded networking would complement Belden's capabilities to create uniquely complete solutions for customers in machine-to-machine applications," said a letter attributed to John Stroup, Belden's chief executive.

Machine-to-machine applications is jargon for electronic components used in all kinds of devices to gather and relay information, a process or system that is informally known as the "Internet of Things." For instance, a soda vending machine can be equipped with sensors and a transmitter to alert a supplier when it needs to be restocked.

Belden's public offer amounted to $13.82 in cash for each Digi share, a 19 percent premium to Digi's share closing price of $11.65 on Friday. Digi shares jumped about 20 percent in after-hours trading.

Digi didn't respond publicly to the offer by late Friday. A call to the company's investor relations office wasn't returned.

In its letter, Belden said it received a letter from Digi on Tuesday indicating Digi's board wasn't interested in discussing Belden's first purchase offer, which it said it made privately last week.

Belden has about $2.3 billion in annual revenue, about 10 times the size of Digi, which had $214 million in revenue last year.