Robert Trout, the venerable world correspondent who has attended every inaugural since 1917 and covered all since 1933, has returned to Washington to coanchor ABC Radio's coverage of President Reagan's swearing-in.

Trout, 75, who now lives in Madrid, was assigned to the roof of the Willard Hotel during the first parade for President Franklin D. Roosevelt, but by the next Roosevelt ceremony he was at the Capitol. And it poured, he recalls. "They never took the canvas off the presidential seal. Mrs. Roosevelt had a bouquet of violets on the chair next to her, and a wind came along and I tried to grab it. But it was too fast."

At the third Roosevelt inaugural, during World War II, the radio reporters wore military uniforms. Trout started his career with a Mount Vernon Hills station that became WTOP-AM (1500), then joined CBS for a long stretch, briefly worked for NBC News, and worked again at CBS until he joined ABC as a special contributing correspondent in 1974.

This is the first inaugural that all the radio networks will be transmitting through satellite -- a fact that makes them all efficiency-happy -- and the first time the radio networks will have a vehicle in the parade. ABC is providing the audio pool from the flatbed truck. Trout will coanchor with Bob Walker and Kate Doordan, and WMAL-AM (630), one of ABC's two local affiliates, will intersperse the network's reports with its own coverage, anchored by Ed Meyer and Karen Leggett.

For the third consecutive inaugural, the Mutual Broadcasting crew in Arlington is providing the audio pool from the inaugural podium for all the networks. Mutual's coverage will be anchored by Bob Witten, Nelson Benton and Jim Bohannon. Some of CBS Radio's reports will be heard on WTOP, but the all-news station will depend on its own team, including traffic reports from Bob Marbourg and analysis by anchors Dave McConnell, Pam Coulter, Jamie Bragg and Joe Connelly. All of the observations on NBC Radio will be anchored by Steve Porter and Sid Davis.

"Inaugural Heritage," a series of 20 one-minute vignettes narrated by actor Robert Stack and former actor Ronald Reagan and prepared by independent producers for the Inaugural Committee, has been distributed free to 11,000 public and commercial radio stations. Produced by Harry O'Connor in cooperation with National Public Radio, the series is to be broadcast today through Sunday.