Inflation, budget cuts and high interest rates have led management at local public radio and television stations to view their future with a combination of cautious optimism and trepidation.

Cuts in the Corporation for Public Broadcasting and the National Telecommunications Information Agency, which provide funds in part to most local stations, along with the rising cost of public utilities and increased postal rates for nonprofit groups have forced these stations to reexamine the vulnerability of their funding.

A substantial increase in public support during the past year at radio stations WPFW, WGTS, WAMU and WETA, and television stations WHMM (Channel 32) and WETA (Channel 26) is the reason for their optimistic outlook.

As nonprofit stations, they have more independence in programming and no pressure from advertisers. However, without commercials and the regular revenue they provide, the nonprofit stations rely almost exclusively on support from listeners, local businesses, foundation grants, and federal funding to keep afloat.

WAMU's program "Morning Edition" is financed by grants from National Public Radio (NPR), a CPB-sponsored public radio network. The news and talk show is the station's most expensive program and attracts the most new members during fund-raising drives, according to Susan Harmon, general manager of the station. Moreover, "it would not have been possible . . . to establish this program without federal funds during the 1970s," she said during testimony before a congressional subcommittee on CPB funding.

Federal funds have played an important role in getting most of the public stations on the air. Through matching grants, funds have been provided to purchase and upgrade technical equipment necessary to broadcast. However, the Reagan administration has recommended that funding be reduced to zero, and that NTIA be abolished in 1983.

WGTS at Columbia Union College in Takoma Park generally features classical and spiritual music. The station is unusual because it is supported entirely by listeners and the college, an affiliate of the Seventh Day Adventist Church.

The station met its goal of $50,000 during its most recent fund-raising campaign. But when not enough money was pledged during the scheduled week-long drive, it was extended three days.

"Fifty-thousand wasn't a goal we would like to get, we had to get it. We would be in a crisis if we didn't raise what we did last time. We stayed on the air until we reached that goal," Wheeler said.

Because of the high number of professionals and government employes in the area, many station executives say people here understand the changes their stations are being put through with Reaganomics.

Elizabeth Campbell, founder and vice president of WETA, said " . . .because we're here in Washington our viewers have heard all the pessimistic talk and read the pessimistic stories that public television is going to fail. People in Washington are aware. They understand the significance of this."

The situation at minority-owned and operated television station WHMM at Howard University has borne out some of the more dire forcasts. The station is running a deficit, and has been hit hard by CPB cutbacks. "The ceiling fell in," said General Manager Arnold Wallace.

The station received $761,400 from CPB this year, but stands to lose from $322,800 to $486,400 of this funding by 1983, depending on congressional action on the CPB budget.

Due to the District's unique position as a federal enclave without a state government to turn to for funds, stations here will not be able to make up lost federal funds with state money, an alternative being exercised by many other PBS stations.