Kate Smith, 79, one of this nation's most popular singers of the golden era of radio, the 1930s and 1940s, who was probably best known for her rousing renditions of "God Bless America," died yesterday of respiratory arrest at Raleigh Community Hospital in Raleigh, N.C.

Miss Smith, a symbol of joyful patriotism to a generation of Americans, suffered brain damage incurred during a diabetic coma 10 years ago that made it difficult for her to walk or talk. Complications of diabetes had forced the amputation of her right leg above the knee in January.

In a stage and radio career that spanned almost 40 years, she is said to have grossed $35 million and had more than 700 of her songs on the Hit Parade, including "The Music Goes Round and Round," "The Last Time I Saw Paris," "White Cliffs of Dover," and her theme song, "When the Moon Comes over the Mountain."

President Franklin D. Roosevelt, introducing her to the visiting King George VI and Queen Elizabeth of England in 1939, said simply, "Your Majesties, This is Kate Smith. This is America."

During World War II she sold more than $600 million worth of war bonds in a series of round-the-clock radio appeals, more than any other single person, and she sold $39 million worth of bonds in a single 17-hour radio marathon.

The war years represented the peak of her career. She made her television debut in 1950 with "The Kate Smith Hour" weekday afternoons on NBC, but she never achieved the popularity on television that she enjoyed earlier on radio. In 1956 she said she was through with regular television appearances, then changed her mind and attempted to return with a variety program on CBS in 1960. Although well reviewed, the show was canceled after six months. After that her public appearances became less and less frequent.

She sang "God Bless America" at the Honor America Day rally in Washington on Independence Day 1970, and later at Philadelphia Flyers hockey games.

In 1979 a New York judge declared her incompetent to manage her own affairs and placed her assets in the hands of three conservators. That same year she moved from Lake Placid to Raleigh where in 1982 President Reagan -- who had appeared with her in a 1945 movie, "This Is the Army" -- awarded her the Medal of Freedom, the nation's highest civilian honor.

At that ceremony the president called Miss Smith "one of the greatest singers of this or any century."

Born in Greenville, Va., Miss Smith moved to Washington as a child and made her first public appearance as a singer with a church choir when she was 4, singing the hymns enthusiastically while holding her hymnbook upside down.

As a child she sang for World War I soldiers in the Washington area, and she received a medal from Gen. John J. Pershing for her work in helping boost military morale. She attended Washington's old Business High School and, at her father's insistence, began training as a student nurse at George Washington University Hospital. But at the age of 18 she gave that up and went to New York and signed for a role in the musical, "Honeymoon Lane," which opened in Atlantic City in 1926.

At that time Miss Smith already weighed more than 225 pounds, and she was cast in the role of a buffoon named Tiny Little who was ridiculed by other members of the cast.

She appeared as a fat girl in other shows, most notably, "Flying High," in 1930 where she was subjected to such comments as "That girl is sitting on top of the world, nothing else would bear her weight." She was said to have wept in her dressing room after several performances and seriously considered leaving show business.

But then in 1931 Miss Smith made her radio debut with a 15-minute show on CBS, and it was there that she adopted "When the Moon Comes Over the Mountain" as her theme song. During the next two decades, millions of listeners would grow to love her rich contralto voice and homespun manner. She opened every show saying, "Hello, Everybody!" and ended with "Thanks for Listenin'."

In 1938 she discovered a song written by Irving Berlin 19 years earlier but never published because the composer thought it too syrupy. It was "God Bless America," and Miss Smith persuaded Berlin to assign her sole performing rights to it. Kate Smith and "God Bless America" have been linked in the public mind ever since.

With her manager, Ted Collins, she established the Kated Corp. in 1940 to produce daily and weekly radio broadcasts, as well as other shows, such as "The Aldrich Family."

During World War II, Miss Smith traveled more than 520,000 miles to entertain troops, and she was constantly urging men and women at home to donate blood and write letters to servicemen. "If you don't write, you're wrong," she would say. She was the first private citizen to receive the Legion of Valor medal from the Red Cross.

In a statement released by the White House last night, Reagan called Miss Smith "a patriot in every sense of the word. She thrilled us all with her stirring rendition of 'God Bless America' and sang with a passion which left few eyes dry. For many years, Kate Smith touched our hearts and souls and made us all swell with the special pride of being Americans . . . . All America loved her and she loved America."

Miss Smith leaves no immediate survivors.