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They're a thing of the past for many people, but in this iTunes-driven age, there's a longing for the antique sounds of analog found on cassette tapes.

That demand is literally music to the ears of those at National Audio Co., which is seeing a surge in requests for classic hits on cassette.

"We attribute our success, as I say often, to stubbornness and stupidity," said Steve Stepp, the company's president.

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Cassettes peaked in the late 1980s, but the rise first of compact discs and then downloadable digital files eclipsed them, and by 2001, they accounted for only 4 percent of all music sales. By 2005, worldwide sales had fallen from almost a billion cassettes to fewer than 1 million, according to industry figures.

But audiophiles refuse to be deterred, preferring "the warmth and presence in an analog recording that you will not hear in the digital recording," Stepp said.

Related: The Walkman Turns 35: What Was the First Song You Played on One?

Using relatively old equipment from the 1970s to produce all of its cassettes, National Audio, which opened in 1969, produced 10 million tapes in 2014, according to a Bloomberg report.

"When you compare the two side by side, you will hear the difference," Stepp said.

Correction: An earlier version of this story misidentified the president of National Audio Co. He is Steve Stepp.

Steve Stepp