In this "White Hart" story, Purvis tells about an experimental physicist who invents a highly successful antinoise generator. The Fourier analysis underpinning of antinoise is explicitly mentioned.

But the physicist's mathematical abilities are weak, so he makes one costly mistake. This weakness is gauged rather accurately: Purvis states he is able to integrate e^x, but not x.e^x.

There is more than one version of this story. The one in Tales from the White Hart is not, in my opinion, the best. I am still trying to locate the version that I originally read (probably in my collection of SF somewhere).

Also look at "He built a crooked house" by Robert A Heinlein