The FFT algorithm was published in 1965. Four years later, researchers developed a more versatile, generalized version called the chirp z-transform (CZT). But a similar generalization of the inverse FFT algorithm has gone unsolved for 50 years.

Until, that is, Stoytchev and Vladimir Sukhoy—an Iowa State doctoral student co-majoring in electrical and computer engineering, and human computer interaction—worked together to come up with the long-sought algorithm, called the inverse chirp z-transform (ICZT).

Like all algorithms, it's a step-by-step process that solves a problem. In this case, it maps the output of the CZT algorithm back to its input. The two algorithms are a little like a series of two prisms—the first separates the wavelengths of white light into a spectrum of colors and the second reverses the process by combining the spectrum back into white light, Stoytchev explained.

Stoytchev and Sukhoy describe their new algorithm in a paper recently published online by Scientific Reports, a Nature Research journal. Their paper shows that the algorithm matches the computational complexity or speed of its counterpart, that it can be used with exponentially decaying or growing frequency components (unlike the IFFT) and that it has been tested for numerical accuracy. https://techxplore.com/news/2019-10-year-old-puzzle.html