Effective inverse FFT (ICZT) found and published

For those interested, i have noticed various mentionings of FFT could never be possible to have it efficiently calculated inversed throughout the past decade around on the area of audio processing.

It seems two scientists managed to untangle that particular issue…:

" Generalizing the inverse FFT off the unit circle"

I’m not sure if the new calculation methods are as speedy as the forward method, but it may be an interesting read to many developers who use FFT for data processinng on any area.

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Practically in laymen terms what does this mean?

Possibly more precise, detailed sounding fft based effects?

From the Abstract

This paper describes the first algorithm for computing the inverse chirp z-transform (ICZT) in O ( n log n ) time. This matches the computational complexity of the chirp z-transform (CZT) algorithm that was discovered 50 years ago. Despite multiple previous attempts, an efficient ICZT algorithm remained elusive until now. Because the ICZT can be viewed as a generalization of the inverse fast Fourier transform (IFFT) off the unit circle in the complex plane, it has numerous practical applications in a wide variety of disciplines. This generalization enables exponentially growing or exponentially decaying frequency components, which cannot be done with the IFFT. The ICZT algorithm was derived using the properties of structured matrices and its numerical accuracy was evaluated using automated tests. A modification of the CZT algorithm, which improves its numerical stability for a subset of the parameter space, is also described and evaluated.

Or to say otherwise: you have FFT which is fast and IFFT which is slow when you would apply exponential algorithms if that would be possible at all.
ICZT is actually the better IFFT counter algorithm to use.

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