Fractional Fourier Transform

A z-Transform with

$$z\equiv e^{2\pi i\alpha/N}$$

for $\alpha\not=\pm 1$. This transform can be used to detect frequencies which are not Integer multiples of the lowest Discrete Fourier Transform frequency.

See also z-Transform

References

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics, 2nd ed. Reading, MA: Addison-Wesley, 1994.