The Discrete Fourier Transform: Conjugate symmetry for even and odd transform size N (real signals)



The DFT defined earlier is valid for integer valued N, i.e., N can be even or odd. In many real world applications, the DFT is evaluated using the FFT algorithm, which originally required signals where the number of samples was a power of 2, i.e., even N (although there are a whole host of more modern implementations, where this requirement is relaxed).

Whatever the low level implementation used to compute the DFT, it is useful to understand how the structure of the resulting spectrum, X[k], depends on the choice of N. That’s the topic of this page.

Conjugate symmetry and the DFT


Even valued N


Odd valued N