  DFT is the numerical implementation of Fourier transform (FT), and it has
many forms. Ordinary DFT (ODFT) and symmetric DFT (SDFT) are the two main forms
of DFT. The most widely used DFT is ODFT, and the phase spectrum of this form
is widely used in engineering applications. However, it is found ODFT has the
problem of phase aliasing. Moreover, ODFT does not have many FT properties,
such as symmetry, integration, and interpolation. When compared with ODFT, SDFT
has more FT properties. Theoretically, the more properties a transformation
has, the wider its application range. Hence, SDFT is more suitable as the
discrete form of FT. In order to promote SDFT, the unique nature of SDFT is
demonstrated. The time-domain of even-point SDFT is not symmetric to zero, and
the author corrects it in this study. The author raises a new issue that should
the signal length be odd or even when performing SDFT. The answer is odd.
However, scientists and engineers are accustomed to using even-numbered
sequences. At the end of this study, the reasons why the author advocates odd
SDFT are given. Besides, even sampling function, discrete frequency Fourier
transform, and the Gibbs phenomenon of the SDFT are introduced.
