According to Digital Signal Processing by Ashok Ambardar, The principal range is defined as follows:
Put another way, a DT sinusoid is periodic in frequency (has a periodic spectrum) with unit period. The range $-0.5\le F \le 0.5$ defines the principal period or principal range.
I see that the major rationale behind this definition is the unit period. If only for the purpose of uniqueness, it seems to me that any interval with a unit period surely meets the requirements. I also think that $0\le F \le1$ is more fit for the purpose, because it is more easy to remember and aesthetically beautiful. In conclusion, my question is:
- Is there a special reason why the principal range is defined that way?