- #1

- 102

- 21

- TL;DR Summary
- I seek a clarification on the periodicity of discrete-time (DT) signals.

Namaste

I seek a clarification on the periodicity condition of discrete-time (DT) signals.

As stated in Oppenheim’s Signals & Systems, for a DT signal, for example the complex exponential, to be periodic, i.e.

e

w/2*pi = m/N, where m/N must be a rational number.

Above is simply to satisfy the condition that e

Please help me see why m=9, N=3, and, thereby, m/N = 3, which is not a rational number, yet still yielding 1 for e

Would greatly appreciate a refutation and a chance to stand corrected.

Thank you.

I seek a clarification on the periodicity condition of discrete-time (DT) signals.

As stated in Oppenheim’s Signals & Systems, for a DT signal, for example the complex exponential, to be periodic, i.e.

e

^{j*w(n+N)}= e^{j*w*n},w/2*pi = m/N, where m/N must be a rational number.

Above is simply to satisfy the condition that e

^{j*w*N}= 1.Please help me see why m=9, N=3, and, thereby, m/N = 3, which is not a rational number, yet still yielding 1 for e

^{j*2*pi*9}, not be considered a valid instance of a periodic discrete-time signal.Would greatly appreciate a refutation and a chance to stand corrected.

Thank you.