I was reading in a book that below stated are the Properties of Discrete-time Sinusoidal Signal:
Property 1. The discrete time sinusoids whose frequency are separated by an integer multiple of 2$\pi$ are identical.
Property 2. The frequency of oscillation of discrete time sinusoids sequence increases as $\omega$ increases from 0 to $\pi$. If $\omega$ is increased from $\pi$ to 2$\pi$ then frequency of oscillation decreases.
I was able to understand the mathematical property implementation of above two property but have some basic questions for clarification:
- Is it that the above properties are applicable for all Discrete-time periodic Signals?
- As per property 1 - if two sinusoids signal has frequency separated by integer multiple of 2$\pi$ - then the signal having the greater frequency will have more cycles than other. Then how they both can be same?
- As per property 2 - what is meant by "frequency of oscillation"? How can a frequency of a signal vary (increase) from 0 to $\pi$ and (decrease) from $\pi$ to 2$\pi$ - isn't it should be same from 0 to $2\pi$?