signal and systems difference b/w discrete time and continuous time

[diksha.k]

As i am going through alan.v.oppenhium book.
I understand that discrete time(dt) signal is got by sampling continuous time signals(ct).
i.e say ts is sampling period then any signal representation is x[n]=e^nts or simply x[n]=e^n.
Now in this book there are distinguishing b/w dt complex exponential and ct complex expo.
I understand ct complex expo but,
there are two cases taken for dt while explaining :I will discuss only the first one now
1) consider dt complex expo (ctce)
y[n]=e^j(w0n) where w0-fundamental frequency.
now increment w0 by 2*pi i.e w0=w0+2*pi.
now my doubt before proceeding is:
when w0 is frequency(rad/sec) how can i add 2*pi(rad) to it?
the analysis of this is made later but this point only i did not get can anyone please explain?

 

[vGoodtimes]

does it say "2*pi rad" specifically, or just "2*pi"? Normally when you say "add a constant to x" there is an assumption that the constant has the same units as x. Otherwise the units of the constant should be given.

 

[diksha.k]

does it say "2*pi rad" specifically, or just "2*pi"? Normally when you say "add a constant to x" there is an assumption that the constant has the same units as x. Otherwise the units of the constant should be given.

no they haven't mentioned like that.
But what i understand is may be they have modified like this:
as i wrote y[n]=e^jw0*n*ts
may be already w0*ts=w0(new value) so,
y[n]=e^jw0n
now w0 has radians as unit..

 

[diksha.k]

equation 1.51 in image is :
y[n]=e^jw0n
And author is comparing it with continuous time(ct) counterpart i.e e^j*w0t
**broken link removed**
you can see the file above i have some doubts in this.
1)line 5 it says : that frequency w0 has range of 0 to 2pi ? w0 is addressed as frequency also w0 has range of 0 to 2pi which is angle range how can i compare like this?
2)And w0 is added to 2*pi with w0 addressed as frequency and 2*pi is in radians i am confident that 2*pi has unit radians because it's said that w0 varies from 0 to 2*pi.
Ok can you tell me in nutshell as to how do you see the analysis what's been made in paragraph