Re: Fw: [Discuss-gnuradio] Hello everyone. I am a new here. I have some questions.

[Tom Rondeau]

Alex Miua wrote:
> ----- Forwarded Message ----
> From: Alex Miua <address@hidden>
> To: Tom Rondeau <address@hidden>
> Sent: Friday, March 21, 2008 10:57:21 PM
> Subject: Re: [Discuss-gnuradio] Hello everyone. I am a new here. I 
> have some questions.
>
> Hello Tom !
>  
> Thank you for your reply. I have the 2nd edition ( Low Price Edition ).
>  
> Here is my question rephrased.
>  
> The sifting property for the cts dirac delta fn has an INTEGRAL.
> The sifting property for the discrete delta fn has an infinite sum in it.
>  
> So we cannot 1st say as is said in the book that delta is the Dirac 
> delta function and the coolly proceed and apply the sifting property 
> of the discrete
> delta function as has been done below.
> Do you see my question ?
>  
> Thank you for your effort,
> Ashim.

Nope, sorry, I still don't see the problem. I'm cool with how they 
present this in the book. It sounds like your problem is based on the 
definition of the Dirac function, and that might be true, but I've never 
much concerned myself with specifics like that. The outcome of their 
math in the sampling process still works.

Tom


> ----- Original Message ----
> From: Tom Rondeau <address@hidden>
> To: Alex Miua <address@hidden>
> Cc: address@hidden
> Sent: Friday, March 21, 2008 10:51:28 PM
> Subject: Re: [Discuss-gnuradio] Hello everyone. I am a new here. I 
> have some questions.
>
> Alex Miua wrote:
> > So I have started reading Discrete Time Signal Processing by Oppenheim
> > / Schafer / Buck.
> > 
> > Chapter 4/ Page 168 says : -
> Which edition are you using? I have the second edition and this is on
> page 142 :)  I'm assuming your copy is a new edition.
> > 
> > x_s(t)=x_c(t)s(t)
> >          =x_c(t) Sigma ( from n = -inf to inf ) [ delta (t-nT) ]
> > 
> > Through the sifting property of the impulse function , x_s(t) can be
> > expressed as :
> > 
> > x_s(t) = Sigma (from - inf to inf ) [ x_c(nT) delta ( t-nT) ]
> > 
> > Now this version of the sifting property is for the DISCRETE impulse
> > function NOT the continuous Dirac delta function, but just before the
> > discussion starts it says that delta(t) is the unit impulse function
> > or the Dirac delta function. Is this a typo ? Shouled this have been
> > the discrete delta function? If it is'nt, how do the above steps hold?
> > 
> > Thank you,
> > Alex.
>
> They are still representing all of this in the time domain. The sampling
> function is a continuous time signal as is x_c(t) as it x_s(t) where the
> discrete time representation is x_s[n] = x_s(nT).
>
> I don't see this as a typo, and I don't see how this changes anything.
>
> Tom