----- 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.
----- 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