Hello everyone. I am a new here. I have some questions

Hello everyone!

I was posting to GNURadio about an year ago but I got busy and then I
stopped. I have again started reading about GNURadio and hope to devote
my free time this entire year on GNURadio.

So I have started reading Discrete Time Signal Processing by Oppenheim /
Schafer / Buck.

Chapter 4/ Page 168 says : -

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.

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Alex M. 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 :slight_smile: I’m assuming your copy is a new edition.
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

Alex-

     =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?

Well, if you have the first printing, you can check here first:

ftp://ftp.prenhall.com/pub/esm/electrical_and_computer_engineering.s-045/oppenheim/DTSP/errata1pph.pdf

But otherwise, my comment would be… a typo in an Oppenheim & Schafer
book? 9 years
after being published and after countless peer reviews? And you found
it? One thing
for sure is you’re not lacking audacity and enthusiasm. Keep going.

-Jeff

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