The module will provide an introduction to sampling a signal in the frequency domain and go through a basic example.

Understanding sampling in the frequency domain
We want to relate
${x}_{c}(t)$ directly to
$x(n)$ . Compute the CTFT of
$${x}_{s}(t)=\sum $$ ∞
∞
x
c
n
T
t
n
T

${X}_{s}()=\int_{()} \,d t$ ∞
∞
n
∞
∞
x
c
n
T
t
n
T
t
n
∞
∞
x
c
n
T
t
∞
∞
t
n
T
t
n
∞
∞
x
n
n
T
n
∞
∞
x
n
n
X
where
$\equiv T$ and
$X()$ is the DTFT of
$x(n)$ .
$${X}_{s}()=\frac{1}{T}\sum $$ ∞
∞
X
c
k
s
$X()=\frac{1}{T}\sum $ ∞
∞
X
c
k
s
1
T
k
∞
∞
X
c
2
k
T where this last part is
$2\pi $ -periodic.

Sampling
Speech
Speech is intelligible if bandlimited by a CT lowpass filter
to the band4 kHz. We can sample speech as slowly as _____?

Note that there is no mention of
$T$ or
${}_{s}$ ! Got questions? Get instant answers now!
Relating x[n] to sampled x(t)
Recall the following equality:
$${x}_{s}(t)=\sum x(nT)(t-nT)$$

Recall the CTFT relation:

$(x(t), \frac{1}{}X(\frac{}{}))$

where
$$ is a scaling of
time and
$\frac{1}{}$ is a scaling in frequency.
${X}_{s}()\equiv X(T)$

Questions & Answers
what is variations in raman spectra for nanomaterials

I only see partial conversation and what's the question here!

what about nanotechnology for water purification

please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.

Damian

yes that's correct

Professor

is there industrial application of fullrenes.
What is the method to prepare fullrene on large scale.?

Rafiq

industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong

Damian

How we are making nano material?

What is meant by 'nano scale'?

What is STMs full form?

LITNING

scanning tunneling microscope

Sahil

how nano science is used for hydrophobicity

Santosh

Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq

Rafiq

what is differents between GO and RGO?

Mahi

what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq

Rafiq

if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION

Anam

analytical skills graphene is prepared to kill any type viruses .

Anam

what is Nano technology ?

write examples of Nano molecule?

Bob

The nanotechnology is as new science, to scale nanometric

brayan

nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale

Damian

Is there any normative that regulates the use of silver nanoparticles?

what king of growth are you checking .?

Renato

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?

why we need to study biomolecules, molecular biology in nanotechnology?

yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..

Adin

biomolecules are e building blocks of every organics and inorganic materials.

Joe

anyone know any internet site where one can find nanotechnology papers?

sciencedirect big data base

Ernesto

Introduction about quantum dots in nanotechnology

nano basically means 10^(-9). nanometer is a unit to measure length.

Bharti

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?

how did you get the value of 2000N.What calculations are needed to arrive at it

Privacy Information Security Software Version 1.1a

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Source:
OpenStax, Intro to digital signal processing. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10203/1.4

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