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Intro to digital signal processing
Dsp systems i
Sampling ct signals: a frequency
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
how can chip be made from sand

Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?

where we get a research paper on Nano chemistry....?

nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review

Ali

what are the products of Nano chemistry?

There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..

learn

Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level

learn

no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts

Bhagvanji

Preparation and Applications of Nanomaterial for Drug Delivery

Application of nanotechnology in medicine

has a lot of application modern world

Kamaluddeen

what is variations in raman spectra for nanomaterials

ya I also want to know the raman spectra

Bhagvanji

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

Nasa has use it in the 60's, copper as water purification in the moon travel.

Alexandre

nanocopper obvius

Alexandre

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

Any one who tell me about Preparation and application of Nanomaterial for drug Delivery

Hafiz

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

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

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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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