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Two-minute miniquiz problem

Problem 6-1


H ( s ) = s ( s + 1 ) ( s + 10 ) size 12{H \( s \) = { {s} over { \( s+1 \) \( s+"10" \) } } } {}

Determine the magnitude of the frequency response in the form of a Bode diagram.


H ( ) = 1 10 ( + 1 ) ( / 10 + 1 ) size 12{H \( jω \) = { {1} over {"10"} } left [ { {jω} over { \( jω+1 \) \( jω/"10"+1 \) } } right ]} {}


1/ Separation of narrowband signals

The input consists of a sum of two sinusoids, more generally the sum of two narrow-band signals such as the signals transmitted by two radio stations. The objective is to devise filters

to separate these two signals. All waveforms have normalized amplitudes.

2/ Extraction of narrow-band signal from wide-band noise

The input consists of a sinusoid, more generally a narrow-band signal, plus some wide-band noise. The objective is to extract the signal from the noise. All waveforms have normalized amplitudes.

3/ Reduction of narrow-band noise from wide-band signal

The input consists of a wide-band signal, in this case an ecg signal recorded from the surface of the chest, plus some narrowband noise, such as pickup from the power lines. The objective is to remove the narrow-band noise. All waveforms have normalized amplitudes.


1/ First-order lowpass and highpass filters

where H(s) = Y (s)/X(s) and RC = 1.

2/ Use of first-order lpf and hpf for signal separation

How much unwanted signal occurs in each output channel? That depends on the frequency separation between the signals. If the two signals are about a decade apart then the attenuation of the unwanted signal will be at most 20 dB with first-order lowpass and highpass filters.

3/ Higher-order lowpass filters, Butterworth filters

If two signals have a small frequency separation or if attenuation of the unwanted signal needs to be very large, higher-order filters are required. The pole-zero diagrams of the class of lowpass Butterworth filters of order 1-9 are shown below.

The system function for the nth-order Butterworth filter, H n ( s ) size 12{H rSub { size 8{n} } \( s \) } {} , is obtained from the property

H n ( s ) H n ( s ) = 1 1 + s c 2n size 12{H rSub { size 8{n} } \( s \) H rSub { size 8{n} } \( - s \) = { {1} over {1+ left [ { {s} over {jω rSub { size 8{c} } } } right ] rSup { size 8{2n} } } } } {}

where ω c size 12{ω rSub { size 8{c} } } {} is the cut-off frequency.

Each additional order of Butterworth filter adds an additional attenuation of −20 dB/decade. The frequency response for the nth-order Butterworth filter, H n ( ) size 12{H rSub { size 8{n} } \( jω \) } {} , is obtained from the property

( H n ( ) ) 2 = 1 1 + ω ω c 2n size 12{ \( \lline H rSub { size 8{n} } \( jω \) \lline \) rSup { size 8{2} } = { {1} over {1+ left [ { {ω} over {ω rSub { size 8{c} } } } right ] rSup { size 8{2n} } } } } {}

The frequency responses are shown for n in the range 1-9 and for ω c = 1 size 12{ω rSub { size 8{c} } "= "1} {} .


1/ Resonant systems arise in many physical contexts

M is mass, B is a friction constant, K is a spring constant, f(t) is an external force, and v(t) is the velocity of the mass.

A second-order system function relates the velocity to the force

H ( s ) = V ( s ) F ( s ) = 1 M s s 2 + B M s + K M size 12{H \( s \) = { {V \( s \) } over {F \( s \) } } = { { { {1} over {M} } s} over {s rSup { size 8{2} } + { {B} over {M} } s+ { {K} over {M} } } } } {}

Such a mechanical system yields a damped oscillation in response to a force provided the damping is not too large. For example, a tuning fork may be modeled by such a mechanical system.

2/ RLC filter

Electric networks also show a similar system function. The impedance of the RLC circuit is also of second-order

Z ( s ) = V ( s ) I ( s ) = 1 sC + 1 R + 1 sL = sL s 2 LC + s L R + 1 size 12{Z \( s \) = { {V \( s \) } over {I \( s \) } } = { {1} over { ital "sC"+ { {1} over {R} } + { {1} over { ital "sL"} } } } = { { ital "sL"} over {s rSup { size 8{2} } ital "LC"+s { {L} over {R} } +1} } } {}

3/ Resonance parameterized

We can parameterize these and any second-order systems efficiently. We illustrate with the electrical network.

Questions & Answers

what is the stm
Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
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for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Mueller Reply
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Source:  OpenStax, Signals and systems. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10803/1.1
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