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Lowpass filtering a square wave

Let a square wave (period T ) serve as the input to a first-order lowpass systemconstructed as a RC filter. We want to derive an expression for the time-domain response of the filter tothis input.

  1. First, consider the response of the filter to a simple pulse, having unit amplitude and width T 2 . Derive an expression for the filter's output to thispulse.
  2. Noting that the square wave is a superposition of a sequence of these pulses, what is the filter'sresponse to the square wave?
  3. The nature of this response should change as the relation between the square wave's period and thefilter's cutoff frequency change. How long must the period be so that the response does not achieve a relatively constant value between transitions in the squarewave? What is the relation of the filter's cutoff frequency to the square wave's spectrum in thiscase?

Mathematics with circuits

Simple circuits can implement simple mathematical operations, such as integration and differentiation. Wewant to develop an active circuit (it contains an op-amp) having an output that is proportional to theintegral of its input. For example, you could use an integrator in a car to determine distance traveled fromthe speedometer.

  1. What is the transfer function of an integrator?
  2. Find an op-amp circuit so that its voltage output is proportional to the integral of its input for allsignals.

Where is that sound coming from?

We determine where sound is coming from because we have two ears and a brain. Sound travels at a relativelyslow speed and our brain uses the fact that sound will arrive at one ear before the other. As shown here , a sound coming from the right arrives at the left ear τ seconds after it arrives at the right ear.

Once the brain finds this propagation delay, it can determine the sound direction. In an attempt to modelwhat the brain might do, RU signal processors want to design an optimal system that delays each ear's signal by some amount then adds themtogether. Δ l and Δ r are the delays applied to the left and right signalsrespectively. The idea is to determine the delay values according to some criterion that is based on what ismeasured by the two ears.

  1. What is the transfer function between the sound signal s t and the processor output y t ?
  2. One way of determining the delay τ is to choose Δ l and Δ r to maximize the power in y t . How are these maximum-power processing delaysrelated to τ ?

Arrangements of systems

Architecting a system of modular components meansarranging them in various configurations to achieve some overall input-output relation. For each of the following , determine the overall transfer function between x t and y t .

System a

System b

System c

The overall transfer function for the cascade (first depicted system) is particularly interesting. What doesit say about the effect of the ordering of linear, time-invariant systems in a cascade?


Let the signal s t t t be the input to a linear, time-invariant filter having the transfer function shown below . Find the expression for y t , the filter's output.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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
how nano science is used for hydrophobicity
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
characteristics of micro business
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Answers please
Nikki Reply

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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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