# 4.10 Frequency domain problems  (Page 3/6)

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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 $\frac{T}{2}$ . 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 $\tau$ 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. ${\Delta }_{l}$ and ${\Delta }_{r}$ 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 $\tau$ is to choose ${\Delta }_{l}$ and ${\Delta }_{r}$ to maximize the power in $y(t)$ . How are these maximum-power processing delaysrelated to $\tau$ ?

## 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 $y(t)$ .

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?

## Filtering

Let the signal $s(t)=\frac{\sin (\pi t)}{\pi t}$ 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.

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO