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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?

Filtering

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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
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emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir 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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