Find the complex Fourier series representations of the following signals without explicitly calculating Fourier integrals.
What is the signal's period in each case?
Find the Fourier series representation for the
following periodic
signals . For the third signal, find the complex
Fourier series for the triangle wave
without performing the usual
Fourier integrals. Hint: How is this signal related toone for which you already have the series?
Phase distortion
We can learn about phase distortion by returning to
circuits and investigate the
following circuit .
Find this filter's transfer function.
Find the magnitude and phase of this transfer
function. How would you characterize thiscircuit?
Let
vin(t) be a square-wave of period
T .
What is the Fourier series for the output voltage?
Use Matlab to find the output's waveform for the cases
T=0.01 and
T=2 .
What value of
T delineates the two kinds of results you found? The
software in
fourier2.m might be
useful.
Instead of the depicted circuit, the square wave is
passed through a system that delays its input, whichapplies a linear phase shift to the signal's
spectrum. Let the delay
τ be
T4 .
Use the transfer function of a delay to compute usingMatlab the Fourier series of the output. Show that the
square wave is indeed delayed.
Approximating periodic signals
Often, we want to approximate a reference signal by a
somewhat simpler signal. To assess the quality of anapproximation, the most frequently used error measure is
the mean-squared error. For a periodic signal
s(t) ,
ε2=1T∫T0(s(t)-˜s(t))2dt
where
s(t) is the reference signal and
˜s(t) its approximation. One convenient way of findingapproximations for periodic signals is to truncate their
Fourier series.
˜s(t)=K∑k=-Kckei2πkTt
The point of this problem is to analyze whether thisapproach is the best (
i.e. , always
minimizes the mean-squared error).
Find a frequency-domain expression for the
approximation error when we use the truncatedFourier series as the approximation.
Instead of truncating the series, let's generalize
the nature of the approximation to including any setof
2K+1 terms: We'll always include the
c0 and the negative indexed term corresponding to
ck .
What selection of terms minimizes the mean-squarederror? Find an expression for the mean-squared error
resulting from your choice.
Find the Fourier series for the
depicted signal . Use
Matlab to find the truncated approximation and bestapproximation involving two terms. Plot the
mean-squared error as a function of
K for both
approximations.
Long, hot days
The daily temperature is a consequence of several
effects, one of them being the sun's heating. If thiswere the dominant effect, then daily temperatures would
be proportional to the number of daylight hours. The
plot shows
that the average daily high temperature does
not behave that way.
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?
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
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
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.
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
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?
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
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?