Sammy is faced with computing
lots of discrete Fourier transforms. He will, of course, use
the FFT algorithm, but he is behind schedule and needsto get his results as quickly as possible. He gets the
idea of computing
two transforms at
one time by computing the transform of
, where
and
are two real-valued signals of which he needs
to compute the spectra. The issue is whether he can retrievethe individual DFTs from the result or not.
What will be the DFT
of this complex-valued signal in terms of
and
, the DFTs of the original signals?
Sammy's friend, an Aggie who knows some signal
processing, says that retrieving the wanted DFTs is easy:“Just find the real and imaginary parts of
.” Show that this approach is too
simplistic.
While his friend's idea is not correct, it does
give him an idea. What approach will work?
Hint : Use the symmetry properties
of the DFT.
How does the number of computations change with
this approach? Will Sammy's idea ultimately lead to afaster computation of the required DFTs?
Discrete cosine transform (dct)
The discrete cosine transform of a
length-
sequence is
defined to be
Note that the number of frequency terms is
:
.
Find the inverse DCT.
Does a Parseval's Theorem hold for the DCT?
You choose to transmit information about the signal
according to the DCT coefficients.
You could only send one, which one would you send?
A digital filter
A digital filter is described by the following
difference equation:
What is this filter's unit sample response?
What is this filter's transfer function?
What is this filter's output when the input is
?
Another digital filter
A digital filter is determined by the following difference equation.
Find this filter's unit sample response.
What is the filter's transfer function?
How would you characterize this filter (lowpass, highpass, special purpose, ...)?
Find the filter's output when the input is the sinusoid
.
In another case, the input sequence is zero for
, then becomes nonzero.
Sammy measures the output to be
.
Can his measurement be correct?In other words, is there an input that can yield this output?
If so, find the input
that gives rise to this output.
If not, why not?
Yet another digital filter
A filter has an input-output relationship given by the difference
equation
.
What is the filter's transfer function?
How would you characterize it?
What is the filter's output when the input equals
?
What is the filter's output
when the input is the depicted discrete-timesquare wave (
[link] )?
A digital filter in the frequency domain
We have a filter with the transfer function
operating on the input signal
that yields the output
.
What is the filter's unit-sample response?
What is the discrete-Fourier transform of the output?
What is the time-domain expression for the output?
Digital filters
A discrete-time system is governed by the difference equation
Find the transfer function for this system.
What is this system's output when the input is
?
If the output is observed to be
, then what is the input?
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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