The ideas of using the DFT to filter a signal and recover a signal from a noisy transmission are addressed based on the ideas of the DFT and convolution.
Introduction
Assume that
is specified.
How can we implement
in a computer?
Discretize (sample)
and
. In order to do this, we should take the DFTs
of
and
to get
and
. Then we will compute
Does
?
Recall that the DFT treats
-point sequences as if they are
periodically extended (
):
Compute idft of y[k]
And the IDFT periodically extends
:
This computes as shown in
:
is called
circular convolution and is denoted by
.
The above symbol for the circular convolution is for an
-periodic extension.
Dft pair
Note that in general:
Regular vs. circular convolution
To begin with, we are given the following two length-3
signals:
We can zero-pad these signals so that we have the following
discrete sequences:
where
and
.
Regular Convolution:
Using the above convolution formula (refer to the
link if you need a review of
convolution ), we can
calculate the resulting value for
to
. Recall that because we have two length-3
signals, our convolved signal will be length-5.
Regular convolution result
Result is finite duration, not periodic!
Circular Convolution:
And now with circular convolution our
changes and becomes a periodically extended
signal:
Circular convolution result
Result is 3-periodic.
illustrates the
relationship between circular convolution and regularconvolution using the previous two figures:
Circular convolution from regular
The left plot (the circular convolution results) has a
"wrap-around" effect due to periodic extension.
"Zero-pad"
and
to avoid the overlap (wrap-around) effect. We
will zero-pad the two signals to a length-5 signal (5being the duration of the regular convolution result):
Now take the DFTs of the zero-padded signals:
Now we can plot this result (
):
The sequence from 0 to 4 (the underlined part of the
sequence) is the regular convolution result. From thisillustration we can see that it is 5-periodic!
We can compute the regular convolution result of a
convolution of an
-point
signal
with an
-point
signal
by padding each signal with zeros to obtain two
length sequences and computing the circular
convolution (or equivalently computing the IDFT of
, the product of the DFTs of the zero-padded
signals) (
).
Note that the lower two images are simply the top images
that have been zero-padded.
Dsp system
The system has a length
impulse response,
Sample finite duration continuous-time input
to get
where
.
Zero-pad
and
to length
.
Compute DFTs
and
Compute IDFTs of
where
.
Reconstruct
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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