We can find the input-output relation for a
discrete-time filter much more easily than for analogfilters. The key idea is that a sequence can be written
as a weighted linear combination of unit samples.
Show that
where
is the unit-sample.
If
denotes the
unit-sample
response —the output of a discrete-time
linear, shift-invariant filter to a unit-sampleinput—find an expression for the output.
In particular, assume our filter is FIR, with the
unit-sample response having duration
. If the input has duration
, what is
the duration of the filter's output to thissignal?
Let the filter be a boxcar averager:
for
and zero otherwise.
Let the input be a pulse of unit height and duration
.
Find the filter's output when
,
an odd integer.
A digital filter
A digital
filter has the
depicted unit-sample reponse.
What is the difference equation that defines this
filter's input-output relationship?
What is this filter's transfer function?
What is the filter's output when the input is
?
A special discrete-time filter
Consider a FIR filter governed by the difference equation
Find this filter's unit-sample response.
Find this filter's transfer function.
Characterize this transfer function(
i.e. , what classic filter category
does it fall into).
Suppose we take a sequence and stretch it out by
a factor of three.
Sketch the sequence
for some example
. What is the filter's output to this
input? In particular, what is the output at theindices where the input
is intentionally zero? Now how would you characterize this
system?
Simulating the real world
Much
of physics is governed by differntial equations, and wewant to use signal processing methods to simulate physical
problems. The idea is to replace the derivative with adiscrete-time approximation and solve the resulting
differential equation. For example, suppose we have thedifferential equation
and we approximate the derivative by
where
essentially
amounts to a sampling interval.
What is the difference equation that must be
solved to approximate the differential equation?
When
, the unit step, what will be the simulated output?
Assuming
is a sinusoid, how should the sampling
interval
be chosen so
that the approximation works well?
Derivatives
The derivative of a sequence makes little sense, but still, we can approximate it.
The digital filter described by the difference equation
resembles the derivative formula.
We want to explore how well it works.
Suppose the signal
is a sampled analog signal:
.
Under what conditions will the filter act like a differentiator?In other words, when will
be proportional to
?
The dft
Let's explore the DFT and its properties.
What is the
length-
DFT of
length-
boxcar
sequence, where
?
Consider the special case where
. Find the inverse DFT of the product of
the DFTs of two length-3 boxcars.
If we could use DFTs to perform linear filtering, it
should be true that the product of the input'sDFT and the unit-sample response's DFT equals
the output's DFT. So that you can use what youjust calculated, let the input be a boxcar signal
and the unit-sample response also be a boxcar. Theresult of part (b) would then be the filter's
output
if we could implement
the filter with length-4 DFTs. Does the actualoutput of the boxcar-filter equal the result found
in the
previous part ?
What would you need to change so that the
product of the DFTs of the input and unit-sampleresponse in this case equaled the DFT of the
filtered output?
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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