This module introduces the ideas behind and design issues of Orthogonal Perfect Reconstruction of FIR filterbanks.
Orthogonal pr filterbanks
The
FIR
perfect-reconstruction (PR) conditions leave some
freedom in the choice of
and
.
Orthogonal PR filterbanks are defined
by causal real-coefficienteven-length-
analysis filters
that satisfy the following two equations:
To verify that these design choices satisfy the FIR-PR
requirements for
and
, we evaluate
under the second condition above. This yields
which corresponds to
and
in the FIR-PR determinant condition
. The remaining FIR-PR conditions then imply that
the synthesis filters are given by
The orthogonal PR design rules imply that
is "power symmetric" and that
form a "power complementary" pair. To see the power
symmetry, we rewrite the first design rule using
and
, which gives
The last two steps leveraged the fact that the
DTFT of a
real-coefficient filter is conjugate-symmetric. Thepower-symmetry property is illustrated in
:
Power complementarity follows from the second orthogonal PR
design rule, which implies
. Plugging this into the previous equation, we find
The power-complimentary property is illustrated in
:
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?
