The
screencast video continues the discussion by
exploring the delay of the all-pass filter of
as a function
of the parameter C.
[video] Calculating the delay of the low pass filter
Implementing the pitch-accurate algorithm
Including the all-pass filter in the basic Karplus-Strong algorithm allows the loop time to be
set to an arbitrary value, making it possible to sound a tone with any desired pitch.
This section guides you through the necessary steps to augment the basic algorithm with an
all-pass filter, including the derivation of necessary equations to calculate the delay linelength and the fractional delay. Work through the derivations requested by each of the exercises.
To begin, the pitch of the output signal is the sampling frequency
divided by the total loop delay in samples:
where
is the fractional delay introduced by the all-pass filter.
Refer to
. Derive a pair of equations that can be used to calculate the length of
the delay line
and the value of the fractional delay
.
(the "floor" operator converts the operand to an integer by selecting the largest integer that is less than the operand);
The all-pass filter delay can be approximated by
(see Moore):
Refer to
. Solve the equation for the all-pass filter coefficient C in terms of the
required fractional delay.
The all-pass filter can be inserted at any point in the loop;
shows the all-pass filter placed after
the low pass filter.
Block diagram of the pitch-accurate Karplus-Strong algorithm
To simplify the derivation of the overall filter transfer function that relates y(n) to x(n), consider the three feedback elements (delay line, low pass filter,
and all-pass filter) to be a single element with transfer function
. Derive the transfer function of the combined element.
The elements are in cascade, so the individual transfer functions multiply together:
Refer to the block diagram of
. Considering that all three elements are represented by a single feedback element G(z),
derive the overall transfer function H(z) for the digital filter in terms of G(z).
Recall the low pass filter transfer function (
):
The all-pass filter transfer function is described by
.
Derive the overall transfer function H(z) in terms of the filter parameters g and C. Write the transfer function
in standard form as the ratio of two polynomials in z.
Project activity: karplus-strong vmi
As in the
prerequisite module , convert the pitch-accurate Karplus-Strong algorithm
into a
virtual musical instrument (
VMI )
that can be played by "MIDI Jam Session." If necessary, visit
MIDI JamSession , download the application VI .zip file, and view the
screencast video in that module to learn more about the application and how to create yourown virtual musical instrument. Your VMI will accept parameters that specify
frequency, amplitude, and duration of a single note, and will produce a corresponding array ofaudio samples using the Karplus-Strong algorithm described in the previous section.
For best results, select a MIDI music file that contains a solo instrument or perhaps a duet.
For example, try "Sonata in A Minor for Cello and Bass Continuo" by Antonio Vivaldi.A MIDI version of the sonata is available at the
Classical Guitar MIDI Archives , specifically
Vivaldi_Sonata_Cello_Bass.mid .
References
Moore, F.R., "Elements of Computer Music," Prentice-Hall, 1990, ISBN 0-13-252552-6.
Karplus, K., and A. Strong, "Digital Synthesis of Plucked String and Drum Timbres,"
Computer Music Journal 7(2): 43-55, 1983.
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?
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Source:
OpenStax, Musical signal processing with labview (all modules). OpenStax CNX. Jan 05, 2010 Download for free at http://cnx.org/content/col10507/1.3
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