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The sampling frequency is 10.00 kHz, and the length of the delay line is 10 samples. What is the pitch of the output signal? If the delay line length is decreased by one sample,what is the new pitch?

1000 Hz (10 kHz divided by 10 samples); 1111 Hz

For each of the two exercises, the first pitch is exactly the same, i.e., 1000 Hz. However, the change in pitch caused by decreasing the delay line by only one sample is substantial (1026 Hz comparedto 1111 Hz). But how perceptible is this difference? The module Musical Intervals and the Equal-Tempered Scale includes a LabVIEW interactive front panel that displays the frequency of each key on a standard 88-key piano.Pitch C6 is 1046 Hz while pitch C♯6 (a half-step higher) is 1109 Hz. These values are similar to the change from 1000 Hz to 1111 Hz caused by altering the delay line length by only one sample,so the change is certainly very audible. The abrupt "jump" in frequency becomes less pronounced at lower pitches where the delay line length is longer.

Flexibility to adjust the overall loop time in a continuous fashion is required to improve pitch accuracy. Moreover, any sources of delay in the loop must be accurately known.So far the delay of the low pass filter has been taken as zero, but in fact the low pass filter introduces a delay of its own.

The screencast video describes first how to calculate the delay of an arbitrary digital filter with transfer function H ( z ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacIcacaWG6bGaaiykaaaa@3860@ .

[video] Calculating the delay of a filter given H(z)

In general, therefore, the delay is the negated slope of the filter's phase function, and the delay varies with frequency.

Now, consider the specific low pass filter used in the basic Karplus-Strong algorithm. The filter coefficient "g" will be taken as 0.5, making the filter a true two-point averager:

H LPF ( z ) = 1 + z 1 2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisamaaBaaaleaacaqGmbGaaeiuaiaabAeaaeqaaOGaaiikaiaadQhacaGGPaGaeyypa0ZaaSaaaeaacaaIXaGaey4kaSIaamOEamaaCaaaleqabaGaeyOeI0IaaGymaaaaaOqaaiaaikdaaaaaaa@414E@

The screencast video continues the discussion by deriving the delay of the low pass filter of . Several techniques for working with complexnumbers in LabVIEW are presented and used to visualize the magnitude and phase response of the filter.

[video] Calculating the delay of the low pass filter

Because the delay of the low pass filter is always 1/2, the pitch may be expressed more precisely as

f 0 = f S N + 1 2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBaaaleaacaaIWaaabeaakiabg2da9maalaaabaGaamOzamaaBaaaleaacaWGtbaabeaaaOqaaiaad6eacqGHRaWkdaWcaaqaaiaaigdaaeaacaaIYaaaaaaaaaa@3D61@

While this result more accurately calculates the pitch, it does nothing to address the frequency resolution problem.

All-pass filter delay

Now, consider the all-pass filter ( APF ) as a means to introduce a variable and fractional delay into the loop. The all-pass filter has a unit magnitude response over allfrequencies, so it does not "color" the signal passing through. However, the all-pass filter has a phase response that is approximately linear for all but the highest frequencies, so it introducesan approximately constant delay. Even better, the slope of the phase response is continuously variable, making it possible to adjust the delay as needed between 0 and 1 samples.

The all-pass filter transfer function is

H APF ( z ) = C + z 1 1 + C z 1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisamaaBaaaleaacaqGbbGaaeiuaiaabAeaaeqaaOGaaiikaiaadQhacaGGPaGaeyypa0ZaaSaaaeaacaWGdbGaey4kaSIaamOEamaaCaaaleqabaGaeyOeI0IaaGymaaaaaOqaaiaaigdacqGHRaWkcaWGdbGaamOEamaaCaaaleqabaGaeyOeI0IaaGymaaaaaaaaaa@45CD@

where | C | < 1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaacaWGdbaacaGLhWUaayjcSdGaeyipaWJaaGymaaaa@3AE4@ to ensure stability.

Questions & Answers

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Introduction about quantum dots in nanotechnology
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
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for screen printed electrodes ?
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s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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Damian Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Musical signal processing with labview -- subtractive synthesis. OpenStax CNX. Nov 07, 2007 Download for free at http://cnx.org/content/col10484/1.2
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