<< Chapter < Page Chapter >> Page >
Subtractive synthesis techniques often require a wideband excitation source such as a pulse train to drive a time-varying digital filter. Traditional rectangular pulses have theoretically infinite bandwidth, and therefore always introduce aliasing noise into the input signal. A band-limited pulse (BLP) source is free of aliasing problems, and is more suitable for subtractive synthesis algorithms. The mathematics of the band-limited pulse is presented, and a LabVIEW VI is developed to implement the BLP source. An audio demonstration is included.
This module refers to LabVIEW, a software development environment that features a graphical programming language. Please see the LabVIEW QuickStart Guide module for tutorials and documentation that will help you:
•Apply LabVIEW to Audio Signal Processing
•Get started with LabVIEW
•Obtain a fully-functional evaluation edition of LabVIEW

Introduction

Subtractive synthesis techniques apply a filter (usually time-varying) to a wideband excitation source such as noise or a pulse train. The filtershapes the wideband spectrum into the desired spectrum. The excitation/filter technique describes the sound-producing mechanism of many types of physical instruments as well as the human voice, makingsubtractive synthesis an attractive method for physical modeling of real instruments.

A pulse train , a repetitive series of pulses, provides an excitation source that has a perceptible pitch, so in a sense the excitation spectrum is "pre-shaped" before applying it to a filter.Many types of musical instruments use some sort of pulse train as an excitation, notably wind instruments such as brass (e.g., trumpet, trombone, and tuba) and woodwinds (e.g., clarinet, saxophone, oboe, and bassoon). Likewise, the humanvoice begins as a series of pulses produced by vocal cord vibrations, which can be considered the "excitation signal" to the vocal and nasal tract that acts as a resonant cavity to amplify and filterthe "signal."

Traditional rectangular pulse shapes have significant spectral energy contained in harmonics that extend beyond the folding frequency (half of the sampling frequency). These harmonics are subject to aliasing , and are "folded back" into the principal alias , i.e., the spectrum between 0 and f s / 2 . The aliased harmonics are distinctly audible as high-frequency tones that, since undesired, qualify as noise.

The band-limited pulse , however, is free of aliasing problems because its maximum harmonic can be chosen to be below the folding frequency. In this module the mathematics of the band-limited pulse aredeveloped, and a band-limited pulse generator is implemented in LabVIEW.

Mathematical development of the band-limited pulse

By definition, a band-limited pulse has zero spectral energy beyond some determined frequency. You can use a truncated Fourier series to create a series of harmonics, or sinusoids, as in :

x ( t ) = k = 1 N sin ( 2 π k f 0 t ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacIcacaWG0bGaaiykaiabg2da9maaqahabaGaci4CaiaacMgacaGGUbGaaiikaiaaikdacqaHapaCcaWGRbGaamOzamaaBaaaleaacaaIWaaabeaakiaadshacaGGPaaaleaacaWGRbGaeyypa0JaaGymaaqaaiaad6eaa0GaeyyeIuoaaaa@49C4@

The screencast video shows how to implement in LabVIEW by introducing the "Tones and Noise" built-in subVI that is part of the "Signal Processing" palette. The video includes a demonstration that relatesthe time-domain pulse shape, spectral behavior, and audible sound of the band-limited pulse.

Download the finished VI from the video: blp_demo.vi . This VI requires installation of the TripleDisplay front-panel indicator.

[video] Band-limited pulse generator in LabVIEW using "Tones and Noise" built-in subVI

The truncated Fourier series approach works fine for off-line or batch-mode signal processing. However, in a real-time application the computational cost of generating individual sinusoids becomes prohibitive, especially when a fairly dense spectrumis required (for example, 50 sinusoids).

A closed-form version of the truncated Fourier series equation is presented in (refer to Moore in "References" section below):

x ( t ) = k = 1 N sin ( k θ ) = sin [ ( N + 1 ) θ 2 ] sin ( N θ 2 ) sin ( θ 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacIcacaWG0bGaaiykaiabg2da9maaqahabaGaci4CaiaacMgacaGGUbGaaiikaiaadUgacqaH4oqCcaGGPaGaeyypa0Jaci4CaiaacMgacaGGUbWaamWaaeaacaGGOaGaamOtaiabgUcaRiaaigdacaGGPaWaaSaaaeaacqaH4oqCaeaacaaIYaaaaaGaay5waiaaw2faaaWcbaGaam4Aaiabg2da9iaaigdaaeaacaWGobaaniabggHiLdGcdaWcaaqaaiGacohacaGGPbGaaiOBamaabmaabaGaamOtamaalaaabaGaeqiUdehabaGaaGOmaaaaaiaawIcacaGLPaaaaeaaciGGZbGaaiyAaiaac6gadaqadaqaamaalaaabaGaeqiUdehabaGaaGOmaaaaaiaawIcacaGLPaaaaaaaaa@60FB@

where

θ = 2 π f 0 t MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdeNaeyypa0JaaGOmaiabec8aWjaadAgadaWgaaWcbaGaaGimaaqabaGccaWG0baaaa@3D44@ . The closed-form version of the summation requires only three sinusoidal oscillators yet can produce an arbitrary number of sinusoidal components.

Implementing contains one significant challenge, however. Note the ratio of two sinusoids on the far right of the equation. The denominator sinusoid periodically passes through zero, leading to a divide-by-zero error. However, because the numerator sinusoidoperates at a frequency that is N times higher, the numerator sinusoid also approaches zero whenever the lower-frequency denominator sinusoid approaches zero. This "0/0" condition converges to either N or -N; the sign can be inferred by looking at adjacent samples.

References

  • Moore, F.R., "Elements of Computer Music," Prentice-Hall, 1990, ISBN 0-13-252552-6.

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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.
Harper
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Musical signal processing with labview -- subtractive synthesis' conversation and receive update notifications?

Ask