<< 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


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@


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.


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

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
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 ?
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?
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?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
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.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
how to synthesize TiO2 nanoparticles by chemical methods
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
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?