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Frequency modulation (FM) in the audio frequency range can create very rich spectra from only two sinusoidal oscillators, and the spectra can easily be made to evolve with time. The mathematics of FM synthesis is developed, and the spectral characteristics of the FM equation are discussed. Audio demonstrations as implemented by LabVIEW VIs illustrate the relationships between the three fundamental FM synthesis parameters (carrier frequency, modulation frequency, modulation index) and the synthesized spectra.
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

Overview

Frequency modulation ( FM ) is most often associated with communications systems; for example, you can find all sorts of music stations on the FM band of your radio. In communicationssystems the baseband signal has a bandwidth similar to that of speech or music (anywhere from 8 kHz to 20 kHz), and the modulating frequency is several orders of magnitude higher; the FM radioband is 88 MHz to 108 MHz.

When applied to audio signals for music synthesis purposes, the modulating frequency is of the same order as the audio signals to be modulated. FM can create very rich spectra, andthe spectra can easily be made to evolve with time. The ability of FM to produce a wide variety of interesting spectra from only two sinusoidal oscillators makes FM a fascinating synthesis technique.

Brief history of fm synthesis

John Chowning was the first to systematically evaluate FM in the audio spectrum, and along with Stanford University, filed for a patent on the technique in 1975 (see U.S. Patent 4,018,121 at U.S. Patent and Trademark Office or at Google Patent Search ). The patent was issued in 1977, and Stanford University licensed the technology to Yamaha Corporation. Six years later in 1983, Yamaha introduced the revolutionary DX7 synthesizer ( ), the first commercially successful instrument based on FM synthesis. The DX7 was also a milestone by introducing two other new technologies: digitalsynthesis and MIDI (Musical Instrument Digital Interface). The "FM sound" defines much of the pop music styles of the 1980s.

Yamaha DX7 synthesizer, the first commercially successful instrument to offer FM synthesis, digital synthesis, and MIDI compatibility. The instrument pictured here is packaged in a road case.Photographer: schoschie ( (External Link) ). Copyright holder has granted permission to display this image under the Creative Commons Attribution-ShareAlike license .

Fm equation

The basic FM equation is presented in :

y ( t ) = A sin ( 2 π f c t + I sin ( 2 π f m t ) ) ,

where the parameters are defined as follows:

  • f c = carrier frequency (Hz)
  • f m = modulation frequency (Hz)
  • I = modulation index

The screencast video continues the discussion by explaining the significance of each part of , and demonstrates in a qualitative fashion how the different parameters of the equation influence the spectrum of the audio signal.

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?
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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.
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Samuel Reply
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?
Joseph Reply
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
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"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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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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