Fundamental theorem of arithmetic

FM synthesis using 2 operators

A 220 Hz carrier tone fc modulated by a 440 Hz modulating tone fm, with various choices of modulation index, β. The time domain signals are illustrated above, and the corresponding spectra are shown below (spectrum amplitudes in dB).

Waveforms for each β

Spectra for each β

In audio and music, Frequency Modulation Synthesis (or FM synthesis) is a form of audio synthesis where the timbre of a simple waveform (such as a square, triangle, or sawtooth) is changed by modulating its frequency with a modulator frequency that is also in the audio range, resulting in a more complex waveform and a different-sounding tone that can also be described as "gritty" if it is a thick and dark timbre. The frequency of an oscillator is altered or distorted, "in accordance with the amplitude of a modulating signal." Template:Harv

FM synthesis can create both harmonic and inharmonic sounds. For synthesizing harmonic sounds, the modulating signal must have a harmonic relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively more complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. non harmonic), atonal and tonal bell-like and percussive sounds can easily be created.

FM synthesis using analog oscillators may result in pitch instability, but FM synthesis can be implemented digitally, and the latter proved so much more reliable that it became the standard. As a result, digital FM synthesis (using the more frequency-stable phase modulation variant) was the basis of Yamaha's groundbreaking DX7, which brought FM to the forefront of synthesis in the mid-1980s.

History

The technique of the digital implementation of frequency modulation, which was developed by John Chowning (Template:Harvnb, cited in Template:Harvnb) at Stanford University in 1967-68, was patented in 1975 and later licensed to Yamaha.

The implementation commercialized by Yamaha (US Patent 4018121 Apr 1977 or U.S. Patent 4,018,121) is actually based on phase modulation, but the results end up being equivalent mathematically, with phase modulation simply making the implementation resilient against undesirable drift in frequency of carrier waves due to self-modulation or due to DC bias in the modulating wave.

As noted earlier, FM synthesis was the basis of some of the early generations of digital synthesizers from Yamaha, with Yamaha's flagship DX7 synthesizer being ubiquitous throughout the 1980s and several other models by Yamaha providing variations of FM synthesis. The most advanced FM synths produced by Yamaha were the 6-operator keyboard SY99 and the 8-operator module FS1R: each features Yamaha's Advanced FM (AFM) alongside and able to be layered or interfaced with other synthesising technologies, respectively AWM2 (Advanced Wave Memory 2) sample-based synthesis in the SY99 and formant synthesis in the FS1R, neither of which combinations have ever been duplicated, as neither have some of the other advanced FM features of these Yamaha devices.

Yamaha had patented its hardware implementation of FM in the 1980s, allowing it to nearly monopolize the market for that technology until the mid-1990s. Casio developed a related form of synthesis called phase distortion synthesis, used in its CZ range of synthesizers. It had a similar (but slightly differently derived) sound quality to the DX series. Don Buchla implemented FM on his instruments in the mid-1960s, prior to Yamaha's patent. His 158, 258 and 259 dual oscillator modules had a specific FM control voltage input, and the model 208 (Music Easel) had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator. These early applications used analog oscillators.

With the expiration of the Stanford University FM patent in 1995, digital FM synthesis can now be implemented freely by other manufacturers. The FM synthesis patent brought Stanford $20 million before it expired, making it (in 1994) "the second most lucrative licensing agreement in Stanford's history". FM today is mostly found in software-based synths such as FM8 by Native Instruments or Sytrus by Image-Line, but it has also been incorporated into the synthesis repertoire of some modern digital synthesizers, usually coexisting as an option alongside other methods of synthesis such as subtractive, sample-based synthesis, additive synthesis, and other techniques. The degree of complexity of the FM in such hardware synths may vary from simple 2-operator FM, to the highly flexible 6-operator engines of the Korg Kronos and Alesis Fusion, to creation of FM in extensively modular engines such as those in the latest synthesisers by Kurzweil Music Systems.

However, new hardware synths that were specifically marketed for their FM capabilities have not been seen since the Yamaha SY99, which itself was split evenly between this and sample-based synthesis in terms of marketing. Yamaha's later FS1R was marketed chiefly as a device for formant synthesis, despite the fact that it was the only standalone 8-operator FM synth that they, or any other hardware manufacturer, had produced, and had other unique features in its FM engine. Yamaha also produced the FVX1, an 8-op FM expander for certain of their organs, but these are rare, and information on how to actually program them has never been released or derived. Yamaha re-released the engine of the DX7 II in the form of the PLG150DX and PLG100DX expansion cards for certain of their synths, including a standalone model enclosed in the table-top unit DX200, but this was simply a re-release of an existing platform. Thus, since the SY99 and FS1R by Yamaha, no manufacturer has released any new hardware synth dedicated solely/mainly to FM synthesis, though it is a main feature of Nord Lead synths manufactured by Clavia.

Spectral analysis

The spectrum generated by FM synthesis with one modulator is expressed as following:

${\begin{aligned}&\sin(f_{c}\cdot t+I\cdot \sin(f_{m}\cdot t))\\&\quad =J_{0}(I)\sin(f_{c}\cdot t)+\sum _{k=1}^{\infty }J_{k}(I)\left[\sin(f_{c}+kf_{m})t+(-1)^{k}\sin(f_{c}-kf_{m})t\right]\end{aligned}}$

where $f_{c}\,,\,f_{m}\,$ are frequencies of carrier and modulator, $I\,$ is modulation index, and $J_{k}(I)\,$  is  $k\,$-th Bessel function of first kind, respectively.

See also

• Chiptune
• Digital synthesizer
• Electronic music
• Sound card
• Sound chip
• Video game music

References

• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang (also available in PDF as digital version 2/13/2007)
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

• An Introduction To FM, by Bill Schottstaedt
• FM tutorial
• Synth Secrets, Part 12: An Introduction To Frequency Modulation, by Gordon Reid
• Synth Secrets, Part 13: More On Frequency Modulation, by Gordon Reid
• Paul Wiffens Synth School: Part 3
• F.M. Synthesis including complex operator analysis
• Part 1 of a 2-part YouTube tutorial on FM synthesis with numerous audio examples