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Digital frequency modulation synthesis
The amplitude of each spectral component is determined by BOTH THE 'DEVIATION' (modulation amount) AND THE FREQUENCY OF MODULATION. To describe these amplitudes mathematically, it is useful to devine an INDEX OF MODULATION:
The amplitudes of the carrier and sideband components are determined by Bessel functions of the first kind and the nth order, Jn(), the argument to which is the MODULATION AMOUNT (I). The zeroth-order Bessel function and amount J0(I), yields a scaling coefficient for the first upper- and lower-side frequencies; the second-order J2(), for the second upper- and lower-side frequencies; and so forth. The higher the order of the side frequency the larger the modulation amount must be for that side frequency to have any significant amplitude. The total bandwidth is approximately equal to twice the sum of the FREQUENCY DEVIATION and the modulation frequency, or
• Subtractive synthesis • FM (Frequency Modulation) ..
If the original CARRIER contains additional partials (it is a more complex sound than just a simple waveform) then SIDEBANDS form in pairs around each partial. The intensity of the SIDEBAND frequencies is governed by the MODULATION INDEX which is in essence the depth or amount of the modulation. The actual MODULATION INDEX (I) is the ratio of the frequency of the modulating signal (mf) to the amplitude of the modulating signal (ma) -- as in ma/mf. The basic FM process may be described by the formula:
The FREQUENCY DEVIATION is equivalent to the AMPLITUDE of the modulating signal. Consequently, the stronger the AMPLITUDE of the modulating signal, the greater the BANDWIDTH (the greater number of sidebands) in the resulting SPECTRUM. [See Computer Music, 2nd ed, Charles Dodge, Schirmer Books, 1997, p. 116). "The distribution of power among the spectral components depends ... on the amount of frequency deviation ... produced by the modulating oscillator.... Increasing the deviation causes the sidebands to acquire more power at the expense of the power in the carrier frequency. The wider the deviation, the more widely distributed is the power among the sidebands and the greater the number of sidebands that have significant amplitudes. Thus the deviation can act as a control on the bandwidth of the spectrum of an FM signal.
Analog and digital modulation facilitate frequency division ..
With the expiration of the Stanford University FM patent in 1995, FM synthesis is now part of the synthesis repertoire of most modern synthesizers, usually in conjunction with , and sometimes techniques.
The harmonic distribution of a simple sine wave signal modulated by another sine wave signal can be represented with - this provides a basis for a simple mathematical understanding of FM synthesis.
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Elements of Music Chapter 1 Flashcards | Quizlet
FM synthesis is a form of "distortion synthesis" or "nonlinear synthesis". It begins with an oscillator generating an audio-frequency "carrier" waveform with a frequency of Fc . An audio-frequency modulating waveform, with a frequency Fm, is then applied to change or "modulate" the frequency of the carrier oscillator.
Start studying Elements of Music Chapter 1
At the same time, the frequency of the modulating signal causes what are termed "sideband" frequencies to appear on either "side" of the carrier frequency. Therefore for each frequency component in the modulating signal, an "upper" sideband appears above Fc, and a "lower" sideband appears below Fc. Clearly a modulating waveform containing many frequencies (e.g. "partials") will create many FM sidebands.
Frequency modulation synthesis - Wikipedia
FM synthesis is very good at creating both harmonic and inharmonic ('clang', 'twang' or 'bong' noises) sounds. Complex (and proper) FM synthesis using analog is not generally feasible due to their inherent pitch instability, but FM synthesis (using the frequency stable phase modulation variant) is easy to implement digitally. As a result, FM synthesis was the basis of some of the early generations of from Yamaha, with Yamaha's flagship synthesizer being ubiquitous throughout the 1980s. Yamaha had patented its hardware implementation of FM, allowing it to nearly monopolize the market for that technology. developed a related form of synthesis called , used in its CZ series of synthesizers. It had a similar (but slightly differently derived) sound quality as the DX series.
Music Theory Flashcards | Quizlet
The amplitude (and position) of each sideband frequency depends on the index of modulation where the actual frequency of a particular sideband is symmetrically related to the carrier frequency. For example, if the carrier frequency is 440 and the modulation frequency is 100 then the sidebands will be symmetrically arranged both above and below the carrier frequency accordingly at both +100 and -100 increments: 440 +100; 440 - 100; 440 +200; 440 -200; 440 +300; 440 - 300, etc. The STRENGTH or amplitude of the individual sidebands will be dictated by the modulation index. So when the value of the modulation amount increases, it gives power (amplitude) to the sideband freuqencies by "stealing" power (amplitude) away from the carrier frequency. Consequently as the sideband frequencies increase in amplitude, the carrier frequency decreases in amplitude.
A simple example of Frequency Modulation synthesis ..
Modulation means using one signal to affect another signal. A simple example of Frequency Modulation synthesis (FM) consists of one oscillator (the MODULATOR), modulating the frequency of another oscillator (the CARRIER). This procedure produces additional frequencies called SIDEBANDS which form symmetrically around the original frequency of the CARRIER. For example, here is a simple FM patch:
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