Frequency Modulation Synthesis: Techniques, Applications, and Analysis

This report provides a comprehensive overview of Frequency Modulation (FM) synthesis, a technique used to create complex audio waveforms by modulating the frequency of a carrier wave. It delves into various synthesis methods, including additive, subtractive, wave-table, vector, and linear arithmetic synthesis, along with physical modeling and section distortion synthesis. The report also discusses the mathematical and musical aspects of FM synthesis, highlighting its connection to human hearing and sound manipulation. Furthermore, it explores different musical instruments and controllers that utilize FM synthesis, such as the Reactables, Percussa Audio Cubes, Kaossilator, and Eigenharp. The report also includes detailed sections on additive synthesis and analysis, exploring how sounds can be broken down and resynthesized. It concludes with a discussion on square and sawtooth waves, which are fundamental waveforms in FM synthesis.

FREQUENCY MODULATION
CCS

Abstract
Frequency Modulation synthesis (FM synthesis) is a process of synthesizing an audio or music,
in which the tone of waveform get changed by modulating its frequency in accordance to the
modulator frequency which is in the broad audio range and give rise to more complex waves.

1.0 Introduction.
1Frequency Modulation can be stated as method of alteration or modulation of carrier
wave containing information in the form of electrical signals by modulating its instantaneous
frequency. This process of encoding the information can be used with both types of data, that are
analog as well as digital. However, in amplitude modulation, amplitude of waves varied whereby
frequency of carrier waves remains constant.
2A visionary, named John Chowning who has worked in the field of electronic industry
and set up many research centers of music in different regions of world stated that, Mathematics
and Music both are considered as expressive languages which have different patterns. According
to Chowning, musicians are highly integrated with their work, that is in compilation of music,
after-then hearing it3. While composing music, every musician has to deal with symbols, which
is why artistic use of technology is made by music first, then others arts came into existence in
the technological forms. Moreover, there is great connection between human hearing power and
nature of sound. According to mathematical investigation it has been perceived that mathematics
and science has given a effective way of comprehension, creation and manipulation of sound.
The spectrum generated by FM synthesis with one modulator is given as follows:
For modulation signal , the carrier signal is
1 Communication Systems" 4th Ed (Simon Haykin, 2001) p. 81
2 David B. Rutledge, The Electronics of Radio, 1st edn (Cambridge University Press., 1999), p. 310. ISBN 978-0-
521-64645-1.
3 H. P. Westman, ed., Reference Data for Radio Engineers (Fifth ed.). (Howard W. Sams & Co., 1970) p. 21-11.

FM and additive synthesis
In the scenario of modern technological world, most of people are not aware and well-versed of
various forms of synthesis. With the ease of use of computer-based synthesis, any synthesized
program can be opened and fiddled around ears and feel the sense. In the modern world, it is
necessary to to be educated enough so that it becomes easier to break the mold. There are
different synthesis methods, which can be used in an effective way.
Subtractive Synthesis
Subtractive method is most common process which introduces the aspect of sound-synthesis. It is
made of simple chain of oscillator, which then run through a filter and then forwarded to an
amplifier to gain the ASDR control and staging. Subtractive method can be effectively used for
analog as well as digital data and for other purpose also, like in instruments and sound effects.
Subtractive synthesizer is that method, through which any harmonic character can be
made by combination of oscillators or by an single oscillator.
Additive Synthesis (and Re-synthesis)
In additive synthesis, different frequencies and multiple sine waves are combined to build a
harmonic structure. Moreover, the additive synthesis is directly connected with the process of re-
synthesis. In addition to this, it also analyses the harmonic structure and then recreate it.
Additive synthesis is just like re- synthesis, excluding the fact that the process of re-synthesis is
re-created from existing sound and nor from a general tone.

Aspect (physical) Modeling Synthesis
Bodily Moulding Reasoning is numerical and makes use of a set made of algorithms to
specify the music and physical distinctive of the sound that is mostly generated by
them. This methods are used for developing real sound devices, as it is created to
make characteristic differentiation among the few elements of device that are being
developed. For example, the physical that build up the device, the dimensions, the
in-elasticity of a tool, the quantity of a resound object (with a view of remaking its
reverberate frequency) and numerous great important points are components into
the formulas that creates every sound’s one of a kind features using quite a lot of
varieties of reasoning (stylish for company).
Wave-table Synthesis
In wave-table synthesis, different switch-table frequencies are used and played in a definite
order. By pressing key, sound moves in different pattern via wave-table, smooth change can be
seen the wave-table instead of spontaneous change.
This process of production of sound can be often used for creating digital noise in sound,
but it is effectively used to create harsh-sounding tones and pads, like digital sounds and bells.
Vector Synthesis
The process named Vector Synthesis is just about specifying the identical as the stated
Wave table Synthesis, most effective it utilizes a two-dimensional system, by which
wave-tables can also be formulated smoother that eventually works in a suitable
manner.

Linear Arithmetic Synthesis
Linear Arithmetic (LA) Synthesis is generally used to formulated via Roland method which
is an attempt to make use of Wave-table Synthesis in order to build up actual-sound
producing instrument spots. This is generated via reducing the number of waves
over the wave-tables within its half by mixing problematic attack i.e. the first half of
wave designs with easy liberate (2d 1/2) wave patterns, as a consequence imitating
more of a remedial atmosphere.
Section Distortion Synthesis
Segment Distortion compounds are reducing synthesizers which has a single variation in
that they nominate a waveshape adaptability of wavetable synthesis within the
generator. So, rather than having a set motions to decide upon the generator, the
individual is given all power to manage over the structure of the wave-form at all set
forms within assorted language and shifting wave-form activity.
Additive synthesis and analysis
4It is recommended that the break down of the rate constituents of a transcribed sound
producing a 'sum of curved' demonstration. By the illustration, it could be re-synthesized that
using accumulative reasoning. The activity of breaking down track into a clip by varying curved
biased which is Short Time Fourier Transform (STFT) analysis.
Through altering the amount of sinusoids demonstration, the generation of timbral
modification can be made before re-synthesising. For instance, a quality sound could be created
4 B. P. Lathi, Communication Systems (John Wiley and Sons 2003) 1968ISBN 0-471-51832-8, p, 214–217

within the sound in-harmonic. Track hybridization or 'morphing' is generally enforced by
accumulative re-synthesis.
Music synthesis techniques
The rising power and the inversely reducing the overall cost of electronics making sound
(particularly in a computer), in conjunction among the regulation of the MIDI and Open Sound
Control (OSC) auditory show in sorted languages which has smoothed the change of audio
instruments into sound controllers and analyzers.
Through the far most ordinary sound controller is the instrumental keyboard. Other
instruments regard the radio drum, EWI offered by AKAI, the guitar like SynthAxe, Buchla
Thunder, Body Synth, the Roland Octapad, the Continuum Finger operated, various musical
keyboards which include the I-CubeX, and Kaossilator Pro, and kits like the Thummer.
The Reactables
It is known as translucent musical table which is round and has a backlit with a
communicating view and display board. Through engaging and influencing areas called tangibles
which has a surface on the table while generating connectivity with the optical show through
motions of the finger, a practical standard electronic instrument is operated via making music or
creating sound effects.
Percussa Audio Cubes
Audio Cubes are stated as a series of independent wireless musical cubes which is
powered by an inner rechargeable battery and computing device and systems. It has got inner
RGB setup and are proficient at identifying every location, placement and region. The blocks are
also capable of detecting areas among between the hands and fingers of the user. By interacting

these blocks a variety of sounds and software of sounds can be addressed. Audio Cubes can be
applied in various places like sound system, music producing and live shows.
Kaossilator
The Oscillator and its advanced version—the Oscillator Pro are consigned musical
devices where the points of a user's finger on the touchpad manages dual notes characteristic,
normally, the position of the note is transformed with a motion of both the sides and the tonal
places, device or other constant changes with a motion from ups and downs. Moreover, the touch
pad can be set to diverse instrumental tones and keys. The device can record an iterating loop of
modifiable dimension, set to any musical time and new loops of sound can be coated on top of
existing ones. This phenomenon lends itself to electronic dance music but is more limited for a
well-ordered series of notes, as the pad is bland on a regular Kaossilator.
Eigenharp
Elgenharp is considered as an electronic instrument that is being operated and helps in
identifying the essence of highly flexible and portable controller with the sound being actually
generated in the software devices.
The Xth-Sense
It is another musical instrument that helps in using muscle sound from the human body which is
also considered as mechanomyogram that helps in making sound effects and music. For instance,
it can be assessed that performer moves their body and produces sounds from the muscle which
are caught by the microphone chip worm on the leg or arm. Further, the sound produced from the
muscle are then used in a sample in regard to undertake modular audio effects a dedicated

software program. Then, the performer regulates the different sampling parameters through
weighting the force, speed and articulation of body movement.
AlphaSphere
Further, the AlphaSphere is considered as a spherical musical tool which involves different
number of tactical pads around 48 and thus responds to touch and pressure. Here, people uses
custom software that helps in using the pads through indefinitely programmed individually or
within groups. It also undertakes pressure parameters, function and also noting among different
settings. Here, the principal concept of AlphaSphere is to upsurge the different level of
expression or feeling at the disposal of musicians using electronic instruments and allows
playing in their own style.
Further, it considered as additive type of synthesis which helps in developing the stated
frequencies and amplitudes in order to lead over time. However, one significant benefit of
additive synthesis is that it helps in using any sound to be presented perfectly. Through carrying
out Fourier analysis of using short windows from which the sound has been produced in order to
get the sequence of time frames of the band at that particular time. With the help of such
presentation, it would help in analyzing the strongest spectral points and synthesize the sound
from the sum of its sinusoids. Such tool is states as the tracking phase named as vocoder. It is a
popular extension within Spectral Modelling Synthesis that incorporates noise.
i. Square wave:
Square waves is stated as a natural form of carrying non-sinusidal periodic waves from which it
helps in presenting an infinite number of individual sinusoidal waves. It assists in identifying the
amplitude alternates at a steady pace among the fixed minimum as well as maximum levels.

However, the transition from minimum to maximum is considered as instant for an idea square
wave which helps in attaining within most physical systems. Such waves are usually encountered
within electronic and signal processing within stochastic matching part and is stated as a two-
state route. It is a similar but not symmetrical wave that involved random duration at the
minimum and maximum levels. Hence, it is called as pulse wave in which square wave is
considered of special type.
In mathematics, there are different definitions of the square wave that are comparable:
It is defined as simply the sign function of a periodic function, an example being a sinusoid:
ii. Sawtooth Wave:

Such wave is considered as a non-sinusodial waveform that helps in identifying the similarity to
the cutting teeth of a saw.
The conventional representation is stated as the form of sawtooth which helps in rising the wave
upward and then drops down steadily. Thus, such a reverse or inverse case it assists in sloping
the waves downward and then rising upwards sharply. However, it can also be considered as
crucial to develop a lopsided triangle wave.
Conclusion
5It can be concluded that using additive synthesis helps in corresponding analysis
techniques that lets to resynthesize upon any sound. Such situation is usually considered as more
difficult with FM. In the traditional time, algorithms of FM were tweaked by ear and intuition.
5 T.G. Thomas, S. C. Sekhar Communication Theory, (Tata-McGraw Hill, 2005), page 136 ISBN 0-07-059091-5.

Thus, scholar helps in searching for the synthesis parameters helps in identifying the match and
give sounds through genetic algorithms. Such approach also helps in fixated upon harmonic
sounds. At the time of initial years of digital music, it helps in concerning of efficiency favored
within FM over additive synthesis and thus developments within algorithms and hardware helps
in making the sound debatable.
Both FM and additive synthesis are very useful in sound design, but there are other
methodologies worth knowing, not physical modeling and least subtractive synthesis.