Chapter-4
Synthesis and Analysis of
Complex Waves
Fourier Synthesis: The process of combining harmonics to form a complex wave.
Fourier Analysis: Determining the harmonic content of a complex wave.
Synthesis of Complex Waves
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Synthesis of Complex Waves
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17
Synthesis of Complex Waves
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17
Summary
The shape of the complex wave
is determined by:
(1) the number and relative
amplitudes of the component
harmonics.
(2) the phases of the higher
harmonics, relative to the
fundamental.
The tone quality or timbre is
affected by moderate changes in
the amplitude of the higher
harmonic but is hardly affected
at all by rather large changes in
the relative phases of the two
harmonics.
Fourier Synthesis of a Triangular Wave
Fourier Synthesis of a Square Wave
Fourier Synthesis of a Sawtooth Wave
Fourier Synthesis of a Pulse Train
Harmonic Amplitudes for
Sine, Triangle, Square, Sawtooth,
and Pulse
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Periodicity and Fundamental
4.2 Fourier Analysis and Fourier Spectra
Since the tone quality of a complex wave is determined primarily by the
amplitudes of the harmonics, it is useful to display the harmonic content
graphically.
Fourier spectrum displays the harmonic content of complex waves.
Fourier Spectra
Fourier Spectra
Wave form and Fourier spectrum of
the note C5 = 523.25 Hz, played on
an alto recorder
Wave form and Fourier spectrum of
the note B3b = 233.08 Hz, played
on a clarinet
Wave form and Fourier spectrum of
the note B4 = 493.88 Hz, played on
a violin
Wave form and Fourier spectrum of
the note G3 = 196.00 Hz, played on
a tenor krummhorn