Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining...
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![Page 1: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/1.jpg)
Chapter-4Synthesis 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.
![Page 2: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/2.jpg)
Synthesis of Complex Waves
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17
![Page 3: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/3.jpg)
Synthesis of Complex Waves
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17
![Page 4: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/4.jpg)
Synthesis of Complex Waves
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17
![Page 5: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/5.jpg)
SummaryThe 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.
![Page 6: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/6.jpg)
Fourier Synthesis of a Triangular Wave
![Page 7: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/7.jpg)
Fourier Synthesis of a Square Wave
![Page 8: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/8.jpg)
Fourier Synthesis of a Sawtooth Wave
![Page 9: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/9.jpg)
Fourier Synthesis of a Pulse Train
![Page 10: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/10.jpg)
Harmonic Amplitudes for Sine, Triangle, Square, Sawtooth,
and Pulse
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17
![Page 11: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/11.jpg)
Periodicity and Fundamental
![Page 12: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/12.jpg)
4.2 Fourier Analysis and Fourier SpectraSince 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.
![Page 13: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/13.jpg)
Fourier Spectra
![Page 14: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/14.jpg)
Fourier Spectra
![Page 15: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/15.jpg)
Wave form and Fourier spectrum of the note C5 = 523.25 Hz, played on
an alto recorder
![Page 16: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/16.jpg)
Wave form and Fourier spectrum of the note B3
b = 233.08 Hz, played on a clarinet
![Page 17: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/17.jpg)
Wave form and Fourier spectrum of the note B4 = 493.88 Hz, played on
a violin
![Page 18: Chapter-4 Synthesis and Analysis of Complex Waves Fourier Synthesis: The process of combining harmonics to form a complex wave. Fourier Analysis: Determining.](https://reader038.fdocuments.in/reader038/viewer/2022102808/56649e2a5503460f94b1842b/html5/thumbnails/18.jpg)
Wave form and Fourier spectrum of the note G3 = 196.00 Hz, played on
a tenor krummhorn