1. 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.

2. Synthesis of Complex Waves http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17

3. Synthesis of Complex Waves http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17

4. Synthesis of Complex Waves http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17

5. 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.

6. Fourier Synthesis of a Triangular Wave

7. Fourier Synthesis of a Square Wave

8. Fourier Synthesis of a Sawtooth Wave

9. Fourier Synthesis of a Pulse Train

10. Harmonic Amplitudes for Sine, Triangle, Square, Sawtooth, and Pulse http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17

11. Periodicity and Fundamental

12. 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.

13. Fourier Spectra

15. Wave form and Fourier spectrum of the note C 5 = 523.25 Hz, played on an alto recorder

16. Wave form and Fourier spectrum of the note B 3 b = 233.08 Hz, played on a clarinet

17. Wave form and Fourier spectrum of the note B 4 = 493.88 Hz, played on a violin

18. Wave form and Fourier spectrum of the note G 3 = 196.00 Hz, played on a tenor krummhorn