Digital Synthesis of Musical Sounds

A THESIS SUBMITTED BY

GAN SEUM-LIM B.Sc. (Hons.)

FOR THE DEGREE OF MASTER OF SCIENCE (M.Sc.)

NATIONAL UNIVERSITY OF SINGAPORE

1992


Abstract

When John M. Chowning proposed the application of the frequency modulation (FM) technique as used in radio transmission to the synthesis of complex musical sounds [Journal of Audio Engineering Society, Sept. 1973, 21:526-534] in 1973, the technology of musical sound synthesis was significantly advanced.

To date, the FM method is still one of the best methods of sound synthesis due to the simplicity with which it can generate rich harmonics. However, the FM method has one major limitation : the inherent symmetry of the generated spectrum around the FM carrier frequency. This limits the type of waveform and frequency spectrum which it can generate.

This thesis reports the investigation and improvement of the FM method further by introducing a new parameter as suggested by J.-P.Palamin & P. Palamin [Journal of Audio Engineering Society, Sept. 1988, 36:671-68] and its implementation in real-time. This new parameter enables the spectrum around the carrier to be asymmetrical. The resulting new technique is called asymmetrical frequency modulation (AFM). The use of AFM in synthesis results in a more effective method of waveform synthesis and can possibly lead to generation of new sounds which are beyond the capabilities of other synthesis methods.

In addition this thesis reports a new modification of the conventional FM method using 2 modulation frequencies. The resulting spectra are much richer in harmonics compared to those generated by the conventional FM method. We call this method the double frequency modulation (DFM) synthesis technique. In this method, the carrier has been removed from the FM equation and two modulators are introduced. We have also demonstrated the real-time generation of musical sounds using one DFM operator.


DIGITAL SYNTHESIS

OF

MUSICAL SOUNDS

A THESIS SUBMITTED BY

GAN SEUM-LIM B.Sc. (Hons.)

FOR THE DEGREE OF MASTER OF SCIENCE (M.Sc.)

NATIONAL UNIVERSITY OF SINGAPORE

1992


ACKNOWLEDGEMENTS

I wish to thank Associate Professor Bernard Tan sincerely for his guidance and supervision.

I am grateful to all the technicians who helped me, one way or the other, in preparing the various instruments used in this research project.

My appreciation to all my friends who gave me their invaluable feedback and suggestions.

I am also grateful to the National University of Singapore for awarding me a Research Scholarship.


Contents

Title Page i

Acknowledgements ii

Contents iii

Summary vi

Chapter 1 : Review of Sound Synthesis

Chapter 2 : Frequency Modulation Synthesis

Chapter 3 : Asymmetrical Frequency Modulation Synthesis

Chapter 4 : Generation of Asymmetrical Frequency Modulation (AFM) Spectra

Chapter 5 : Double Frequency Modulation (DFM) Synthesis

Chapter 6 : Spectral Analysis of Signals

Chapter 7 : Real-time AFM & DFM Synthesis of Musical Sounds

Chapter 8 :Analysis of AFM Real-time Synthesis Results

Chapter 9 :Analysis of DFM Real-time Synthesis Results

Chapter 10:Conclusion

Appendix 1 :

Appendix 2 : Listing for "AFMSPRT.C"

Appendix 3 : Listing for "DFMPSRT2.C"

Appendix 4 : Listing for "MemOutput.asm"

Appendix 5 : Listing for "AFM Not Realtime.c"

Appendix 6 : Listing for "DFM Not Realtime.c"

Appendix 7 : Listing for "AFM Realtime.asm"

Appendix 8 : Listing for "AFM Realtime.c"

Appendix 9 : Listing for "DFM Realtime.asm"

Appendix 10 : Listing for "DFM Realtime.c"

Bibliography & References


Summary

When John M. Chowning proposed the application of the frequency modulation (FM) technique as used in radio transmission to the synthesis of complex musical sounds [14] in 1973, the technology of musical sound synthesis was significantly advanced.

To date, the FM method is still one of the best methods of sound synthesis due to the simplicity with which it can generate rich harmonics. However, the FM method has one major limitation : the inherent symmetry of the generated spectrum around the FM carrier frequency. This limits the type of waveform and frequency spectrum which it can generate.

This thesis reports the investigation and improvement of the FM method further by introducing a new parameter as suggested by Palamin & Palamin [1] and its implementation in real-time. This new parameter enables the spectrum around the carrier to be asymmetrical. The resulting new technique is called asymmetrical frequency modulation (AFM). The use of AFM in synthesis results in a more effective method of waveform synthesis and can possibly lead to generation of new sounds which are beyond the capabilities of other synthesis methods.

In addition this thesis reports a new modification of the conventional FM method using 2 modulation frequencies. The resulting spectra are much richer in harmonics compared to those generated by the conventional FM method. We call this method the double frequency modulation (DFM) synthesis technique. In this method, the carrier has been removed from the FM equation and two modulators are introduced. We have also demonstrated the real-time generation of musical sounds using one DFM operator.