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MATHEMATICS OF THE
DISCRETE FOURIER TRANSFORM (DFT)
WITH AUDIO APPLICATIONS
SECOND EDITION

JULIUS O. SMITH III

Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University, Stanford, California 94305 USA



INTRODUCTION TO DIGITAL FILTERS
WITH AUDIO APPLICATIONS

JULIUS O. SMITH III

Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University, Stanford, California 94305 USA



PHYSICAL AUDIO SIGNAL PROCESSING
FOR VIRTUAL MUSICAL INSTRUMENTS AND AUDIO EFFECTS

JULIUS O. SMITH III

Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University, Stanford, California 94305 USA

August 2007 Edition



SPECTRAL AUDIO SIGNAL PROCESSING

JULIUS O. SMITH III

Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University, Stanford, California 94305 USA

March 2007 DRAFT