MUS421/EE367B Lecture 2
Review of the Discrete Fourier Transform (DFT)

Julius O. Smith III ( send email )
Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University
Stanford, California 94305

Detailed Contents (and Navigation)

• Domains of Definition
• Geometric Interpretation of the Fourier Transform
• Signal and Transform Notation
• The Discrete Fourier Transform
  • Inverse DFT
  • The DFT, Cont'd
  
  
• Properties of the DFT
  • Linearity
  • Time Reversal
  • Symmetry
  • Shift Theorem
  • Convolution
  • Correlation
  • Autocorrelation
  • Power Theorem
  • Stretch
  • Repeat or Scale
  • Zero-Padding $\leftrightarrow$ Interpolation
  • Downsampling $\leftrightarrow$ Aliasing
  
  
• About this document ...

For more details, see

• Mathematics of the DFT (Music 320 text):
  http://ccrma.stanford.edu/~jos/mdft/
• Appendices A-D of Spectral Audio Signal Processing (our text):
  http://ccrma.stanford.edu/~jos/sasp/