MUS421/EE367B Lecture 1
Introduction and Overview

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)

• Administrative Information
  • Units
  • Important Pointers
  
  
• Why The Fourier Transform
• Applications of the
  Short-Time Fourier Transform (STFT)
  • Applications, Cont'd
  • Emerging Applications in Audio Coding
  • Final Project (4th Unit)
  • Main Pointer
  
  
• Notation
• Introduction to Audio Spectrum Analysis
• Example of Windowing
  • Summary
  • The Rectangular Window
  • Rectangular Window Transform (Cont'd)
  • Sidelobe Roll-Off Rate
  
  
• Frequency Resolution
  • One Sine and One Cosine
    (``Phase Quadrature'' Case)
  • One Sine and One Cosine
    (``Phase Quadrature'' Case)
    All Four Resolutions Overlaid
  • Resolution Bandwidth (resolving sinusoids)
  • Choosing Window Length to Resolve Sinusoids
  
  
• Spectral Interpolation
  • Zero Padding
  • Ideal Spectral Interpolation
  • Interpolating a DFT
  • Practical Zero Padding
  • More Reasons for Zero Padding
  • Critically Sampled Window Transform
  • 2X Oversampled Window Transform
  • Oversampled Spectral Peaks
  • Zero-Centered Zero-Padding
  • Zero-Centered Spectra
  • fftshift
  
  
• About this document ...

Course Overview

• The focus of this course is spectral modeling and signal processing using the short-time Fourier transform (STFT).
• Applications include musical sound synthesis and audio signal processing.