Signal Operators

It will be convenient in the Fourier theorems of §7.4 to make use of the following signal operator definitions.

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Subsections

• Operator Notation
• Flip Operator
• Shift Operator
  • Examples
  
  
• Convolution
  • Commutativity of Convolution
  • Convolution as a Filtering Operation
  • Convolution Example 1: Smoothing a Rectangular Pulse
  • Convolution Example 2: ADSR Envelope
  • Convolution Example 3: Matched Filtering
  • Graphical Convolution
  • Polynomial Multiplication
  • Multiplication of Decimal Numbers
  
  
• Correlation
• Stretch Operator
• Zero Padding
• Causal (Periodic) Signals
• Causal Zero Padding
• Zero Padding Applications
• Ideal Spectral Interpolation
• Interpolation Operator
• Repeat Operator
• Downsampling Operator
• Alias Operator

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Order a Hardcopy of Mathematics of the DFT

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Next: Operator Notation

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.