Delay-Line and Signal Interpolation

It is often necessary for a delay line to vary in length. Consider, for example, simulating a sound ray as in Fig.2.8 when either the source or listener is moving. In this case, separate read and write pointers are normally used (as opposed to a shared read-write pointer in Fig.2.2). Additionally, for good quality audio, it is usually necessary to interpolate the delay-line length rather than ``jumping'' between integer numbers of samples. This is typically accomplished using an interpolating read, but interpolating writes are also used (e.g., for true Doppler simulation, as described in §5.9).

• Delay-Line Interpolation
  • Linear Interpolation
    • One-Multiply Linear Interpolation
    • Fractional Delay Filtering by Linear Interpolation
  • First-Order Allpass Interpolation
    • Minimizing First-Order Allpass Transient Response
  • Linear Interpolation as Resampling
    • Convolution Interpretation
    • Frequency Response of Linear Interpolation
    • Triangular Pulse as Convolution of Two Rectangular Pulses
    • Linear Interpolation Frequency Response
    • Special Cases
  • Large Delay Changes
  
  
• Lagrange Interpolation
  • Interpolation of Uniformly Spaced Samples
  • Fractional Delay Filters
  • Lagrange Interpolation Optimality
  • Explicit Lagrange Coefficient Formulas
  • Lagrange Interpolation Coefficient Symmetry
  • Matlab Code for Lagrange Interpolation
  • Maxima Code for Lagrange Interpolation
  • Faust Code for Lagrange Interpolation
  • Lagrange Frequency Response Examples
    • Orders 1 to 5 on a fractional delay of 0.4 samples
    • Order 4 over a range of fractional delays
    • Order 5 over a range of fractional delays
  • Avoiding Discontinuities When Changing Delay
  • Lagrange Frequency Response Magnitude Bound
  • Even-Order Lagrange Interpolation Summary
  • Odd-Order Lagrange Interpolation Summary
  • Proof of Maximum Flatness at DC
  • Variable Filter Parametrizations
    • Table Look-Up
    • Polynomials in the Delay
    • Farrow Structure
    • Farrow Structure Coefficients
    • Differentiator Filter Bank
  • Recent Developments in Lagrange Interpolation
  • Relation of Lagrange to Sinc Interpolation
  
  
• Thiran Allpass Interpolators
  • Thiran Allpass Interpolation in Matlab
  • Group Delays of Thiran Allpass Interpolators
  
  
• Windowed Sinc Interpolation
  • Theory of Ideal Bandlimited Interpolation
  • From Theory to Practice
  • Implementation
    • Choice of Table Size and Word Lengths
  • Summary of Windowed Sinc Interpolation
  
  
• Delay-Line Interpolation Summary