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
- First-Order Allpass Interpolation
- Linear Interpolation as Resampling
- 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
- 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
- Recent Developments in Lagrange Interpolation
- Relation of Lagrange to Sinc Interpolation

- Thiran Allpass Interpolators

- Windowed Sinc Interpolation
- Theory of Ideal Bandlimited Interpolation
- From Theory to Practice
- Implementation
- Summary of Windowed Sinc Interpolation

- Delay-Line Interpolation Summary

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University