An Audio Synthesis Textbook For Musicians, Digital Artists and Programmers by Mike Krzyzaniak
<-- Up to: 1 Linear Interpolation-->

  1. //CubicInterpolation.c
  2. //gcc MKAiff.c CubicInterpolation.c -o CubicInterpolation
  5. void cubicInterpolateBuffer(float* previous3Frames, int numChannels, float* input, int inNumFrames, float* output, int outNumFrames)
  6. {
  7. int i, j, index;
  8. double distance, prev, prevPrev, next, nextNext;
  9. double a, b, c, d;
  11. for(i=0; i<outNumFrames; i++)
  12. {
  13. for(j=0; j<numChannels; j++)
  14. {
  15. distance = i * (inNumFrames / (double)outNumFrames);
  16. index = ((int)distance) * numChannels + j;
  17. nextNext = input[index ];
  18. next = distance < 1 ? previous3Frames[index + 2*numChannels] : input[index - numChannels];
  19. prev = distance < 2 ? previous3Frames[index + numChannels ] : input[index - 2*numChannels];
  20. prevPrev = distance < 3 ? previous3Frames[index ] : input[index - 3*numChannels];
  21. distance -= (int)distance;
  22. a = nextNext - next - prevPrev + prev;
  23. b = prevPrev - prev - a;
  24. c = next - prevPrev;
  25. d = prev;
  26. output[i*numChannels+j] = ((a * distance * distance * distance) + (b * distance*distance) + (c * distance) + (d));
  27. }
  28. }
  29. for(j=0; j<numChannels*3; j++)
  30. previous3Frames[j] = input[(inNumFrames - 3) * numChannels + j];
  31. }

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AIFF Template Linear Interpolation

Explanation of the Concepts

This is a cubic interpolation algorithm that is capable of stretching out or contracting a buffer of interleaved audio data.

In general, linear interpolation is somewhat inelegant, and a somewhat higher-fidelity result can be achieved by attempting to draw some sort of curve between the known sample-points. A cubic polynomial of the form

ax^3 + bx^2 + cx + d

works quite well, and results in a curve like this:
Cubic

Explanation of the Code

Code Explanation

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